U.S. patent application number 16/567913 was filed with the patent office on 2020-05-21 for information processing apparatus, method for the same, and computer program.
This patent application is currently assigned to KABUSHIKI KAISHA TOSHIBA. The applicant listed for this patent is KABUSHIKI KAISHA TOSHIBA. Invention is credited to Hideyuki AISU, Hideki KUBO, Tomoshi OTSUKI, Hideo SAKAMOTO, Takufumi YOSHIDA.
Application Number | 20200156679 16/567913 |
Document ID | / |
Family ID | 67956453 |
Filed Date | 2020-05-21 |
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United States Patent
Application |
20200156679 |
Kind Code |
A1 |
OTSUKI; Tomoshi ; et
al. |
May 21, 2020 |
INFORMATION PROCESSING APPARATUS, METHOD FOR THE SAME, AND COMPUTER
PROGRAM
Abstract
According to one embodiment, an information processing apparatus
includes processing circuitry. The processing circuitry reads out
diagram information indicating a schedule of at least one vehicle
tripping along a trip path, wherein the diagram information
includes a plurality of events and the events include stop places
and departure times from and/or arrival times at the stop places,
and calculates a delay probability distribution for a first event
of the plurality of events included in the diagram information. The
processing circuitry calculates the delay probability distribution
for the first event based on: event-to-event delay time information
between the first event and a second event preceding the first
event; and a required time interval between the first event and the
second event.
Inventors: |
OTSUKI; Tomoshi; (Kawasaki,
JP) ; SAKAMOTO; Hideo; (Kawasaki, JP) ; AISU;
Hideyuki; (Kawasaki, JP) ; YOSHIDA; Takufumi;
(Funabashi, JP) ; KUBO; Hideki; (Fuchu,
JP) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
KABUSHIKI KAISHA TOSHIBA |
Minato-ku |
|
JP |
|
|
Assignee: |
KABUSHIKI KAISHA TOSHIBA
Minato-ku
JP
|
Family ID: |
67956453 |
Appl. No.: |
16/567913 |
Filed: |
September 11, 2019 |
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
B61L 27/0027 20130101;
B61L 27/0016 20130101; B61L 27/0022 20130101 |
International
Class: |
B61L 27/00 20060101
B61L027/00 |
Foreign Application Data
Date |
Code |
Application Number |
Nov 20, 2018 |
JP |
2018-217656 |
Claims
1. An information processing apparatus, comprising: processing
circuitry configured to read out diagram information indicating a
schedule of at least one vehicle tripping along a trip path,
wherein the diagram information includes a plurality of events and
the events include stop places and departure times from and/or
arrival times at the stop places, and calculate a delay probability
distribution for a first event of the plurality of events included
in the diagram information, wherein the processing circuitry
calculates the delay probability distribution for the first event
based on: event-to-event delay time information between the first
event and a second event preceding the first event; and a required
time interval between the first event and the second event.
2. The information processing apparatus according to claim 1,
wherein the diagram information includes first to n-th line
information, the first to n-th line information include the
plurality of events including: stop places of the first to n-th
vehicles; and departure times from or arrival times at the stop
places of the first to n-th vehicles, the first event is an event
selected from the events included in one line information among the
first to n-th line information, and the second event is at least
one event selected from the events included at least one of the
other line information than the one line information.
3. The information processing apparatus according to claim 2,
wherein the second event is also selected from the events included
in the one line information.
4. The information processing apparatus according to claim 2,
wherein the processing circuitry sorts the plurality of events
included in the first to n-th line information in chronological
order and the processing circuitry repeats to select one of the
events as the first event in the sorted order and the processing
circuitry calculates, for the selected first event, the delay
probability distribution for the first event.
5. The information processing apparatus according to claim 1,
wherein the processing circuitry identifies a margin time between
the first event and the second event, based on a difference between
(a) a time duration between the time of the first event and the
time of the second event; and (b) the required time interval
between the first event and the second event, and the processing
circuitry generates a first probability distribution based on an
convolution operation of the event-to-event delay time information
and a delay probability distribution for the second event, the
processing circuitry shifts the first probability distribution
based on the margin time, and the shifted first probability
distribution is the delay probability distribution for the first
event.
6. The information processing apparatus according to claim 5,
wherein the processing circuitry generates the shifted first
probability distribution for each of a plurality of the second
events, and the processing circuitry combines the shifted first
probability distributions to generate the delay probability
distribution for the first event.
7. The information processing apparatus according to claim 1,
wherein the processing circuitry performs round-up processing if
the first event is prohibited from taking place earlier than the
time of the first event, and the round-up processing is that in the
delay probability distribution for the first event, a probability
for a negative-valued delay time is added to a probability for a
delay time of 0, and the probability for the negative-valued delay
time is changed to 0.
8. The information processing apparatus according to claim 1,
wherein at least one of the plurality of events includes a time of
passing through one of the stop places.
9. The information processing apparatus according to claim 1,
wherein the diagram information includes at least one line
information, the at least one line information includes the
plurality of events that include: the stop places of the vehicle;
and the departure times from and/or arrival times at the stop
places, and the processing circuitry calculates the delay
probability distribution for each of the events on the at least one
line information, the processing circuitry shifts the times of the
events on the at least one line information by respective delay
expected values based on the delay probability distributions and
the processing circuitry generates an expected line information
including the shifted times of the events.
10. The information processing apparatus according to claim 9,
wherein the processing circuitry calculates an indicator
representing punctuality, quick-deliverability, or transportation
capacity, based on the expected line information.
11. An information processing method, comprising: reading out:
diagram information indicating a schedule of at least one vehicle
tripping along a trip path, wherein the diagram information
includes a plurality of events, and the events include stop places
and departure times from and/or arrival times at the stop places;
event-to-event delay time information between a first event of the
plurality of events and a second event preceding the first event in
the plurality of events; and a required time interval between the
first event and the second event; and calculating a delay
probability distribution for the first event based on the diagram
information, event-to-event delay time information and the required
time interval.
12. A non-transitory computer readable medium having a computer
program stored therein which when the computer program is executed
by a computer, causes the computer to perform processes including,
comprising: reading out: diagram information indicating a schedule
of at least one vehicle tripping along a trip path, wherein the
diagram information includes a plurality of events, and the events
include stop places and departure times from and/or arrival times
at the stop places; event-to-event delay time information between a
first event of the plurality of events and a second event preceding
the first event in the plurality of events; and a required time
interval between the first event and the second event; and
calculating a delay probability distribution for the first event
based on the diagram information, event-to-event delay time
information and the required time interval.
Description
CROSS REFERENCE TO RELATED APPLICATIONS
[0001] This application is based upon and claims the benefit of
priority from the prior Japanese Patent Application No.
2018-217656, filed on Nov. 20, 2018, the entire contents of which
are incorporated herein by reference.
FIELD
[0002] The present disclosure relates to an information processing
apparatus, a method for the same, and a non-transitory computer
readable medium.
BACKGROUND
[0003] For railway companies and the like, delays in service
planning diagrams, which is simply called diagrams, are serious
problems bringing about decreases in sales and increases in costs
such as penalty payment. Accordingly, it is preferable to create a
diagram that is as robust as possible to withstand delays. If a
diagram can be evaluated by using as less historic data on
operations as possible, such a diagram evaluation method is of
great worth.
[0004] Diagram evaluation methods include a method in which a
probability of delay at each station is calculated as one example.
There is, for example, a method in which a probability of delay at
each station is output by using the Bayesian network scheme.
However, if the Bayesian network is used, big historic data, such
as journal information for a certain period of time, is required to
acquire information on correlations of delays between stations.
There is, as another example, also a method in which Monte Carlo
simulation is performed by using a diagram and past delay
probability records and a frequency distribution for a delay at
each station is created. However, Monte Carlo simulation generally
takes a long time to convergence and therefore has a problem that a
large number of repetitions are required.
BRIEF DESCRIPTION OF THE DRAWINGS
[0005] FIG. 1 is a block diagram of a diagram evaluation apparatus,
which is an information processing apparatus according to the
present embodiment;
[0006] FIGS. 2A and 2B shows an outline of the present
embodiment;
[0007] FIG. 3 shows an example of an interface screen (input
screen) on which diagram information is input;
[0008] FIG. 4 shows part of the diagram information in the form of
a table;
[0009] FIG. 5 shows a plurality of train lines included in the
diagram information, in the form of graphs;
[0010] FIG. 6 shows another example of the diagram information;
[0011] FIG. 7 shows a plurality of train lines included in the
diagram information shown in FIG. 6, in the form of graphs;
[0012] FIG. 8 shows examples of statistical values;
[0013] FIG. 9 shows an example of a geometric distribution as an
event-to-event delay probability distribution;
[0014] FIG. 10 shows an example of a screen on which an average
delay time is input;
[0015] FIG. 11 shows an example of the screen on which an average
delay time is input;
[0016] FIG. 12 shows an example of the screen on which an average
delay time is input;
[0017] FIG. 13 shows examples of minimum required time interval
information;
[0018] FIG. 14 shows examples of minimum required time interval
information;
[0019] FIG. 15 shows an example of a screen on which a minimum
required time interval and a margin time are input for train line
on a train;
[0020] FIG. 16 shows an example of event delay probability
distributions generated by a delay probability distribution
calculator;
[0021] FIG. 17 is a diagram of graphs representing event delay
probability distributions for events 1 to 4;
[0022] FIG. 18 is a flowchart showing an outline of processing in
which the event delay probability distributions are generated by
the delay probability distribution calculator;
[0023] FIG. 19 is a detailed flowchart of Step_A in FIG. 18;
[0024] FIG. 20 shows an example of event information generated
through the processing in FIG. 18;
[0025] FIG. 21 is a detailed flowchart of Step_D in FIG. 18;
[0026] FIG. 22 shows an outline of the processing in Step_D when
two preceding events exist;
[0027] FIG. 23 shows a specific example of Step_D;
[0028] FIG. 24 shows another specific example of Step_D;
[0029] FIGS. 25(A) to 25(C) show a specific example of processing
for generating a combined probability distribution;
[0030] FIG. 26 is a diagram for describing a specific example of
round-up processing;
[0031] FIG. 27 shows an example of an output table including delay
probability distributions generated through the processing
according to the present embodiment;
[0032] FIG. 28 shows an example of generation of an expected train
line;
[0033] FIG. 29 is a diagram for describing a delay limit excess
probability;
[0034] FIG. 30 is a diagram for describing an expected trip
time;
[0035] FIG. 31 is a diagram for describing a train line rate at a
specific station in a specific time slot;
[0036] FIG. 32 is a diagram for describing a train line rate at a
specific time;
[0037] FIG. 33 is a diagram for describing an arrival and departure
rate at specific stations in a specific time slot; and
[0038] FIG. 34 shows a hardware configuration of the diagram
evaluation apparatus (information processing apparatus) according
to the present embodiment.
DETAILED DESCRIPTION
[0039] According to one embodiment, an information processing
apparatus includes processing circuitry. The processing circuitry
reads out diagram information indicating a schedule of at least one
vehicle tripping along a trip path, wherein the diagram information
includes a plurality of events and the events include stop places
and departure times from and/or arrival times at the stop places,
and calculates a delay probability distribution for a first event
of the plurality of events included in the diagram information. The
processing circuitry calculates the delay probability distribution
for the first event based on: event-to-event delay time information
between the first event and a second event preceding the first
event; and a required time interval between the first event and the
second event.
[0040] Hereinafter, embodiments will be described with reference to
drawings.
[0041] FIG. 1 is a block diagram of a diagram evaluation apparatus
100, which is an information processing apparatus according to the
present embodiment. The diagram evaluation apparatus 100 includes a
diagram information input unit 110, an event-to-event delay time
information input unit 120, a minimum required time interval input
unit 130, a delay probability distribution calculator 500, a
display 400, and a plurality of storages. The plurality of storages
include a diagram information storage 210, an event-to-event delay
time information storage 220, a minimum required time interval
storage 230, an event information storage 240, and an event delay
probability distribution storage 300. The diagram evaluation
apparatus 100 makes it possible to generate a probability
distribution of delay time in each event (event delay probability
distribution) in diagram information rapidly, and thus to evaluate
the diagram information rapidly. The diagram information defines
schedules of vehicles such as trains or buses (trains will be
assumed hereinafter) tripping along a trip path. Examples of each
event in the diagram information include an arrival event that is
an arrival at a certain station at a certain time, a departure
event that is a departure from a certain station at a certain time,
and a pass event that is a pass through a certain station at a
certain time. Prior to a description of the diagram evaluation
apparatus 100, an outline of the present embodiment will be
described.
[0042] Generally, in generation of diagram information, a delay of
a train is supposed, and a time point of an event (departure time,
arrival time, or the like) is determined in many cases by adding a
margin time to a minimum value of a run time between stations or a
minimum value of a dwell time at a station. Moreover, a restriction
related to a time interval (time interval restriction) is provided
in many cases between a train line of a certain train (self train
line) and a train line of another train preceding the certain train
(preceding train line). If a delay time on the preceding train line
exceeds a predetermined value, the delay time influence on the
train of the self train line. Specifically, there are two types of
delays: a delay on the self train line itself (primary delay) and a
delay due to the preceding train line (secondary delay). In more
detail, delays include a delay due to a preceding event on the self
train line and a delay due to a preceding event on the preceding
train line. The two type of a delay on the self train line and a
delay from the preceding train line influences on the train of the
self train line.
[0043] FIGS. 2A and 2B show the outline of the present embodiment.
FIG. 2A shows graphs (networks) of a train line 11 of a certain
train and a train line 12 of another train. Circles in the diagrams
are nodes, which represent events. The train line 11 includes an
event 11a of departure from A station, an event 11b-1 of arrival at
B station, an event 11b-2 of departure from the B station, an event
11c-1 of arrival at C station, an event 11c-2 of departure from the
C station, and an event 11d of arrival at D station (the nodes
corresponding to the events are denoted by the same reference
signs). A time in a diagram is set on each event.
[0044] A rightward direction along a plane of the drawing is a time
direction. The train line 12 is a train line of another train that
trips along the same path as the train line 11 (a train line
following the train line 11). The train line 12 includes an event
12a of departure from the A station, an event 12b-1 of arrival at
the B station, an event 12b-2 of departure from the B station, an
event 12c-1 of arrival at the C station, an event 12c-2 of
departure from the C station, and an event 12d of arrival at the D
station. It is assumed that only one track exists for each of an
inbound line (from the A station toward the D station) and an
outbound line (from the D station toward the A station) at each
station. Here, an arrival event of the other train at the C station
(event 12c-1) will be considered. A delay in the event 12c-1 is
influenced on a delay in the first preceding event 12b-2 on the
train line 12 (primary delay) and a delay in the event 11c-2 on the
preceding train line (train line 11) at the same C station
(secondary delay). The delay in the event 12c-1 may be influenced
on events at the C station (event 11c-1 and the like) other than
the event 11c-2. Specific examples of the primary delay include a
delay in a run time from the previous B station and a delay in a
dwell time of departure from (departure time at) the preceding B
station. Specific examples of the secondary delay include a delay
in departure from the C station on the preceding train line 11. A
required time interval, which is a time interval to be left, and a
margin time are provided between events. In the embodiment, a case
is described in which the required time interval is a minimum
required time interval which is a minimum time interval to be left.
For example, the minimum required time interval or a longer time
interval needs to be left between the event 11a-1 and the event
12a-1. As an example, a time interval between the event 11a-1 and
the event 12a-1 in the diagram is the minimum required time
interval plus the margin time. If a time period from departure of a
train from the A station until departure of another train from the
A station exceeds the minimum required time interval but is not
longer than the minimum required time interval plus the margin
time, no delay occurs between the event 11a-1 and the event 12a-1.
That is, if a delay time (an excess time interval over the minimum
required time interval) between the event 11a-1 and the event 12a-1
is not longer than the margin time, no delay occurs between the
events.
[0045] Although the description is focused on an arrival event
(event 12c-1) in FIG. 2A, the same is true for a departure event.
In FIG. 2B, a departure event (event 12c-2) at the C station will
be considered. A delay in the event 12c-2 is influenced on a delay
in the first preceding event 12c-1 on the train line 12 (primary
delay) and a delay in an event on the preceding train line 11
(departure event 11c-1 at the C station) (secondary delay).
Specific examples of the primary delay include a delay in arrival
at the C station and a delay in dwell time at the C station (a
prolonged boarding and alighting time, or the like). A minimum time
interval to be left (minimum required time interval) and a margin
time are provided between events. For example, the minimum required
time interval (a minimum required boarding and alighting time) or a
longer time interval is required to be left between the event 12c-2
and the event 12c-1. As an example, a time interval between the
event 12c-2 and the event 12c-1 in the diagram is the minimum
required time interval plus the margin time. If a time interval
from arrival at the C station until departure from the C station
exceeds the minimum required time interval but is not longer than
the minimum required time interval plus the margin time, no delay
occurs between the event 12c-2 and the event 12c-1. That is, if a
delay time (an excess time interval over the minimum required time
interval) between the two events is not longer than the margin
time, no delay occurs between the events.
[0046] In the present embodiment, a delay probability distribution
for each event is calculated, taking into consideration at least
one of such two types of delays (primary delay, secondary delay)
and the required time interval required between events (for
example, the minimum required time interval). The delay probability
distribution for each event is calculated, further taking into
consideration the margin time between events. Thus, the delay
probability distribution for each event can be calculated rapidly,
and therefore the diagram can be evaluated rapidly. Hereinafter,
the diagram evaluation apparatus 100 will be described in
detail.
[0047] The diagram information input unit 110 in FIG. 1 acquires
(or receives) diagram information and stores the diagram
information in the diagram information storage 210. As an example,
the diagram information input unit 110 is an input unit such as a
keyboard, a mouse, or a touch panel operated by an operator of the
diagram evaluation apparatus 100. In such a case, the diagram
evaluation apparatus 100 includes a function for providing an
interface screen on which the diagram information is input. The
interface screen is displayed on the display 400.
[0048] The display 400 is a display device such as an LCD (liquid
crystal display), a CRT (cathode ray tube), or a PDP (plasma
display) that displays data or information.
[0049] The diagram information input unit 110 may be an acquirer
that acquires the diagram information from an external apparatus or
a storage medium. In such a case, the external apparatus is, as an
example, an external server connected to the diagram evaluation
apparatus 100 through a wired or wireless communication network.
The storage medium is, as an example, a storage medium disposed
within the diagram evaluation apparatus 100 or a storage medium
externally connected. Examples of the storage medium include a
memory device, a hard disk, an SSD, and an optical disk. A trigger
for the acquisition of the diagram information may be an
instruction from the operator (i.e., a user) of the diagram
evaluation apparatus 100, or may be any other condition (for
example, it becoming a predetermined time).
[0050] FIG. 3 shows an example of the interface screen (input
screen) on which the diagram information is input. The operator can
input the diagram information from the screen.
[0051] The diagram information is information of a diagram to be
evaluated. The diagram represents a series of events such as
departure, arrival, and pass in association with times and stop
locations (places) with respect to a plurality of vehicles (trains,
buses, or the like). The events refer to departure, arrival, pass,
and the like. Examples of the stop locations (places) include
stations, bus stops, detention spaces, depots, and signal stations.
A series of events along a trip path including a plurality of
places, with respect to a vehicle, is referred to as a train line
or line information. In the following, trains will mainly be
assumed as the vehicles. However, the same is true for other kinds
of vehicles such as buses, by appropriately replacing words as
necessary according to differences between tripping systems. For
example, in the description of the specification, a station is
replaced with a bus stop, and the like.
[0052] FIG. 3 shows an example of the screen on which the train
line on a certain train is input. The input screen includes a
timetable menu M1 and a margin time menu M2. In the FIG. 3, the
screen for the timetable menu M1 is displayed.
[0053] The train is operated from A station to C station. The train
departs from the A station, dwells at B station, and dwells at the
C station. Since the train dwells at the A station, the B station,
and the C station, each respective dwell/pass item (indicating
whether the train dwells or passes) is set for "dwell". A time
point of departure (hereinafter, a departure time) from the A
station, a time point of arrival (hereinafter, an arrival time) and
a departure time at the B station, and an arrival time at the C
station are set. A run time from the A station to the B station
(time of duration from the departure time at the A station until
the arrival time at the B station) and a dwell time at the B
station (time of duration from the arrival time at the B station
until the departure time at the B station) are set. It is set that
the train dwells at a first track at each station. Each of
departure from the A station at 8:00, arrival at the B station at
8:10, departure from the B station at 8:12, arrival at the C
station at 8:32, and the like corresponds to one event, and a
series of such events corresponds to a train line (or line
information).
[0054] In a train number item, a train number (here, "000001") can
be set. In a type item, it can be set whether the train is local
(dwelling at each station) or express. A value ("dwell" or "pass")
in the dwell/pass item for each station may be automatically input
depending on whether the train is local or express. In a
regular/irregular item, it can be set whether the train is operated
regularly or irregularly. As an example, in case of "regular", the
train line is applied on weekdays, and in case of "irregular", the
train line is applied on weekends.
[0055] FIG. 4 shows part of the diagram information input from the
diagram information input unit 110, in the form of a table. FIG. 5
shows graphs respectively representing each train line in the
diagram information in FIG. 4. In more detail, FIG. 5 shows
respective network structures of the train lines.
[0056] The table in FIG. 4 includes three train lines on mutually
different vehicles (trains) tripping from the A station to the C
station. As an example, the vehicles correspond to first to n-th
vehicles. Three train lines correspond to respective train lines of
the first to n-th vehicles. The diagram information includes
columns of train line id, time, station, and type of an event. A
type is a type of an event indicating departure, arrival, pass, or
the like. In the table shown in the diagram, the diagram
information includes information for the train line 1 that departs
at 8:00, the train line 2 that departs at 8:20, and the train line
3 that departs at 8:30. The train line 1 corresponds to the train
line illustrated in FIG. 3. The train line 1 and the train line 3
do not include a pass event because the vehicles dwell at all
stations. On the other hand, in the train line 2, since the vehicle
passes through the B station, a pass event is set on the B
station.
[0057] FIG. 5 shows the train lines 1 to 3 included in the diagram
information in FIG. 4, each in the form of a graph (network graph).
A horizontal axis corresponds to time, and a vertical axis
corresponds to distance. The horizontal axis shows relative time,
and in the present example, "0" corresponds to 8:00. Each graph
(network graph) includes nodes corresponding to events and arcs
connecting the nodes. More specifically, the graph of the train
line 1 includes nodes e1, e2, e3, and e4 corresponding to
chronological events (events 1, 2, 3, and 4, respectively) included
in the train line 1, and arcs connecting the nodes. Similarly, the
graph of the train line 2 includes node e5, e6, and e7
corresponding to chronological events (events 5, 6, and 7,
respectively) included in the train line 2, and arcs connecting the
nodes. The graph of the train line 3 includes nodes e8, e9, e10,
and e11 corresponding to chronological events (events 8, 9, 10, and
11, respectively) included in the train line 3, and arcs connecting
the nodes.
[0058] FIG. 6 is a table showing another example of the diagram
information, and FIG. 7 shows the diagram information shown in FIG.
6, in the form of graphs (network graphs). The diagram information
in FIG. 6 includes information of a train line 4 and a train line
5. Each of the train line 4 and the train line 5 is a train line in
case of an operation making one and a half round trip between the A
station and the C station. A train line in case of an operation
making two or more round trips may also be defined.
[0059] In the train lines shown in FIGS. 4 to 7, first departure is
from the A station. However, a train line that departs from a
midway station (for example, the B station) may be defined. A train
line that departs first from the C station may be defined.
[0060] The diagram information in the form of a table and in the
form of graphs are shown in FIGS. 4 to 7. However, the diagram
information may be structured in any other form as long as the form
is processible at subsequent stages.
[0061] The event-to-event delay time information input unit 120
acquires event-to-event delay time information and stores the
event-to-event delay time information in the event-to-event delay
time information storage 220. As an example, the event-to-event
delay time information input unit 120 is an input unit such as a
keyboard, a mouse, or a touch panel operated by the operator. In
such a case, the diagram evaluation apparatus 100 includes a
function of providing an interface screen on which the
event-to-event delay time information is input. The interface
screen is displayed on the display 400. The event-to-event delay
time information input unit 120 may be an acquirer that acquires
the event-to-event delay time information from an external
apparatus or a storage medium. In such a case, examples of the
external apparatus, the storage medium, and a trigger for an
acquisition timing are similar to those in the case of the diagram
information input unit 110.
[0062] The event-to-event delay time information is an
event-to-event delay probability distribution, which is a
distribution of delay time between events, or information required
to generate an event-to-event delay probability distribution.
Examples of the information include parameters of a probability
distribution. The parameters of a probability distribution, which
has statistics such as a mean, a variance, and a median as
parameters, may be used for the event-to-event delay time
information. As an example, the event-to-event delay probability
distribution is a normal distribution or a geometric distribution.
Specific examples of the event-to-event delay probability
distribution include a distribution of delay in a run time between
stations, or a distribution of delay in a dwell time at a station.
The run time corresponds to a time duration from a departure time
(a time point of a departure event) at a station until an arrival
time or a pass time (a time point of an arrival event or a time
point of a pass event) at a next station. The dwell time
corresponds to time duration from an arrival time (a time point of
an arrival event) at a station until a departure time (a time point
of a departure event) at the same station.
[0063] An example in which a geometric distribution is used will be
illustrated as an example of the event-to-event delay time
distribution. Expression 1 expresses a probability function for a
geometric distribution, where "D(k)" is a probability of the delay
time being "k".
[Expression 1]
D(k)=(1-p).sup.kp (k=0,1,2, . . . ) (1)
[0064] The geometric distribution has only one parameter, "p".
Accordingly, a distribution can be determined only by providing one
statistical value to the parameter. As examples of statistical
values, FIG. 8 shows examples of an average value of delay in the
run time between stations and an average value of delay in the
dwell time at each station, for each type (local, express, or the
like). In case of using a geometric distribution, the distribution
can be determined by using such one average value.
[0065] The geometric distribution can be determined as "p=1/(x+1)"
when the average value of delay time is "x". A discrete
distribution where the delay time is "k" can be calculated by
Expression 1. "k" is a stochastic variable.
[0066] FIG. 9 shows an example illustrating a distribution in case
of using a geometric distribution for the event-to-event delay
probability distribution. A horizontal axis corresponds to "k"
(delay time), and a vertical axis corresponds to "D(k)" (a
probability of the delay time being "k"). In the example, the
probability function returns a non-negative value first when k=0.
However, the distribution is shifted rightward or leftward and
thereby the probability function may return a non-negative value
first when "k" is a negative value or a positive value.
[0067] Note that since the stochastic variable takes all
non-negative integers in an ordinary geometric distribution, the
geometric distribution is represented by respective probabilities
corresponding to an unlimited number of integers. Accordingly, the
equation (1) may be modified so that a limited number of integers
are taken by neglecting the region where values of the stochastic
variable is too small.
[0068] As another example of the distribution of delay time, a
negative binomial distribution or the like obtained by generalizing
geometric distributions may be used. A distribution having two or
more parameters, such as a normal distribution or a gamma
distribution, may also be used. In such a case, a distribution is
calculated not from one statistical value (an average value or the
like) but from a plurality of statistical values. A histogram,
which is generated from historic delay time data, can also be used
for the event-to-event delay probability distribution. Different
types of distributions may be used for different types of vehicles
that run. Different types of distributions may also be used for
different time slots (rush hours and non-rush hours, or the
like).
[0069] If the information required to generate the event-to-event
delay probability distribution is input into the event-to-event
delay time information input unit 120, the delay probability
distribution calculator 500, which will be described later,
calculates the event-to-event delay probability distribution from
the input information. As an example of an input other than the
above-described parameter of a probability distribution, a
distribution of run time or a dwell time may be input. In such a
case, the delay probability distribution calculator 500, which will
be described later, can obtain the event-to-event delay probability
distribution by calculating differences from a minimum required
time interval, which will be described later and by regarding the
calculated differences as delay times.
[0070] In processing in the present embodiment, it is assumed that
an average value of delay time is input as a parameter, as the
information required to generate the event-to-event delay
probability distribution. The delay probability distribution
calculator 500, which will be described later, generates a
geometric distribution (the event-to-event delay probability
distribution) based on the parameter and the above-mentioned
equation (1).
[0071] FIGS. 10, 11, and 12 show examples of the screen on which an
average value of delay time (average delay time) is input as the
information to generate the event-to-event delay probability
distribution.
[0072] FIG. 10 shows an example in which "one minute (00:01)" is
input as an average delay in the dwell time at the B station. In
items of minimum required time interval, margin time, and dwell
time, a minimum required time interval for dwell time at the B
station, a margin time, and a dwell time are stored, respectively.
The minimum required time interval and the margin time will be
described later. Here, it is assumed that the minimum required time
interval, the margin time, and the dwell time have been input
beforehand on another screen. However, it is not excluded to input
the minimum required time interval, the margin time, and the dwell
time on the screen. The same is true in FIGS. 11 and 12 described
below. The average delay time is an average of excess time
durations over the minimum required time interval. The dwell time
can be identified from the diagram information. The dwell time is
not shorter than the minimum required time interval and is
calculated by the minimum required time interval plus the margin
time.
[0073] FIG. 11 shows an example in which "three minutes (00:03)" is
input as an average delay in turnaround at the C station. A
turnaround time duration at the C station is time duration from
arrival of a train at the C station until departure of the train
from the C station if the train makes a return trip after arriving
at the C station. In the minimum required time interval item, the
margin time item, and a turnaround time duration item, a minimum
required time interval for the turnaround at the C station, a
margin time, and a turnaround time duration are stored beforehand,
respectively. The average delay time in the turnaround is an
average of excess time durations over the minimum required time
interval. The turnaround time duration can be identified from the
diagram information and is. The turnaround time duration is
calculated by the minimum required time interval plus the margin
time, as an example.
[0074] FIG. 12 shows an example in which "two minutes (00:02)" is
input as an average delay in run from the A station to the B
station (from departure from the A station until dwell at the B
station). In the screen shown in the diagram, a
"Dwell.fwdarw.Dwell" tab is selected. In the minimum required time
interval item, the margin time item, and a run time item, a minimum
required time interval for the run from the A station to the B
station, a margin time, and a run time are stored beforehand,
respectively. The average delay time is an average of excess time
durations over the minimum required time interval. The run time can
be identified from the diagram information. The run time is
calculated by the minimum required time interval plus the margin
time as an example.
[0075] If a "Dwell.fwdarw.Pass" tab is selected, an average delay
from departure from a certain station until pass through another
station can be input. If a "Pass.fwdarw.Dwell" tab is selected, an
average delay from pass through a certain station until arrival
(dwell) at another station can be input. If a "Pass.fwdarw.Pass"
tab is selected, an average delay from pass through a certain
station until pass through another station can be input. An average
delay time between events other than those recited in FIGS. 10 to
12 may also be input.
[0076] The minimum required time interval input unit 130 acquires
minimum required time interval information and stores the minimum
required time interval information in the minimum required time
interval storage 230. As an example, the minimum required time
interval input unit 130 is an input unit such as a keyboard, a
mouse, or a touch panel operated by the operator. In such a case,
the diagram evaluation apparatus 100 includes a function of
providing an interface screen on which the minimum required time
interval information is input. The interface screen is displayed on
the display 400. The minimum required time interval input unit 130
may be an acquirer that acquires the minimum required time interval
information from an external apparatus or a storage medium. In such
a case, examples of the external apparatus, the storage medium, and
a trigger for an acquisition timing are similar to those in the
case of the diagram information input unit 110.
[0077] The minimum required time interval information is
information including a minimum required time interval, which is a
minimum time interval to be left between events within a single
train line or between events on a plurality of train lines. A
restriction by the minimum required time interval will be referred
to as a time interval restriction in some cases. Instead of the
minimum required time interval information, required time interval
information including a required time interval which is a time
interval required to be left between events within a single train
line or between events on a plurality train lines.
[0078] FIGS. 13 and 14 show examples of the minimum required time
interval information. FIG. 13 shows examples of a minimum run time
between stations and examples of a minimum dwell time at each
station. The minimum run time and the minimum dwell time may be
defined for each type (local, express, or the like) and for each of
inbound and outbound directions. The minimum required time interval
may be defined for each train line, or may be defined in common for
all train lines. FIG. 14 shows examples of a lower limit value of
an arrival-departure time interval at each station, as a
restriction between the event and an event on a preceding train
line.
[0079] An example of the time interval restriction between events
on a plurality of train lines will be illustrated. A restriction
exists that is a minimum time interval to be left between an
arrival time at a certain station (for example, the B station) on a
preceding train line and a departure time at a first previous
station (for example, the A station) on a self train line. Here,
the preceding train line is a train line of a train operated, prior
to the self train line, along the same path, or part thereof, as
the self train line. It is assumed here that overtaking does not
occur between the train operated according to the preceding train
line and a train operated according to the self train line. If
overtaking occurs, it may be regarded that a relationship between
the preceding train line and the self train line is reversed at and
after a location where the overtaking occurs or the relationship is
reversed at and after a time when the overtaking occurs. The
preceding train line may be an immediately preceding train line, or
may refer to a plurality of train lines including a train line
further preceding the preceding train line. A scope of the
preceding train line may be defined arbitrarily.
[0080] Other various types of time interval can be considered. For
example, if a station has a plurality of tracks, there are an
arrival-arrival time interval and a departure-departure time
interval between different tracks. If a turnaround is made at a
station, there is a time interval related to the turnaround (if a
turnaround is made, a restriction between events before and after
the turnaround; for example, a time interval from arrival at the
station until departure for a return trip, or the like). Different
values of the time interval restriction may be provided for
different types of vehicles or different time slots for tripping
(rush hours and non-rush hours, or the like). For example, during
rush hours, the value of the restriction may be set larger or
smaller than during non-rush hours. If overtaking (a certain
vehicle overtaking another vehicle) or a wait occurs, the value of
the time interval restriction may be made different from a value
when no overtaking or wait occurs. Time interval restrictions may
also be set between an arrival time and a pass time and between a
departure time and a pass time.
[0081] FIG. 15 shows an example of the screen on which the minimum
required time interval and the like are input for line information
on a certain train. The screen in FIG. 15 is displayed by opening
the margin time menu M2 on an input screen similar to the input
screen shown in FIG. 3. Note that the screen is a screen concerning
a different train line (a different train) from the train line on
the screen in FIG. 3. A description of the same items as the items
described in the timetable menu M1 in FIG. 3 will be omitted.
[0082] The minimum required time interval can be set in the margin
time menu M2. In a minimum required time interval item, a minimum
required time interval is set. Note that in a dwell/run item, a
dwell time or a run time identified from the diagram information is
set. In a margin time item, a margin time is set. In a total margin
item, a total margin time is set. A difference between the dwell
time or the run time and the minimum required time interval
corresponds to the margin time. The margin time may be manually
input by the operator. The margin time may be calculated based on
the diagram information and the minimum required time interval and
the calculated margin time automatically input on the screen. In
the processing in the present embodiment, the margin time is
calculated based on the diagram information and the minimum
required time interval, which will be described later, and
therefore the margin time set on the input screen is not used;
however, the processing can be changed so that the margin time set
on the input screen is used.
[0083] In the example shown in the diagram, the minimum required
time interval at the A station is set to one minute (00:01). The
minimum required time interval before a train passes through the B
station is set to eight minutes (00:08). The minimum required time
interval with respect to the C station is set to one minute
(00:01).
[0084] The minimum required time interval input unit 130 may input
information required to acquire the minimum required time interval
information, not inputting the minimum required time interval
information. In this case, the delay probability distribution
calculator 500 calculates the minimum required time interval
information based on the input information and other additional
information. For example, the minimum required time interval input
unit 130 inputs information on the margin time between stations or
the like. The delay probability distribution calculator 500 can
obtain the minimum required time interval by calculating a
difference between a time difference in the diagram information
(factoring in a margin time) and a margin time indicated by the
input information. The minimum required time interval may also be
calculated based on a distance between stations, a maximum velocity
of each vehicle or an acceleration performance of each vehicle, or
the like.
[0085] The delay probability distribution calculator 500 in FIG. 1
includes an event information generator 510, an evaluation order
determiner 515, and a delay probability evaluator 520. The delay
probability evaluator 520 includes a convolution calculator 521, a
margin shifter 522, a combined probability calculator 523, and a
round-up processor 524.
[0086] The delay probability distribution calculator 500 reads the
diagram information from the diagram information storage 210, the
average value of delay time (information to generate the
event-to-event delay probability distribution) from the
event-to-event delay time information storage 220, and the minimum
required time interval information from the minimum required time
interval storage 230, and calculates the event delay probability
distribution. The event delay probability distribution is, for
example, a probability distribution of delay time (delay
probability distribution) with respect to the event such as
arrival, departure, or pass at each station. As an example, the
event delay probability distribution corresponds to a first delay
probability distribution according to the present embodiment. The
delay probability distribution calculator 500 stores the generated
event delay probability distribution in the event delay probability
distribution storage 300. The display 400 displays the event delay
probability distribution stored in the storage 300.
[0087] FIG. 16 shows an example of event delay probability
distributions generated by the delay probability distribution
calculator 500. A vertical axis corresponds to identifies (ids) of
events, and a horizontal axis corresponds to delay times. An event
x is an event whose id is "x". Time is separated into one-minute
units, but may be separated into other units such as five-minute
units.
[0088] Events 1 to 4 are events belonging to the train line 1 in
FIG. 4, and the event 1 represents departure from the A station,
the event 2, arrival at the B station, the event 3, departure from
the B station, and the event 4, arrival at the C station. Events 5
to 7 are events belonging to the train line 2 in FIG. 4, and the
event 5 represents departure from the A station, the event 6, pass
through the B station, and the event 7, arrival at the C station.
Events 8 to 11 are events belonging to the train line 3 in FIG. 4,
and the event 8 represents departure from the A station, the event
9, arrival at the B station, the event 10, departure from the B
station, and the event 11, arrival at the C station.
[0089] In the event 1, the probability of the delay time being 0 is
100%, with respect to departure of a vehicle of the train line 1
from the A station. That is, the probability that the vehicle of
the train line 1 departs from the A station without delay is
100%.
[0090] In the event 2, probabilities larger than 0 are distributed
over a range of delay times of -2 to 13, with respect to arrival of
the vehicle of the train line 1 at the B station. For example, with
respect to the vehicle of the train line 1, the probability of
delay in arrival at the B station is 14.8% for a delay time of 0,
9.9% for a delay time of 1, and 22.2% for a delay time of -1. A
delay time of -1 means one minute early arrival at the B
station.
[0091] In the event 6, with respect to a vehicle of the train line
2, the probability of a delay time of 0 in the pass time at the B
station is 10.0%, and the probability of a delay time of -1 is
22.2%. A delay time of -1 means one minute early pass though the B
station.
[0092] In the departure-related events 1, 3, 5, 8, and 10, all
probabilities for negative-valued delay times are 0%. That is, the
probability of early departure, which means that a vehicle departs
earlier than a departure time, is 0%. Hereinafter, early arrival,
early pass, and early departure will collectively be referred to as
early departure and the like in some cases.
[0093] FIG. 17 shows the probability distributions for the events 1
to 4 belonging to the train line 1 (the first train line) in FIG.
16, in the form of graphs. Similar graphs may be created for the
other train lines 2 to 4. The operator may designate a train line
for which graphs are generated, and the graphs may be created only
for the designated train line.
[0094] The created graphs may be displayed on the display 400 to
allow the operator to check. The operator can intuitionally
evaluate the diagram information by checking the graphs. The event
delay probability distributions in the form of a table (see FIG.
16) may be displayed on the display 400. Thus, the operator can
also collectively check the delay probability distributions for the
events on each train line and evaluate the diagram information.
[0095] Hereinafter, a detailed description will be given of
processing in which the delay probability distribution calculator
500 generates such event delay probability distributions.
[0096] FIG. 18 is a flowchart showing an outline of the processing
in which the delay probability distribution calculator 500
generates the event delay probability distributions.
[0097] The event information generator 510 generates event
information based on the diagram information and average values of
delay time, and stores the generated event information in the event
information storage 240 (Step_A). As an example, the event
information includes an identifier of a train line, an identifier
of a vehicle, identifiers of events (departure, arrival, pass, and
the like), information on times and places (stations or the like),
the average delay times (the average values of delay time), minimum
required time intervals, and the like.
[0098] The evaluation order determiner 515 sorts the event
information in chronological order (in order from an earliest time
to a latest time) (Step_B). A string of the sorted event
information is referred to as an event list.
[0099] The delay probability evaluator 520 repeats processing for
sequentially reading out the event information (assumed to be "N")
from a top of the event list (Step_C) and processing for
calculating a delay probability distribution for the read event
information N (Step_D) (NO in Step_E). When all the event
information stored in the event list has been processed (YES in
Step_E), the processing in the present flowchart is terminated.
Thus, the delay probability distribution is generated for each
event and stored in the event delay probability distribution
storage 300.
(Details of Step_A)
[0100] FIG. 19 shows a detailed flowchart of Step_A in FIG. 18.
FIG. 20 shows an example of the event information generated through
the processing in Step_A in the form of a table. FIG. 20
corresponds to the examples shown in FIGS. 4 and 5. The processing
in the flowchart in FIG. 19 will be described with reference to
FIG. 20.
[0101] In Step_A1, arrival, departure, and pass on each train line
in the diagram information are set as events. Moreover, a time is
set on each event based on the diagram information. The identifiers
(IDs) of the events 1 to 11 and the respective times of the events
are set in the table in FIG. 20. Other items in the table are set
through processing described below.
[0102] Each of the set events is selected in turn (in chronological
order), and Steps A2 to A4 described below are repeatedly performed
on the selected event as a target event. Note that although arrival
at, departure from, and pass through a station are regarded as
events here, an event may be set in a unit other than a station,
for example, in a unit of a closed section.
[0103] In Step_A2, it is determined, depending on a type of the
target event, whether or not early departure or the like (early
departure, early arrival, or early pass) is permissible to the
target event, and permissibility information indicating a
determined result is set on the target event. As an example, "True"
is set when the permissibility information is "permissible", and
"False" is set when the permissibility information is "not
permissible", but such settings are not restrictive. Early arrival
means that a train arrives earlier than a time of an arrival event.
Early pass means that a train passes earlier than a time of a pass
event. Early departure means that a train departs earlier than a
time of a departure event. In the present embodiment, it is
determined that early arrival and early pass are permissible and
that early departure is not permissible. It is determined here that
only early departure is not permissible, but such determinations
are not restrictive. When the target event is the event 1, the
event 1 is a departure event, and since early departure is not
permissible, "False" is set as the permissibility information.
[0104] In Step_A3, connection information of connection between the
target event and an event immediately preceding the target event on
the self train line (a train line to which the target event
belongs) is generated. The connection information includes an ID of
the event preceding the target event on the self train line (self
train line preceding event ID), a margin time from the preceding
event, and the average delay time of the target event. Hereinafter,
generation of the connection information will be described in
detail.
[0105] If the target event is a first event on the self train line
(for example, in case of the event 1 in FIG. 20), "-1" is set as
the self train line preceding event ID. In other cases, the event
ID of an event immediately preceding the target event on the self
train line is set as the self train line preceding event ID. For
example, since an event immediately preceding the event 2 on the
train line 1 is the event 1, "1" is set as the self train line
preceding event ID for the event 2.
[0106] A type (here, local/express) of the self train line is
determined, and based on a result of the determination, the margin
time from the immediately preceding event is calculated. For
example, the margin time is calculated as follows:
Margin time=(time difference between the target event and the
immediately preceding event in the diagram information)-(minimum
required time interval between the target event and the immediately
preceding event).
[0107] For example, for the margin time of the event 2, 2 is
obtained by subtracting the minimum required time interval between
the event 2 and the event 1 from a time difference between the
event 2 and the event 1 in the diagram information. Although the
margin time is obtained through calculation here, the margin time
may be input on the above-described input screen, and the input
information may be acquired. The minimum required time interval can
be specified by the minimum required time interval information,
depending on a type of the self train line.
[0108] Further, an average value of delay time (average delay time)
between the target event and the preceding event on the self train
line is set. In the example shown in the diagram, for the event 2,
2 is set as the average delay time between the event 2 and the
event 1.
[0109] In Step_A4, for the target event, connection information of
connection between the target event and a preceding event on the
preceding train line is generated. The connection information
includes an ID of the preceding event on the preceding train line
(preceding train line event ID) and the margin time from the
preceding event on the preceding train line.
[0110] If the target event is a departure event and if a preceding
train line exists, an arrival event, a pass event, or a departure
event at the same station as the station of the departure event is
identified from the preceding train line, and the identified event
is set as the preceding train line event ID. For example, if the
target event is the event 10 on the train line 3, the event 10 is a
departure event, and the preceding train line 2 exists as a train
line preceding the train line 3. Accordingly, the event 6, which is
a pass event at the same station as the station (B station) of the
event 10, is identified from the preceding train line 2. Although
the event at the same station on the preceding train line is set as
the preceding event here, such a setting is not restrictive. For
example, an event at a station that is passed through prior to the
same station may be set as the preceding event (the same is true
hereinafter).
[0111] If the target event is an arrival event and if a preceding
train line exists, a departure event, a pass event, or an arrival
event at the same station as the station of the arrival event is
identified from the preceding train line, and the identified event
is set as the preceding train line event ID. For example, if the
target event is event 7 on the train line 2, the event 7 is an
arrival event, and the preceding train line 1 exists as a train
line preceding the train line 2. Accordingly, the event 4, which is
a departure event at the same station as the station (C station) of
the event 7, is identified from the preceding train line 1.
[0112] If the target event is a pass event and if a preceding train
line exists, a departure event, a pass event, or an arrival event
at the same station as the station of the pass event is identified
from the preceding train line, and the identified event is set as
the preceding train line event ID. For example, if the target event
is the event 6 on the train line 2, the event 6 is a pass event,
and the preceding train line 1 exists as a train line preceding the
train line 2. Accordingly, the event 3, which is an arrival event
at the same station as the station (B station) of the event 6, is
identified from the preceding train line 1.
[0113] Note that since a train line preceding the train line 1 does
not exist, all of the respective preceding train line event IDs for
the events included in the train line 1 are set to a predetermined
value (here, "-1").
[0114] The preceding train line event IDs are set for departure,
arrival, and pass events on a train line that has the preceding
train line. However, the preceding train line event IDs may be set
for only one or two of arrival, departure, and pass. For example,
the preceding train line event IDs may be set only for departure
events. The preceding train line may be an immediately preceding
train line only, or a plurality of train lines may be specified as
preceding train lines.
[0115] When a preceding train line event ID of a value other than
"-1" is set for the target event, the margin time allowable between
the target event and the preceding event on the preceding train
line is calculated. For example, the margin time is calculated as
follows:
Margin time=(time difference between the target event and the
preceding event on the preceding train line in the diagram
information)-(minimum required time interval between the target
event and the preceding event on the preceding train line).
[0116] Thus, the event information on the target event is
generated. When the processing in Step_A2 to Step_A4 is completed
for each event set in Step_A1 (Step_A5), the event information on
all events is generated and stored in the event information storage
240. Thus, the processing in the present flowchart is
terminated.
(Regarding Step_B and Step_C)
[0117] In the processing in Step_B in FIG. 18, the evaluation order
determiner 515 performs topological sorting of the event
information. The topological sorting is such processing that any
event always comes after an event (preceding event) having an
earlier time than the any event. That is, the topological sorting
is processing to guarantee that when each event information is
processed in turn in Step_C and Step_D, event information on all
preceding events has been already processed before the current
event information is processed.
[0118] As the specific processing in Step_B, the evaluation order
determiner 515 only sorts the event information in chronological
order (in order of time in the table in FIG. 20). In Step_C, the
delay probability evaluator 520 only reads out the event
information in the sorted order. Accordingly, a further description
will be omitted.
[0119] FIG. 21 is a detailed flowchart of Step_D in FIG. 18. A
description will be given of processing for calculating an event
delay probability distribution for the event information read out
of the event list in Step_C (referred to as the event information
N). An event indicated by the event information N will be stated as
the event N. As an example, the event N corresponds to a first
event according to the present embodiment.
[0120] Note that for the probability distribution in each step
described below, a discrete probability distribution whose domain
is divided into a plurality of parts is assumed. The domain may
include a negative-value part. Here, as an example, a discrete
distribution in one-minute units with a range from -5 minutes to 15
minutes will mainly be considered. The range from -5 minutes to 15
minutes corresponds to a range of five minutes early arrival to a
delay of 15 minutes.
[0121] First, an outline of the flow in FIG. 21 will be described.
First, all events s preceding the event N are identified. As an
example, each event s corresponds to a second event according to
the present embodiment. For each event s, the convolution
calculator 521 performs delay probability convolution processing
(Step_D1), and the margin shifter 522 performs margin shift
processing (Step_D2). Thus, probability distributions of delay time
in the event N that are reached via the individual events s,
respectively, (delay probability distributions W(k)) are obtained.
Further, the combined probability calculator 523 combines the
probability distributions to obtain a combined probability
distribution Y(k) (Step_D3). Lastly, if the event N is prohibited
from taking place earlier than the time of the event N, the
round-up processor 524 performs round-up processing on the combined
probability distribution (Step_D4). For example, if the event N is
a departure event and early departure is prohibited, the round-up
processing is performed.
[0122] If the number of the events s (second events) preceding the
event N (first event) is one, performing of Step_D3 is omitted. If
the event N is permitted to take place earlier than the time of the
event N, performing of Step_D4 is omitted. In the present
embodiment, it is assumed that only departure events are prohibited
from taking place earlier than the times thereof (that is, early
departure is prohibited), and that arrival events and pass events
are not prohibited from taking place earlier than the times thereof
(early arrival and early pass).
[0123] Hereinafter, each step in FIG. 21 will be described in
detail.
[0124] FIG. 22 shows an outline of the processing in Step_D when
two events preceding the event N exist: a preceding event s
(assumed to be N1) on the self train line and a preceding event s
(assumed to be N2) on the preceding train line. As an example, if
the event N is the event 6, the event N1 is the event 5 and the
event N2 is the event 3.
[0125] In Step_D1, if a delay probability distribution (event delay
probability distribution) for the preceding event N1 on the self
train line is X.sub.1(i), and an event-to-event delay probability
distribution between the event N1 (second event) and the event N
(first event) is D(k), the convolution processing on the
distributions is performed through calculation using an equation
provided below. Thus, a delay probability distribution V.sub.1(k)
for the event N is obtained. As an example, V.sub.1(k) corresponds
to a first probability distribution according to the present
embodiment. As an example, X.sub.1(i) corresponds to a second event
delay probability distribution according to the present embodiment.
As an example, the event N corresponds to the first event according
to the present embodiment. As an example, the event N1 corresponds
to the second event according to the present embodiment.
[ Expression 2 ] V 1 ( k ) = i = min k X 1 ( i ) D ( k - i ) ( 2 )
##EQU00001##
[0126] X.sub.1(i) represents a probability that the delay time in
the preceding event N1 is "i". For example, X.sub.1(-1) represents
a probability that the delay time in the preceding event N1 is -1,
X.sub.1(0) represents a probability that the delay time in the
preceding event N1 is 0, X.sub.1(1) represents a probability that
the delay time in the preceding event N1 is 1, and X.sub.1(2)
represents a probability that the delay time in the preceding event
N1 is 2.
[0127] D(k-i) represents a probability that the delay time between
the preceding event N1 and the event N is "k-i". For example, D(0)
represents a probability that the delay time between the preceding
event N1 and the event N is 0, D(1) represents a probability that
the delay time between the preceding event N1 and the event N is 1,
and D(2) represents a probability that the delay time between the
preceding event N1 and the event N is 2.
[0128] V.sub.1(k) represents a probability that the delay time in
the event N is "k". For example, V.sub.1(-1) represents a
probability that the delay time in the event N is -1, V.sub.1(1)
represents a probability that the delay time in the event N is 1,
and V.sub.1(2) represents a probability that the delay time in the
event N is 2.
[0129] FIG. 23 shows a specific example of Step_D. Here, a case is
shown where the event N is the event 2 (arrival event). An event
preceding the event 2 is the event 1. No train line preceding the
self train line (train line 1) exists. The delay probability
distribution (X.sub.1(i)) for the preceding event 1 on the self
train line is shown at a top of FIG. 23 (same as the uppermost row
of the table in FIG. 16). If an event (here, the event 1) has no
preceding event, a predetermined initial distribution is given as
the delay probability distribution for the event. An example of the
initial distribution is a distribution indicating that no delay
occurs (the delay time is 0 with a probability of 1 (100%)). The
uppermost row of the table in FIG. 16 corresponds to such a
case.
[0130] It is assumed that the event-to-event delay probability
distribution between the event 2 and the event 1 is the equation
(1): D(k)=(1-p).sup.kp, where p=1/(x+1). "x" is an average value of
delay time between the event 2 and the event 1. The value of "x" is
2, identified from a row of "ID=2" of the table in FIG. 20.
Accordingly, p=1/(2+1)=1/3. Accordingly, the calculation of the
equation (2) results in the following equations.
V 1 ( 0 ) = i = - 5 0 X 1 ( i ) D ( 0 - i ) = X 1 ( 0 ) D ( 0 - 0 )
= 1 1 3 = 0.333 V 1 ( 1 ) = i = - 5 1 X 1 ( i ) D ( 1 - i ) = X 1 (
0 ) D ( 1 ) = 1 2 9 = 0.222 V 1 ( 2 ) = i = - 5 2 X 1 ( i ) D ( 2 -
i ) = X 1 ( 0 ) D ( 2 ) = 1 4 27 = 0.148 V 1 ( 3 ) = i = - 5 3 X 1
( i ) D ( 3 - i ) = X 1 ( 0 ) D ( 3 ) = 1 2 9 = 0.222 [ Expression
3 ] ##EQU00002##
[0131] Note that when i=0, X.sub.1(0)=1 (100%), and otherwise,
X.sub.1(i) results in 0 (see the table at the top of FIG. 23). When
"k=0, 1, 2, 3" and "p=1/3" are substituted into
"D(k)=(1-p).sup.kp", resultants are "D(0)=1/3", "D(1)=0.222",
"D(2)=0.148", and "D(3)=0.088".
[0132] Although calculation in case of "k=0, 1, 2, 3" is performed
here, calculation can be similarly performed in case of "k=-5 to
-1, 4 to 15". Thus, the delay probability distribution V.sub.1(k)
for the event N in case of "k=-5 to 15" is calculated. An example
of the calculated delay probability distribution is shown in the
middle of FIG. 23.
[0133] In Step_D2, assuming that the margin time is "Margin" or
"M", margin shift processing for shifting the probability
distribution V.sub.1(k) calculated in Step_D1 based on the margin
time is performed. An equation used in the margin shift processing
is shown below. Thus, a probability distribution W.sub.1(k)
subjected to margin shift is obtained. As an example, the
probability distribution W.sub.1(k) subjected to margin shift
corresponds to the first probability distribution shifted based on
the margin time according to the present embodiment. The value of
"Margin" is determined depending on the preceding event (see FIG.
20). In FIG. 22, the margin time from the preceding event N1 is
stated as "M1", and the margin time from the preceding event N2 is
stated as "M2".
[Expression 4]
W.sub.1(k)=V.sub.1(k+Margin) (3)
[0134] An example where margin shift is performed on the
probability distribution V.sub.1(k) shown in the middle of FIG. 23
will be illustrated. Since "Margin" is 2,
W.sub.1(1)=V.sub.1(1+2)=V.sub.1(3)=0.099 (9.9%). That is, the value
of "V.sub.1(3)=0.099 (9.9%)" is shifted to a time that is a time of
"Margin" (2 minutes) earlier.
[0135] Similarly, the following are calculated:
W.sub.1(0)=V.sub.1(0+2)=V.sub.1(2)=0.148 (14.8%);
W.sub.1(-1)=V.sub.1(-1+2)=V.sub.1(1)=0.222 (22.2%); and
W.sub.1(-2)=V.sub.1(-2+2)=V.sub.1(0)=0.333 (33.2%). A reason why
margin shift is performed in such a manner is that a delay within a
limit of "Margin" is allowable. The resultant probability
distribution W.sub.1(k) obtained by performing the margin shift of
V.sub.1(k) in FIG. 23 is shown at the bottom of FIG. 23.
[0136] Note that Step_D3 and Step_D4 are omitted because the number
of events preceding the event 2 is one (only the preceding event on
the self train line) and the preceding event is an arrival event
(not a departure event). Accordingly, the probability distribution
W(k) shown at the bottom of FIG. 23 is output as the event delay
probability distribution Y(k) for the event 2.
[0137] FIG. 24 shows another specific example of Step_D. An example
where the event N is the event 3 (departure event) is shown here.
The event N1 preceding the event 3 is the event 2. No train line
preceding the self train line (train line 1) exists. The delay
probability distribution (MD) for the preceding event 2 on the self
train line is shown at the top of FIG. 24. The delay probability
distribution (X.sub.1(i)) for the preceding event 2 corresponds to
the event delay probability distribution Y(k) obtained in Step_D
for the event 2 (same as the table at the bottom of FIG. 23).
[0138] In Step_D1 in FIG. 24, a convolution operation of the delay
probability distribution X.sub.1(i) (=Y(k)) for the preceding event
2 and the event-to-event delay probability distribution D.sub.1(k)
between the event 3 and the event 2 is performed according to the
equation (2). Thus, the delay probability distribution V.sub.1(k)
for the event N is obtained. The obtained probability distribution
V.sub.1(k) is shown in a second table from the top of FIG. 24.
Details of the convolution operation are described earlier and
therefore omitted.
[0139] In Step_D2, margin shift processing is performed on the
probability distribution V.sub.1(k) calculated in Step_D1 according
to the equation (3), whereby the probability distribution
W.sub.1(k) subjected to margin shift is obtained. The value of
"Margin" of the event 3 from the event 2 is 0 (see FIG. 20). The
probability distribution W.sub.1(k) subjected to margin shift is
shown in a third table from the top of FIG. 24. Details of the
margin shift processing are described earlier and therefore
omitted. Processing in Step_D4 in FIG. 24 will be described
later.
[0140] Next in Step_D3 in FIG. 22, if two or more events preceding
the event N exist, that is, if delays are influenced (or rippled)
from the two or more events to the event N, a combined probability
distribution Z(k) is generated by combining W.sub.i(k) calculated
for each preceding event i. More specifically, for example, if
preceding events 1 to h ("h" is an integer larger than 2) exist,
combinations of values of "k" (stochastic variable) among the
preceding events 1 to h are generated. If the number of the
preceding events is "h" and the number of possible values of "k" is
"g", "h.times.g" combinations are obtained. For each combination, a
product of W.sub.1(k) to W.sub.h(k) is calculated and a largest one
of the values of "k" is selected, whereby sets of the value of "k"
and the product are obtained. The obtained set are classified based
on the values of "k", and a plurality of groups as many as the
number of the values of "k" are obtained. The sets including a same
value of "k" belong to each group. A total sum of the products
included in the set is calculated for each set, and the value of
the total sum is obtained as a delay probability (combined
probability) for the value of "k" corresponding to the group. Thus,
the respective delay probabilities (combined probabilities) for the
values of "k" are obtained as a combined probability
distribution.
[0141] A specific example of the processing for generating the
combined probability distribution in Step_D will be described using
FIGS. 25(A) to 25(C). For simplicity, it is assumed that "k" takes
discrete values in one-minute units in a range of -1 to 2. The
number "h" of preceding events is assumed to be 2. The preceding
events are assumed to be a preceding event 1 and a preceding event
2.
[0142] FIG. 25(A) shows the probability distribution W.sub.1(k) for
the preceding event 1 and the probability distribution W.sub.2(k)
for the preceding event 2 individually.
[0143] FIG. 25(B) shows a table in which the values of "k" for the
preceding event 1 are shown as items horizontally, and the values
of "k" for the preceding event 2 are shown as items vertically. In
an upper side in each cell of the table, a largest one of the value
of "k" for the preceding event 1 and the value of "k" for the
preceding event 2 (if the values are the same, any one of the
values) is stored. In a lower side in each cell, a product of
"W.sub.1(k)" for the corresponding value of "k" for the preceding
event 1 and "W.sub.2(k)" for the corresponding value of "k" for the
preceding event 2 is stored. The product corresponds to an
occurrence probability if the preceding event 1 and the preceding
event 2 are independent of each other.
[0144] For example, in case of an uppermost right cell of the
table, the value of "k" for the preceding event 1 is 2, and the
value of "k" for the preceding event 2 is -1. Accordingly, "2",
which is a larger one of 2 and -1, is stored. Moreover, the delay
probability W.sub.1(2) for the preceding event 1 when the value of
"k" is 2 is 10%, and the delay probability W.sub.2(-1) for the
preceding event 2 when the value of "k" is -1 is 50%. Accordingly,
a product of the delay probabilities is obtained as
"10%.times.50%=5%". Accordingly, 5% is stored in the cell. In other
cells, a largest one of the values of "k" and a product are stored
similarly.
[0145] The cells of the table in FIG. 25(B) are classified into
groups of cells, each including a same value (largest value) of
"k", and a total sum of the products included in the cells is
calculated for each group. Thus, a delay probability is obtained
for each value of "k".
[0146] FIG. 25(C) shows a table in which the total sum is
calculated and stored for each value of "k". For example, an
example where the total sum is calculated when "k" is 2 will be
illustrated. First, cells including "2" are identified from the
table in FIG. 25(B). Eight cells in a rightmost column and in a
downmost row are identified. A total sum of the products (values in
the lower side) in the identified cells is calculated to obtain
"5+4+1+0+0+0+0+0=10%". Similarly, a total sum of 20% is obtained
when "k" is -1, a total sum of 43% is obtained when "k" is 0, and a
total sum of 27% is obtained when "k" is 1. Thus, the total sum
(delay probability) is obtained for each value of "k". A collection
(or set) of such total sums corresponds to the combined probability
distribution.
[0147] If only one preceding event exists in Step_D3 in FIG. 22,
the probability distribution W(k) for the preceding event is output
in Step_D3 as it is. For example, the probability distribution W(k)
for the event 2 shown at the bottom of FIG. 23 is output in Step_D3
as it is because only the event 1 is the event preceding the event
2.
[0148] If the number of preceding events is 0, a predetermined
initial distribution may be output in Step_D3. An example of the
initial distribution is a distribution indicating that no delay
occurs (the delay time is 0 with a probability of 1 (100%)), as
mentioned earlier.
[0149] In Step_D4, a type (departure, arrival, or pass) of the
event N is determined, and it is determined, depending on the type,
whether or not early departure, early arrival, or early pass is
prohibited. If no prohibition is laid, the combined probability
distribution W(k) for the event N calculated in Step_D3 is output
as the delay probability distribution Y(k) for the event N. If
prohibition is laid, round-up processing for rounding up a
probability for a negative-valued delay time is performed according
to an equation (4) provided below, and the combined probability
distribution subjected to round-up processing is output as the
delay probability distribution Y(k) for the event N. In the
round-up processing, all probabilities for negative-valued delay
times in the combined probability distribution are added to a
probability for a delay time of 0, and the probabilities for the
negative-valued delay times are changed to be 0.
[ Expression 5 ] Y ( k ) = 0 ( k < 0 ) Y ( k ) = i = min 0 W ( i
) ( k = 0 ) Y ( k ) = W ( k ) ( k > 0 ) ( 4 ) ##EQU00003##
[0150] FIG. 26 is a diagram for describing a specific example of
the round-up processing. The same table (combined probability
distribution) as in FIG. 25(C) is shown in an upper side of FIG.
26. The table includes a negative-valued delay time, which is -1,
and a probability for the delay time is 20%. Accordingly, 20% is
added (rounded up) to a probability of 43% for a delay time of 0.
The probability for "-1" is changed to 0%. Thus, as shown in a
lower side of FIG. 26, the probability for the delay time of 0
becomes 63%. In this manner, the combined probability distribution
is partially adjusted. The combined probability distribution after
the round-up processing is output as the delay probability
distribution Y(k) for the event N.
[0151] Here, a specific example of performing of Step_D4 in the
above-described example shown in FIG. 24 will be described. Since
the event 3 is a departure event (prohibited from early departure),
the round-up processing is performed on the probability
distribution W(k) for the event 3 obtained in Step_D2.
Probabilities of 17.1%, 19.4%, and 16.7% corresponding to "k=-1,
-2, -3", respectively, in the probability distribution W(k) are
added to 13.5% corresponding to "k=1" Accordingly, the probability
corresponding to "k=1" becomes 66.7%, and all the Respective
Probabilities Corresponding to "k=-1, -2, -3" Become 0. The
probability distribution obtained through the round-up processing
is shown at the bottom of FIG. 24. Such a probability distribution
is output as the delay probability distribution Y(k) for the event
3.
[0152] Through the processing as described above, a delay
probability distribution for each event as shown in FIG. 16 is
obtained eventually. In the above-described example, a case where
the number of preceding events is one or two is described. However,
the processing can be similarly performed if the number of
preceding events is three or larger. That is, the same is also true
when there are three or more propagation paths of delay.
[0153] Note that a description has been given of a scheme in which
a delay probability distribution for each event is obtained by
performing Step_C to Step_E only once for each node by propagating
a probability distribution(s). However, in the processing, the
probability distribution appears only as a distribution of delay
time from a preceding node. If the distribution is replaced with a
non-stochastic variable, the processing can be replaced with
simpler processing despite time-consuming repetition processing
being required.
[0154] For example, the processing in Step_D is simplified if one
delay time is generated from a probability distribution by using a
random number. Actually, if a delay time for each node is assumed
to be a non-stochastic variable, the convolution processing in
Step_D1 is modified to processing for adding a delay time generated
randomly using a random number for a current node to a delay time
(of a non-stochastic variable) at a preceding node. Step_D2 is
modified to processing for subtracting "Margin" from the delay time
obtained in Step_D1. Step_D3 is modified to processing for
selecting a largest value of the delay times at the preceding nodes
calculated in Step_D2. Step_D4 is modified to processing for
selecting a larger one of the delay time calculated in Step_D3 and
0.
[0155] As described above, when Step_D is performed once, one delay
time of a non-stochastic variable for an event under processing is
determined. Accordingly, one delay time for each node is obtained
by performing Step_C to Step_E once for each node. Thereafter, the
node information is initialized, and Step_C to Step_E are performed
once again for each node by using another random number, whereby a
delay time of a different value from the previous value for each
node can be obtained. Accordingly, a histogram of delay times for
all events can be created as a result by repeatedly performing
Step_C to Step_E. Accordingly, a delay probability distribution for
each event may be created from the histogram obtained by
repetitions.
[0156] In the above-described example, the targets are a plurality
of trains (a plurality of train lines), that is, delay probability
distributions for all the events included in the train lines are
generated (see FIG. 16). However, delay probability distributions
may be generated only for a part of trains or a part of stations
(for example, a terminal station, a junction station, and the
like). Delay probability distributions may be generated only for
trains or stations designated by a user. An output format of delay
probability distributions is not limited to the format shown in
FIG. 16.
[0157] FIG. 27 shows an example of an output table including delay
probability distributions generated through the processing
according to the above-described present embodiment, for a train
line of a train (here, a train of train number 0001) that departs
from S station (station of origin) and dwells at each of A station,
B station, C station, D station, E station, F station, G station,
and H station (terminal). The delay probability distribution for
each even is shown by using a discrete distribution in five-minute
units with a range of -10 minutes to 60 minutes. A 90% value
(percentile value) and an expected value of delay time in each
event are shown on a right side of the table. Calculation of the
90% value and the expected value is performed by the delay
probability evaluator 520.
[0158] In a station column, station names and down arrows
(hereinafter, arrows) are alternately stored. A row containing an
arrow corresponds to an arrival event at a station indicated by a
station name in a next row. A row containing a station name
corresponds to a departure event at the corresponding station.
[0159] For example, a low below the S station corresponds to an
arrival event at the A station, and the delay probability
distribution for the event is that the probability of a delay of
-10 minutes (the delay probability for 10 minute early arrival) is
0%, the probability of a delay of -5 minutes is 1%, the probability
of a delay of 0 minutes is 60%, the probability of a delay of 5
minutes is 28%, the probability of a delay of 10 minutes is 1%, the
probability of a delay of 15 minutes is 0%, and so on. The 90%
value for the delay probability distribution is 5 minutes, and the
expected value is 2 minutes. A row of the A station corresponds to
a departure event at the A station, and the delay probability
distribution for the event is that the probability of a delay of
-10 minutes (the delay probability for 10 minute early arrival) is
0%, the probability of a delay of -5 minutes is 0%, the probability
of a delay of 0 minutes is 75%, the probability of a delay of 5
minutes is 25%, the probability of a delay of 10 minutes is 0%, the
probability of a delay of 15 minutes is 0%, and so on. The 90%
value for the delay probability distribution is 5 minutes, and the
expected value is 2 minutes.
[0160] At the bottom of the table, an average value of the delay
probabilities for the arrival events (average delay probability for
run) and an average value of the delay probabilities for the
departure events (average delay probability for dwell) are shown
for each delay time. Calculation of such average values is
performed by the delay probability evaluator 520. Moreover, a
largest value of the 90% values of delay time in the arrival events
and a largest value of the 90% values of delay time in the
departure events are shown. An average value of the expected values
for the arrival events and an average value of the expected values
for the departure events are shown. Calculation of such largest
values and such average values of the expected values is performed
by the delay probability evaluator 520.
[0161] As described above, according to the present embodiment, the
delay probability distribution for arrival at, departure from, or
pass through each station can be generated from the diagram
information, without using historic data other than the
event-to-event delay probability distributions. Accordingly, big
historic data is not required. Moreover, according to the present
embodiment, creation of a frequency distribution through Monte
Carlo simulation can be eliminated, and rapid evaluation of the
diagram information is possible.
Modification Example 1
[0162] By giving a predetermined delay distribution to a certain
train and a certain station, probabilities of delay rippled to each
subsequent train and each subsequent station and expected delay
times may be calculated. The calculation is performed by the delay
probability evaluator 520. For the predetermined delay
distribution, for example, an extreme distribution that delays due
to an accident at a specific station or the like are supposed may
be used.
[0163] Statistical values such as probabilities of delays of X and
more minutes occurring at a terminal or midway station, an expected
value of delay time, a dispersion (variance) of delay time, and an
X-th percentile value of delay time may be calculated. The expected
value and X-th percentile value of delay time are described in FIG.
27.
Modification Example 2
[0164] In the embodiment described hereinabove, a delay probability
distribution for each event is generated as in FIG. 16. However,
the delay probability distributions may be combined with a source
diagram (planned train lines) to thereby create expected train
lines. The created expected train lines may be displayed on the
display 400. The creation of the expected train lines is performed
by the delay probability evaluator 520. The expected train lines
are train lines that are expected to be followed when the diagram
(planned train lines) is actually operated.
[0165] FIG. 28 shows an example of the creation of an expected
train line. An expected train line 32 is created by shifting
respective times of nodes 31a, 31b, 31c, 31d, and 31e on a planned
train line 31 by delay expected values 33a, 33b, 33c, 33d, and 33e,
respectively. That is, nodes 32a to 32e on the expected train line
32 are created by adding the delay expected values 33a to 33e to
the respective times of the nodes 31a to 31e on the planned train
line 31, respectively. The delay expected values 33a to 33e are
indicators indicating average delay times, and may be calculated
based on expected values, modes, medians or the like, of delay
probability distributions for the nodes 31a to 31e on the planned
train line 31.
Modification Example 3
[0166] Evaluation indicators for a diagram, such as punctuality,
quick-deliverability, and transportation capacity of the diagram,
may be created by using the expected train lines created in the
modification example 2. The creation of the evaluation indicators
is performed by the delay probability evaluator 520. The created
evaluation indicators may be displayed on the display 400.
[Punctuality]
[0167] An example of the indicator of punctuality is a delay
expected value rate. An example of calculation of the delay
expected value rate is shown below.
Delay expected value rate(%)=.SIGMA.(delay expected values between
corresponding nodes)/total number of nodes (5)
[0168] As shown by the equation (5), the delay expected value rate
is obtained by averaging the delay expected values between nodes on
an expected train line and corresponding nodes on a planned train
line by all nodes. In the above-described example shown in FIG. 28,
the delay expected value rate is calculated by dividing a sum of
the delay expected values 33a to 33e by the total number of the
nodes (=5).
[0169] Another example of the indicator of punctuality is a delay
limit excess probability.
[0170] FIG. 29 is a diagram for describing the delay limit excess
probability. A delay probability distribution for a certain node
and a location of a delay time N [minute] are shown. An example of
calculation of the delay limit excess probability in this case is
shown below.
Delay limit excess probability(%)=.SIGMA.(probabilities of delays
of N and more minutes occurring at a current node)/total number of
nodes (6)
[0171] As shown by the equation (6), the delay limit excess
probability is obtained by averaging probabilities of delays of N
and more minutes on an expected train line by all nodes. In the
above-described example shown in FIG. 28, probabilities of delays
of N and more minutes are calculated based on each of the delay
probability distributions for the nodes 31a to 31e and added up,
and the resultant sum is divided by the total number of the nodes
(=5), whereby the delay limit excess probability is calculated.
[0172] The delay limit excess probability is a significant
indicator to some railway companies because a penalty is incurred
if a delay of a predetermined time or longer occurs. Note that if
penalty amounts for delays of N and more minutes are predetermined
for a certain train or a certain station (or certain trains or
certain stations), an expected value of penalty amount may be
derived.
[0173] Note that in evaluation of punctuality, a mean may be
calculated only for a part of midway stations or a terminal
station. If statistical values on origin and destination stations
of passengers (OD: Origin Destination) are known, a mean per
passenger may be calculated. In the equations (5) and (6), a
divisor (the total number of nodes) is an example and is not
limited to the total number of nodes.
[0174] [Quick-Deliverability]
[0175] An example of the indicator of quick-deliverability is a
time duration required for an expected train line (an expected trip
time).
[0176] FIG. 30 shows an example of the expected trip time. The
expected trip time represents a time duration to from a start point
to a terminal point of an expected train line. Note that an average
velocity required from the start point to the terminal point of the
expected train line may be evaluated from "d/te" by using the
indicator of quick-deliverability and a total distance d tripped. A
mean of time durations for a plurality of train lines may be
evaluated. If the passenger ODs are known, a mean per passenger may
be evaluated.
[Transportation Capacity]
[0177] Examples of the indicator of transportation capacity include
(1) a train line rate at a specific station in a specific time
slot, (2) a train line rate at a specific time, and (3) an arrival
and departure rate at specific stations in a specific time
slot.
[0178] FIG. 31 is a diagram for describing the train line rate at a
specific station in a specific time slot. The train line rate at a
specific station in a specific time slot is a value obtained by
dividing the number of trains (the number of train lines) that
departs from and arrive at a certain station within a specified
time slot by a time length t of the time slot. An example of
calculation of the train line rate at a specific station in a
specific time slot is shown below.
Train line rate at a specific station in a specific time
slot=number of all train lines at the station in the time slot/t
(7)
[0179] FIG. 31 shows a case of calculating the train line rate at a
station X in a time slot from seven o'clock to nine o'clock. The
number of trains (the number of train lines) that pass through the
specific station from seven o'clock to nine o'clock is six. The
number of trains (the number of train lines) corresponds to the
number of nodes (circles) in FIG. 30. A higher train line rate
indicates a greater transportation capacity.
[0180] FIG. 32 is a diagram for describing the train line rate at a
specific time. The train line rate at a specific time is a value
obtained by dividing the number of trains (the number of train
lines) that are in operation at a certain time by a distance d from
a start point to a terminal point. An example of calculation of the
train line rate at a specific time is shown below.
Train line rate at a specific time=number of all train lines at the
specific time/d (8)
[0181] FIG. 32 shows a case of calculating the train line rate at 8
o'clock. The number of trains (the number of train lines) that are
in operation at 8 o'clock is three. The number of trains (the
number of train lines) corresponds to the number of nodes (circles)
in FIG. 32. A higher train line rate indicates a greater
transportation capacity.
[0182] FIG. 33 is a diagram for describing the arrival and
departure rate at specific stations in a specific time slot. The
arrival and departure rate at specific stations in a specific time
slot is a value obtained by dividing the number of arrivals and
departures at specific stations within a specific time slot by a
product of: a time length t of the specific time slot; and a
distance d of a range where the specific stations are located. An
example of calculation of the arrival and departure rate at
specific stations in a specific time slot is shown below.
Arrival and departure rate at specific stations in a specific time
slot=number of arrivals and departures at the specific stations in
the specific time slot/(t.times.d) (9)
[0183] In FIG. 33, the number of arrivals and departures at
specific stations (here, three stations including a start point, a
station X, and a terminal point) from 7 o'clock to 9 o'clock
corresponds to the number of all nodes (circles) within a hatched
area in FIG. 33. A higher arrival and departure rate indicates a
greater transportation capacity (convenience) because as the
arrival and departure rate is higher, occasions for passengers to
board and alight increase.
[0184] Note that in the description of the equations (7) to (9),
the number of nodes shown in FIGS. 31 to 33 may be replaced with
the number of passengers based on the number of seats or the
maximum number of passengers allowed in each train. Thus, the
passenger-based transportation capacity can be evaluated. If the
passenger ODs and a target value of the transportation capacity are
known, whether or not the transportation capacity reaches the
target value may be used as an evaluation indicator.
[0185] While certain embodiments have been described, these
embodiments have been presented by way of example only, and are not
intended to limit the scope of the inventions. Indeed, the novel
embodiments described herein may be embodied in a variety of other
forms; furthermore, various omissions, substitutions and changes in
the form of the embodiments described herein may be made without
departing from the spirit of the inventions. The accompanying
claims and their equivalents are intended to cover such forms or
modifications as would fall within the scope and spirit of the
inventions.
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