CN110807651A - Intercity railway passenger ticket time-sharing pricing method based on generalized cost function - Google Patents
Intercity railway passenger ticket time-sharing pricing method based on generalized cost function Download PDFInfo
- Publication number
- CN110807651A CN110807651A CN201910918238.5A CN201910918238A CN110807651A CN 110807651 A CN110807651 A CN 110807651A CN 201910918238 A CN201910918238 A CN 201910918238A CN 110807651 A CN110807651 A CN 110807651A
- Authority
- CN
- China
- Prior art keywords
- time
- passenger
- time period
- railway
- transportation
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
- 238000000034 method Methods 0.000 title claims abstract description 33
- 238000009826 distribution Methods 0.000 claims abstract description 30
- 239000002245 particle Substances 0.000 claims abstract description 28
- 239000000126 substance Substances 0.000 claims description 27
- 238000011084 recovery Methods 0.000 claims description 13
- 238000007667 floating Methods 0.000 claims description 11
- 238000012546 transfer Methods 0.000 claims description 7
- 230000008859 change Effects 0.000 claims description 5
- 238000013459 approach Methods 0.000 claims description 4
- 230000008569 process Effects 0.000 claims description 4
- 230000007547 defect Effects 0.000 abstract description 4
- 230000001105 regulatory effect Effects 0.000 abstract description 4
- 239000002699 waste material Substances 0.000 abstract description 2
- 238000005259 measurement Methods 0.000 description 11
- 230000000694 effects Effects 0.000 description 4
- 238000004364 calculation method Methods 0.000 description 3
- 238000010276 construction Methods 0.000 description 2
- 230000003247 decreasing effect Effects 0.000 description 2
- 238000011161 development Methods 0.000 description 2
- 238000004458 analytical method Methods 0.000 description 1
- 230000006399 behavior Effects 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 150000001875 compounds Chemical class 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 238000005188 flotation Methods 0.000 description 1
- 230000006872 improvement Effects 0.000 description 1
- 238000007726 management method Methods 0.000 description 1
- 230000009467 reduction Effects 0.000 description 1
- 238000011160 research Methods 0.000 description 1
- 231100000817 safety factor Toxicity 0.000 description 1
- 238000006467 substitution reaction Methods 0.000 description 1
- 238000009827 uniform distribution Methods 0.000 description 1
Images
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
- G06Q30/00—Commerce
- G06Q30/02—Marketing; Price estimation or determination; Fundraising
- G06Q30/0283—Price estimation or determination
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- G06N3/00—Computing arrangements based on biological models
- G06N3/004—Artificial life, i.e. computing arrangements simulating life
- G06N3/006—Artificial life, i.e. computing arrangements simulating life based on simulated virtual individual or collective life forms, e.g. social simulations or particle swarm optimisation [PSO]
-
- G06Q50/40—
Abstract
The invention provides an intercity railway passenger ticket time-sharing pricing method based on a generalized cost function, which belongs to the technical field of railway transportation service management, and is characterized in that an initial ticket price is set, a passenger flow balanced distribution model is constructed by taking the minimum generalized cost as a target, and a passenger travel time period and travel mode selection are determined; constructing a time-sharing pricing model which corresponds to a passenger trip time period and a trip mode and aims at maximizing railway income; and solving a passenger flow balanced distribution model and a time-sharing pricing model by adopting a method of combining a particle swarm algorithm with inertia and a Frank-wolfe algorithm to obtain a passenger ticket pricing result. The invention plays the role of ticket price in regulating and guiding passenger flow, the passenger flow in high peak time period is reduced to some extent, the passenger flow in each time period is priced more uniformly, the passenger flow in time-sharing pricing is more balanced, the defects of oversaturated passenger flow in high peak time period, too little passenger flow in low valley time period and transport energy waste are overcome, the traffic pressure is relieved, the inter-city railway transportation efficiency is improved, and the resource utilization rate is improved.
Description
Technical Field
The invention relates to the technical field of railway transportation service management, in particular to an intercity railway passenger ticket time-sharing pricing method based on a generalized cost function, which can transfer passenger flow in peak hours and relieve traffic pressure.
Background
The intercity railway plays an important role in intercity travel with the advantages of large transportation volume, high speed, high frequency, little pollution, comfortable riding environment and the like. But the problems of unbalanced daily passenger flow distribution, single ticket price and difficulty in regulating passenger flow through ticket price are increasingly obvious along with the development of intercity high-speed rails. The intercity high-speed rail serves intercity passenger flow, is influenced by factors such as social and economic development degree, urbanization degree and population quantity in a channel, and directly shows that the passenger flow has obvious passenger flow peak and passenger flow valley periods in one day, particularly in early peak periods from morning to noon along with factors such as holidays, commuting, going to and from school and the like. The passenger flow is large in peak hours, so that great pressure is brought to stations and trains, and partial passenger flow is possibly lost due to limited capacity of passengers in the time period preferred; and the passengers have low boarding rate in the low-ebb period of passenger flow, which causes a great deal of transportation waste.
Disclosure of Invention
The invention aims to provide an intercity railway passenger ticket time-sharing pricing method based on a generalized cost function, which transfers part of peak passenger flow or passenger flow in other transportation modes to a valley time by means of discounting in the valley time and appropriately increasing the price in the peak time, so as to solve at least one technical problem in the background technology.
In order to achieve the purpose, the invention adopts the following technical scheme:
the invention provides an intercity railway passenger ticket time-sharing pricing method based on a generalized cost function, which comprises the following flow steps:
step S110: setting an initial fare, constructing a passenger flow balanced distribution model by taking the minimum generalized cost as a target, and determining a passenger trip time period and trip mode selection;
step S120: constructing a time-sharing pricing model which corresponds to the travel time period and the travel mode of the passenger and aims at maximizing railway income;
step S130: and solving a passenger flow balanced distribution model and a time-sharing pricing model by adopting a method of combining a particle swarm algorithm with inertia and a Frank-wolfe algorithm to obtain a passenger ticket pricing result.
Preferably, the step S110 specifically includes:
the fare change of each passenger transport time interval causes the passenger transport volume to be transferred, so as to realize the goal of maximizing profits, and a fare floating proportion model of each time interval is determined:
wherein R (p) represents the operating profit of the intercity railway, N represents the set of intercity railway operating time periods, N represents the time period,
indicating the traffic volume of the railway at the nth time period,
representing upper decision variables, fare of intercity railways in the nth time period, crWhich represents a fixed cost for the passenger,
representing the number of open columns of the railway, C, in the nth time periodrRepresenting the fixed cost of the inter-city railway train;
the following constraints are satisfied:
wherein the content of the first and second substances,represents the upper limit of the ticket price of the intercity railway,
the original fare of the intercity railway is represented,
represents the intercity railway fare upper limit, N1Representing the set of intercity railway passenger flow peak-to-peak and valley-to-valley periods, N2Representing an intercity railway passenger flow peak hour set;
based on the first balance principle of Wardrop, intercity passenger flow is distributed to different transportation modes in each time period:
wherein the content of the first and second substances,representing the generalized cost of the nth time period and the kth transportation mode in the equilibrium state,
representing the generalized cost of the nth transportation mode and the kth transportation mode;
the travel cost of passengers in each transportation mode in each time period is minimum:
the following constraints are met:
the total number Q of passengers in the intercity passage is unchanged before and after time-sharing pricing:
maximum operational energy constraint: because the schedule of intercity railway and highway departure is fixed, the number of trains and the number of fixed members in each time interval are unchanged, and the passenger capacity in each time interval of a peak can not exceed the operation capacity:
non-negative constraints:
the economy, the rapidness, the convenience, the comfort, the reliability and the safety of different transportation modes at different time periods are integrated to determine a generalized cost functionThe following were used:
wherein the content of the first and second substances,respectively show the economic efficiency
Quickness and convenience
Convenience of use
Comfort feature
Reliability of
The weighting coefficients of the transport mode, namely the preference coefficients of the passengers going out at different time intervals to the economy, the rapidity, the convenience, the comfort and the reliability of the transport mode,
indicating security.
Preferably, the economic measure is the cost to be paid for one transportation, and the intercity railway fare is in an intercity transportation channel
And road fare
Is a factor in measuring economy:
wherein the content of the first and second substances,represents the fare for the nth time period of the kth mode of transportation,
the traffic volume in the nth time period of the kth transportation mode is shown, r is a railway transportation line, and h is a road transportation line.
Preferably, the shortcut measurement index is a time cost for completing one trip, and includes a running time and a connection time, and the connection time refers to a connection time between an inter-city traffic mode and an intra-station traffic time:
wherein, VotnRepresenting the time value of the traveler selecting the trip in the nth time period,
the selection of the nth time period, the arrival and departure transfer time of the passengers in the k transportation mode,indicating that the time for getting on and off the passengers in the nth time period and the kth transportation mode are selected,
indicating the travel time of the traveller selecting the nth time period and the kth mode of transportation.
Preferably, the convenience measurement index is the waiting time between the arrival of intercity passengers at a station and the departure of passengers on a train, and the value of the convenience measurement index is related to the average departure interval and the arrival rate of the passengers;
when the inter-city train departure interval is divided into a plurality of small interval sub-periods, the arrival process of passengers is approximately regarded as poisson distribution;
the ith passenger arrival time is tauiIs a random variable, inThe expected value of the sum of the waiting times of arriving passengers in time is:
time of arrival of passenger (τ)1,τ2,...τξ) Independently of each other, and in
The oral administration is uniformly distributed, therefore,
at a departure interval of a trainE [ tau ] of total waiting time of passengersi]The expected value is
Comprises the following steps:
combining the time value, the nth time period can be obtained, and the convenience of the kth transportation mode is as follows:
preferably, comfort is quantified in terms of the time required for a passenger to recover from fatigue, as a function of the time required for the passenger to recover from fatigue as follows:
the comfort is calculated as:
preferably, the reliability represents the punctual rate of a certain transportation mode, and the measure is the average delay time of a fixed transportation mode within a time period:
wherein the content of the first and second substances,
representing the average delay time of the nth time period and the kth transportation mode;
the safety measure is the accident rate:
Preferably, in step S120, the step of constructing a passenger ticket time-sharing pricing model includes:
decision variables
Influence the selection of the travel mode and the travel time interval of the passenger, and decide the passenger flow of various transport modes of variables
The fare decision is influenced, and the balance of the two parties is finally reached.
Preferably, the step S130 specifically includes:
firstly, substituting initial fare of each time period, solving a passenger flow balanced distribution model by utilizing a frank-wolfe algorithm, and substituting the obtained passenger flow into a fare floating proportion model to solve by utilizing a particle swarm algorithm; the iteration times are set, repeated iteration is carried out to continuously approach the optimal solution, and the algorithm steps are as follows:
step S141: initializing a particle swarm; generating a population size N, a position X of each particleiAnd train speed ViSetting the maximum iteration times Gen, and making i equal to 0; xiRepresenting the fare of each time period of the intercity railway;
step S142: positioning the population at XiSubstituting into a passenger flow balanced distribution model, and solving by using Frank-wolfe algorithm to obtain the current optimal fare
Optimal solution Y ofi *；Yi *The passenger flow of different transportation modes in each time period is represented;
step S143, if i is larger than or equal to Gen, the algorithm is terminated and output
And Yi *(ii) a Otherwise, go to step S144;
step S144: will be provided with
And Yi *Substituting into the floating proportion model of the fare to calculate XiAnd recording the individual and global optimal positions so far;
step S145: successively updating the particle positions to obtain new generation particle positions, Xi＝Xi+1(ii) a Let i be i +1, go to step S142.
The invention has the beneficial effects that: after the time-sharing pricing strategy is implemented, the regulating and guiding effects of the ticket price on the passenger flow are exerted to a certain extent, the passenger flow in the high peak time period is reduced to a certain extent, the passenger flow in each time period is priced more uniformly, the passenger flow in each time period is priced in a time-sharing manner to be more balanced, the defects that the passenger flow is supersaturated in the high peak time period and the passenger flow is too little in the low valley time period and the transport energy is wasted are overcome, the traffic pressure is relieved, the inter-city railway transportation efficiency is improved, and the resource utilization rate is improved.
Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
FIG. 1 is a flowchart of a method for solving a passenger ticket time-sharing pricing model by combining a particle swarm algorithm with inertial weight and a Frank-wolfe algorithm according to an embodiment of the present invention.
Fig. 2 is a flowchart of an algorithm for solving a lower-layer passenger flow equilibrium distribution model by using a frank-wolfe algorithm according to an embodiment of the present invention.
Detailed Description
The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
As used herein, the singular forms "a", "an", "the" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises" and/or "comprising," when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or modules, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, modules, and/or groups thereof.
It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the prior art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.
For the convenience of understanding of the embodiments of the present invention, the following description will be further explained by taking specific embodiments as examples with reference to the drawings, and the embodiments are not to be construed as limiting the embodiments of the present invention.
It will be understood by those of ordinary skill in the art that the figures are merely schematic representations of one embodiment and that the elements or devices in the figures are not necessarily required to practice the present invention.
Examples
As shown in fig. 1, an embodiment of the present invention provides a time-sharing pricing method for intercity railway tickets based on a generalized cost function, including the following steps:
step S110: setting an initial fare, constructing a passenger flow balanced distribution model by taking the minimum generalized cost as a target, and determining a passenger trip time period and trip mode selection;
step S120: constructing a time-sharing pricing model which corresponds to the travel time period and the travel mode of the passenger and aims at maximizing railway income;
step S130: and solving a passenger flow balanced distribution model and a time-sharing pricing model by adopting a method of combining a particle swarm algorithm with inertia and a Frank-wolfe algorithm to obtain a passenger ticket pricing result.
The step S110 specifically includes:
the fare change of each passenger transport time interval causes the passenger transport volume to be transferred, so as to realize the goal of maximizing profits, and a fare floating proportion model of each time interval is determined:
wherein R (p) represents the operating profit of the intercity railway, N represents the set of intercity railway operating time periods, N represents the time period,
indicating the traffic volume of the railway at the nth time period,representing upper decision variables, fare of intercity railways in the nth time period, crWhich represents a fixed cost for the passenger,
representing the number of open columns of the railway, C, in the nth time periodrRepresenting the fixed cost of the inter-city railway train;
the following constraints are satisfied:
wherein the content of the first and second substances,
represents the upper limit of the ticket price of the intercity railway,
the original fare of the intercity railway is represented,
represents the intercity railway fare upper limit, N1Representing the set of intercity railway passenger flow peak-to-peak and valley-to-valley periods, N2Representing an intercity railway passenger flow peak hour set;
based on the first balance principle of Wardrop, intercity passenger flow is distributed to different transportation modes in each time period:
wherein the content of the first and second substances,
representing the generalized cost of the nth time period and the kth transportation mode in the equilibrium state,
representing the generalized cost of the nth transportation mode and the kth transportation mode;
the travel cost of passengers in each transportation mode in each time period is minimum:
the following constraints are met:
the total number Q of passengers in the intercity passage is unchanged before and after time-sharing pricing:
maximum operational energy constraint: because the schedule of intercity railway and highway departure is fixed, the number of trains and the number of fixed members in each time interval are unchanged, and the passenger capacity in each time interval of a peak can not exceed the operation capacity:
non-negative constraints:
the economy, the rapidness, the convenience, the comfort, the reliability and the safety of different transportation modes at different time periods are integrated to determine a generalized cost function
The following were used:
wherein the content of the first and second substances,
respectively show the economic efficiency
Quickness and convenience
Convenience of use
Comfort feature
Reliability of
The weighting coefficients of the transport mode, namely the preference coefficients of the passengers going out at different time intervals to the economy, the rapidity, the convenience, the comfort and the reliability of the transport mode,indicating security.
The economic measure is the cost to be paid for a transport, and therefore, in intercity transport channels, intercity railway fares
And road fareIt becomes a major factor in measuring economy:
wherein the content of the first and second substances,
representing the fare for the nth time period of the kth mode of transportation,
the lower decision variable, the nth time interval, the passenger flow of the kth transportation mode, the railway transportation line and the h tableAnd (5) displaying a road transportation line.
The shortcut measurement index is time cost for completing one trip, and comprises running time and connection time, wherein the connection time refers to connection time between an inter-city traffic mode and an intra-city traffic mode and intra-station traffic time:
wherein, VotnRepresenting the time value of the traveler selecting the trip in the nth time period,
the selection of the nth time period, the arrival and departure transfer time of the passengers in the k transportation mode,
indicating that the time for getting on and off the passengers in the nth time period and the kth transportation mode are selected,
indicating the travel time of the traveller selecting the nth time period and the kth mode of transportation.
The convenience measurement index is the waiting time between the arrival of intercity passengers at a station and the departure of passengers taking a train, and the value of the convenience measurement index is related to the average departure interval and the arrival rate of the passengers;
when the inter-city train departure interval is divided into a plurality of small interval sub-periods, the arrival process of passengers can be approximately regarded as poisson distribution;
the ith passenger arrival time is tauiIs a random variable, in
The expected value of the sum of the waiting times of arriving passengers in time is:
time of arrival of passenger (τ)1,τ2,...τξ) Independently of each other, and in
The oral administration is uniformly distributed, therefore,
at a departure interval of a train
E [ tau ] of total waiting time of passengersi]The expected value is
Comprises the following steps:
combining the time value, the nth time period can be obtained, and the convenience of the kth transportation mode is as follows:
comfort can be quantified by the time required for a passenger to recover from fatigue, which can be calculated as follows:
wherein the content of the first and second substances,
representing the time of the passenger in the n-th mode of transportation, parameter αkRepresents travel time of the kth transportation mode
The time minimum recovery time is H/(1+ α), parameter βkThe recovery time per unit travel time is mild (h)-1) The larger the value is, the longer the fatigue recovery time is;
the comfort is calculated as:
the reliability represents the punctual rate of a certain transportation mode, and the measurement index is the average delay time of a fixed transportation mode in a time interval:
wherein the content of the first and second substances,
representing the average delay time of the nth time period and the kth transportation mode;
the safety measure is the accident rate:
wherein the content of the first and second substances,and gamma and lambda are undetermined coefficients, and represent the accident rate of the nth transportation mode and the kth transportation mode.
In step S120, the time-sharing pricing model of the passenger tickets is constructed as follows:
decision variables
Influence the selection of the travel mode and the travel time interval of the passenger, and decide the passenger flow of various transport modes of variables
The fare decision is influenced, and the balance of the two parties is finally reached.
The step S130 specifically includes:
firstly, substituting initial prices in each time period, solving a passenger flow balanced distribution model by utilizing a frank-wolfe algorithm, and substituting the obtained passenger flow into a ticket price floating proportion model to solve by utilizing a particle swarm algorithm; the iteration times are set, repeated iteration is carried out to continuously approach the optimal solution, and the algorithm steps are as follows:
step S141: initializing a particle swarm; generating a population size N, a position X of each particleiAnd train speed ViSetting the maximum iteration times Gen, and making i equal to 0; xiRepresenting the fare of each time period of the intercity railway;
step S142: positioning the population at XiSubstituting into a passenger flow balanced distribution model, and solving by using Frank-wolfe algorithm to obtain the current optimal fare
Optimal solution Y ofi *；Yi *The passenger flow of different transportation modes in each time period is represented;
step S143, if i is larger than or equal to Gen, the algorithm is terminated and output
And Yi *(ii) a Otherwise, go to step S144;
step S144: will be provided with
And Yi *Substituting into the floating proportion model of the fare to calculate XiAnd recording the individual and global optimal positions so far;
step S145: successively updating the particle positions to obtain new generation particle positions, Xi＝Xi+1(ii) a Let i be i +1, go to step S142.
Example 2
The embodiment 2 of the invention provides an intercity railway passenger ticket time-sharing pricing method based on a generalized cost function, which comprises the following flow steps:
step 1): and (4) model assumption.
Step 2): and establishing an upper layer planning model.
Step 3): and establishing a lower-layer planning model, which comprises a lower-layer user balance model and a generalized cost function construction part.
Step 4): and perfecting a time-sharing pricing double-layer model.
Step 5): and solving the double-layer planning model by using a method of combining a particle swarm algorithm with inertial weight and a Frank-wolfe algorithm.
The assumptions for model construction in step 1) include:
1) the passenger flow distribution in each time interval in one day is unbalanced, and the phenomena of peaks and valleys are obvious.
2) The total amount of passenger flow in the intercity passage is not changed and the passengers only select intercity railway and highway public transportation.
3) The intercity railway train schedule is fixed and the trains are dispatched evenly in each time period.
4) Each time period for arriving passengers follows an even distribution of different intensities.
5) The intercity railway connects two central cities without stopping in the midway.
6) Frequent price changes may reduce passenger satisfaction, resulting in the selection of other modes of transportation by some passengers. It is assumed that the period and number of passenger changes to intercity rail fares are within acceptable ranges and that the amount of passenger lost due to instability caused by fare flotation is not considered.
7) The travel passengers are completely rational, the passengers can always select the traffic mode with the minimum generalized cost per se to travel, and the final balanced flow distribution state can be achieved in the transportation channel.
8) The transport supply capacity in the tunnel is sufficient and greater than the total passenger demand.
In step 2): the goal of the upper level of planning is to maximize profits for intercity rail operators. The change of the fare of each time slot causes the transfer of the passenger capacity, so that the fare floating proportion of each time slot needs to be reasonably determined to realize the maximization of the profit.
The railway has certain public welfare and passengers have certain acceptance degree on fare floating, and the reduction and the improvement of the fare must be limited. The ticket price should be reasonably established by intercity railway operation enterprises considering both the cost and the market demand under the government macro regulation. In the model, the inter-city railway fare is properly adjusted up on the basis of the original fare in the peak period and properly decreased in the valley or peak-balancing period, and the inter-city railway fare does not exceed a certain range. Therefore, the constraint conditions of the upper-layer planning model are mainly the upper and lower limit constraints of the fare:
the step 3) comprises the following steps:
1) constructing a lower-layer user balance model:
the lower-layer planning model describes the selection behaviors of the departure time and the travel mode of the passengers. Based on the first balance principle of Wardrop, intercity passenger flow is distributed to different transportation modes in each time period:
in the formula:
the generalized cost of the kth transportation mode in the nth time period under the balanced state;
when the inter-city railway fare changes in a certain period, the original balance also changes, and further a new balance state of each period and transportation mode is generated: in all the selectable time periods of various transportation modes, the generalized travel cost of the transportation mode in a certain time period selected by the passenger is equal to and not more than the travel cost of the transportation mode in the unselected time period. Therefore, the objective function of the lower-layer planning is that the travel cost of passengers of each transportation mode in each time interval is minimum.
The constraints of the underlying plan are mainly three aspects:
1a) the total number Q of passengers in the intercity passage is not changed before and after time-sharing pricing.
2a) Maximum operational energy constraint: because the schedule of intercity railway and highway departure is fixed, the number of trains and the number of fixed members in each time interval are unchanged, and the passenger capacity can not exceed the operation capacity in each time interval of a peak.
Wherein the content of the first and second substances,representing the maximum capacity of the kth mode of transportation for the n time period.
3a) Non-negative constraints:
2) and (3) constructing a generalized cost function:
the generalized cost function describes the cost paid by passengers during travel, which is broadly defined as the sum of various factors that have an effect on travel [10]. The traditional generalized cost is an increasing function related to the amount of traffic. Generalized cost function
To pairThe derivative of (2) is greater than 0, the objective function is a convex function, and the constraint set is a convex set, so that the lower-layer planning model is a convex planning problem and has a unique solution.
Based on domestic and foreign research results, six service characteristics of economy, rapidness, convenience, comfort, reliability and safety in different time periods are considered, and a generalized cost function for intercity passengers is formulated
The details are as follows.
In the formula (I), the compound is shown in the specification,
representing service characteristic weight coefficients, namely preference coefficients of passengers going out at different time intervals on economy, rapidness, convenience, comfort, reliability and safety of transportation mode characteristics, and obtaining values of each index by performing questionnaire survey on the passengers at different time intervals;
and
when n is respectively expressed, the economy, the rapidness, the convenience, the comfort, the reliability and the safety of k traffic modes are respectively expressed, and the specific form and the calculation method are as follows.
1a) Economy of use
The economic measure of the passenger is the cost required to be paid for one-time transportation, and generally refers to the fare of a main transportation tool. Thus, in intercity transportation channels, intercity railway fares
And road fare
Becomes a major factor in measuring economy.
Wherein the content of the first and second substances,
indicating the nth time period, the kth mode of transportation fare,
indicating the nth time interval passenger flow of the kth transportation mode.
2a) Quickness and convenience
The measure of the quickness is the time cost for completing one trip, including the running time and the connection time. And intercity passengers do not have intermediate transfer conditions, and the connection time mainly refers to the connection time between an intercity traffic mode and an intra-city traffic mode and the intra-station traffic time.
In the formula: votn-selecting the time value (yuan/h) of the travelers in the nth time period;
Order toThe quickness of the kth transportation mode in the nth period can be expressed as follows:
3a) convenience of use
The passenger convenience measurement index is the waiting time between the arrival of intercity passengers at a station and the departure of passengers in a train, and the value of the passenger convenience measurement index is closely related to the average departure interval and the passenger arrival rate. When the inter-city train departure interval is divided into a plurality of small interval sub-periods, the arrival process of passengers can be approximately regarded as poisson distribution.And (3) parameters representing the distribution of arrival of k-th transport mode passengers at station poisson in the nth time period.Representing departure intervals of k transportation modes in n time periods;
the number of departure in the n periods and the k transportation modes is shown, and then the average passenger flow in the departure interval
Comprises the following steps:
the ith passenger arrival time is tauiIs a random variable, in
The expected value of the sum of the waiting times of arriving passengers in time is:
time of arrival of passenger (τ)1,τ2,…τξ) Independently of each other, and inThe oral administration is carried out from the uniform distribution,thus, it is possible to provide
At a departure interval of a train
Summation of waiting times of passengers
The expected value is
Comprises the following steps:
average number of passengers arriving
Obeying a Poisson distribution, τiIn that
Are uniformly distributed, therefore
In conclusion, according toAnd combined with equations (15) and (16) at a departure interval
The total expected value of passenger waiting time is:
combining the time value, the nth time period can be obtained, and the convenience of the kth transportation mode is as follows:
order to
In the nth period, the convenience of the kth transportation mode is simplified as follows:
4a) comfort feature
The comfort of the passenger mainly depends on the travel time of the train, software and hardware service facilities and the like, and according to documents, the comfort can be quantified by the time required by the passenger to recover the fatigue, and the index mainly depends on the travel time. The longer the general travel time is, the longer the time required by the passenger to recover the fatigue is, the poorer the comfort is, and otherwise, the comfort is good; on the other hand, the more crowded the train, the less comfortable, and conversely, the better comfortable. The time required for the passenger to recover from fatigue is as follows:
in the formula, H represents passenger limit fatigue recovery time (H);
representing the time of the passenger in the n-th mode of transportation, parameter αkRepresents travel time of the kth transportation mode
The time minimum recovery time is H/(1+ α), parameter βkThe recovery time per unit travel time is mild (h)-1) The larger the value is, the longer the fatigue recovery time is.
Thus, the comfort is calculated as:
order to
In the nth period, the comfort of the kth transportation mode is simplified as follows:
5a) reliability of
The reliability represents the stability of the service level of a certain transportation mode in a time period, the main index point rate is measured, and the measurement index is the average delay time of a fixed transportation mode in the time period. For an intercity railway, the punctuality rate is less influenced by the passenger flow volume, and the punctuality rate in each time period is higher, so that the reliability is higher; for a highway, the road surface is crowded in the peak period of passenger flow, vehicles cannot run at normal speed, and delay is easily caused.
In the formula:
-the average delay time of the kth transport mode in the nth time period.
Order to
In the nth period, the reliability of the kth transportation mode is simplified as follows:
6a) safety feature
The safety is also an important factor influencing the travel mode and travel time period selection of passengers, and the measurement index is the accident rate. Safety factors influencing inter-city railway operation mainly come from three aspects of people, machines and rings, and managers, operators, equipment facilities, natural environments and the like which are specific to different transportation modes are possible to become potential safety hazards of train operation. In addition, the potential safety hazards are different at different time periods. The probability of a security incident occurring to a mass flow during peak traffic hours is greater. On one hand, the loss of facility equipment is easily increased due to large passenger flow in the peak period, and the failure rate of the facility equipment is increased; on the other hand, accidents such as trampling and the like are easily caused by the congestion of getting on and off the bus in a large passenger flow. The large passenger flow is always one of the important contents of the emergency plan of the high-speed railway, so that the safety in different time periods is very necessary to be considered.
The accident rate is as follows:
wherein the content of the first and second substances,
and gamma and lambda are undetermined coefficients, and represent the accident rate of the nth transportation mode and the kth transportation mode.
By integrating the above six service characteristics, in the nth period, the generalized trip cost of the kth transportation mode is as follows:
the method for constructing the inter-city railway time-sharing pricing double-layer planning model based on the generalized cost function in the claim 1 is characterized in that in the step 4): the inter-city railway time-sharing pricing double-layer planning model in one day is as follows:
the inter-city railway time-sharing pricing problem can be regarded as a leader-follower problem. Under the premise that the fares of other transportation modes are not changed, the leader making the fares of intercity railways is a transportation enterprise, and followers are passengers in all time periods. The upper-level plan is a leader, and the decision variable is the fare of each time period
The leader influences the selection of the travel mode and the travel time period of the passenger through the fare. The lower-layer planning decision maker is a passenger, and the decision variable is the passenger flow of various transportation modes in each time intervalThe lower-layer passengers make selections under the decision of the upper-layer fare, and the selection of the lower-layer passengers further influences the decision of the upper-layer fare, so that the balance of the two parties is finally achieved.
Step 5): the method adopts a method of combining a particle swarm algorithm with inertial weight and a Frank-wolfe algorithm to solve a double-layer planning model, and the main idea is that initial prices of all time periods of upper-layer planning are substituted into the lower-layer planning, a Frank-wolfe algorithm is used for solving a lower-layer passenger flow balanced distribution model, and passenger flow obtained by the lower layer is substituted into the upper-layer planning and is solved by the particle swarm algorithm; and (4) setting iteration times, and repeatedly iterating the upper layer result and the lower layer result to continuously approach the optimal solution. The algorithm flow is shown in fig. 2, and the algorithm steps are as follows:
step 1: initializing the particle swarm. Generating a population size N, a position X of each particlei(fare for each time period of intercity railway) and velocity ViAnd setting the maximum iteration number Gen, and enabling i to be 0.
Step 2: positioning the population at XiSubstituting into the lower-layer plan, and solving by using Frank-wolfe algorithm to obtain the current optimal fare
Bottom mostYouyejie Yi *(traffic volume for each time interval of different transportation modes).
Step3, if i is larger than or equal to Gen, the algorithm is terminated and output
And Yi *(ii) a Otherwise, go to Step 4.
Step 4: mixing XiAnd Yi *Substituting into upper layer program to calculate XiAnd recording the individual and global optimal positions so far.
Step 5: successively updating the particle positions to obtain new generation particle positions, Xi＝Xi+1. Let i equal i +1, go to Step 2.
In order to verify the intercity railway time-sharing pricing model based on the passenger generalized travel cost and the application effect of the time-sharing pricing strategy in the actual situation, data calculation and analysis of the application effect are carried out on the Jingjin intercity railway. The method comprises the steps of dividing the operation time of the Jingjin intercity railway into 16 time periods, then supposing that passengers in the Jingjin intercity passenger transport channel can select two transportation modes of the intercity railway and the highway, then investigating the preference weight of the passengers on each attribute of the transportation modes in the form of questionnaires, calculating the time value of the passengers in different time periods, and obtaining an upper-layer objective function railway income convergence map and a lower-layer objective function passenger generalized expense convergence map by referring to the delay of the intercity railway and the highway in each time period, the safety value of the city railway and the highway in each time period and using MATLAB programming calculation by using a particle. As the number of iterations increases, the optimal solution and the objective function value will change continuously; however, when the iteration number reaches a certain value, the optimal solution and the objective function are stable, which indicates that the convergence state is reached. When iterated 60 times, the model converges gradually. The upper layer target is gradually increased, the lower layer target is gradually decreased, and after the time-sharing pricing strategy is implemented, the passenger flow volume in the peak time period is still larger, but is reduced to some extent on the original basis. The passenger flow in each time period is priced more uniformly, the passenger flow in each time period is priced more uniformly in a time-sharing manner, and the defects that the passenger flow is supersaturated in the peak time period, the passenger flow is too little in the low ebb time period and the transport energy is wasted are overcome. After the time-sharing pricing strategy is implemented, the regulation and guidance functions of the ticket price on the passenger flow are exerted to a certain extent.
In summary, the method provided by the embodiment of the invention plays a role in regulating and guiding the passenger flow by the fare to a certain extent, the passenger flow in the high peak time period is reduced, the passenger flow in each time period is priced more uniformly in a time-sharing manner, the defects that the passenger flow is supersaturated in the high peak time period, the passenger flow in the low valley time period is too little, and the transport energy is wasted are overcome, the traffic pressure is relieved, the transport efficiency of the intercity railway is improved, and the resource utilization rate is improved.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (10)
1. A intercity railway passenger ticket time-sharing pricing method based on a generalized cost function is characterized by comprising the following flow steps:
step S110: setting an initial fare, constructing a passenger flow balanced distribution model by taking the minimum generalized cost as a target, and determining a passenger trip time period and trip mode selection;
step S120: constructing a time-sharing pricing model which corresponds to the travel time period and the travel mode of the passenger and aims at maximizing railway income;
step S130: and solving a passenger flow balanced distribution model and a time-sharing pricing model by adopting a method of combining a particle swarm algorithm with inertia and a Frank-wolfe algorithm to obtain a passenger ticket pricing result.
2. The inter-city railway passenger ticket time-sharing pricing method based on the generalized cost function of claim 1, wherein in the step S110, the constructed passenger flow equilibrium distribution model specifically comprises:
the fare change of each passenger transport time interval causes the passenger transport volume to be transferred, so as to realize the goal of maximizing profits, and a fare floating proportion model of each time interval is determined:
wherein R (p) represents the operating profit of the intercity railway, N represents the set of intercity railway operating time periods, N represents the time period,
indicating the traffic volume of the railway at the nth time period,
representing upper decision variables, fare of intercity railways in the nth time period, crWhich represents a fixed cost for the passenger,
representing the number of open columns of the railway, C, in the nth time periodrRepresenting the fixed cost of the inter-city railway train;
the following constraints are satisfied:
wherein the content of the first and second substances,
represents the upper limit of the ticket price of the intercity railway,
the original fare of the intercity railway is represented,
represents the intercity railway fare upper limit, N1Representing the set of intercity railway passenger flow peak-to-peak and valley-to-valley periods, N2Representing an intercity railway passenger flow peak hour set;
based on the first balance principle of Wardrop, intercity passenger flow is distributed to different transportation modes in each time period:
wherein the content of the first and second substances,
representing the generalized cost of the nth time period and the kth transportation mode in the equilibrium state,representing the generalized cost of the nth transportation mode.
3. The inter-city railway ticket time-sharing pricing method based on the generalized cost function of claim 2, characterized in that,
the travel cost of passengers in each transportation mode in each time period is minimum:
the following constraints are met:
the total number Q of passengers in the intercity passage is unchanged before and after time-sharing pricing:
maximum operational energy constraint: because the schedule of intercity railway and highway departure is fixed, the number of trains and the number of fixed members in each time interval are unchanged, and the passenger capacity in each time interval of a peak can not exceed the operation capacity:
non-negative constraints:
the economy, the rapidness, the convenience, the comfort, the reliability and the safety of different transportation modes at different time periods are integrated to determine a generalized cost function
The following were used:
wherein the content of the first and second substances,respectively show the economic efficiency
Quickness and convenience
Convenience of use
Comfort feature
Reliability of
The weighting coefficients of the transport mode, namely the preference coefficients of the passengers going out at different time intervals to the economy, the rapidity, the convenience, the comfort and the reliability of the transport mode,
means for indicating anAnd (4) completeness.
4. The generalized cost function-based intercity railway ticket time-sharing pricing method according to claim 3, wherein the economic measure is a cost to be paid for one transportation, and the intercity railway ticket price is in an intercity transportation channel
And road fare
Is a factor in measuring economy:
wherein the content of the first and second substances,
represents the fare for the nth time period of the kth mode of transportation,
the traffic volume in the nth time period of the kth transportation mode is shown, r is a railway transportation line, and h is a road transportation line.
5. The generalized cost function-based inter-city railway passenger ticket time-sharing pricing method according to claim 4, wherein the measure of the quickness is a time cost for completing one trip, and the measure of the quickness comprises a running time and a connection time, and the connection time refers to a connection time between an inter-city traffic mode and an intra-station traffic time:
wherein, VotnRepresenting the time value of the traveler selecting the trip in the nth time period,
the selection of the nth time period, the arrival and departure transfer time of the passengers in the k transportation mode,
indicating that the time for getting on and off the passengers in the nth time period and the kth transportation mode are selected,
indicating the travel time of the traveller selecting the nth time period and the kth mode of transportation.
6. The inter-city railway passenger ticket time-sharing pricing method based on the generalized cost function of claim 5, characterized in that the convenience measure is the waiting time from the arrival of inter-city passengers at a station to the departure of a passenger train, and the value of the convenience measure is related to the average departure interval and the passenger arrival rate;
when the inter-city train departure interval is divided into a plurality of small interval sub-periods, the arrival process of passengers is approximately regarded as poisson distribution;
the ith passenger arrival time is tauiIs a random variable, in
The expected value of the sum of the waiting times of arriving passengers in time is:
time of arrival of passenger (τ)1,τ2,...τξ) Independently of each other, and inThe oral administration is uniformly distributed, therefore,
at a departure interval of a train
E [ tau ] of total waiting time of passengersi]The expected value is
Comprises the following steps:
combining the time value, the nth time period can be obtained, and the convenience of the kth transportation mode is as follows:
7. the inter-city railway ticket time-sharing pricing method based on the generalized cost function of claim 6, wherein the comfort is quantified by the time required for the passenger to recover from fatigue, and the time function required for the passenger to recover from fatigue is as follows:
the comfort is calculated as:
8. the inter-city railway ticket time-sharing pricing method based on the generalized cost function of claim 7, wherein the reliability represents a punctual rate of a certain transportation mode, and the measure index is an average delay time of a fixed transportation mode in a time period:
wherein the content of the first and second substances,
representing the average delay time of the nth time period and the kth transportation mode;
the safety measure is the accident rate:
9. The inter-city railway passenger ticket time-sharing pricing method based on the generalized cost function of claim 8, wherein in the step S120, the passenger ticket time-sharing pricing model is constructed as follows:
decision variables
Influence the selection of the travel mode and the travel time interval of the passenger, and decide the passenger flow of various transport modes of variables
The fare decision is influenced, and the balance of the two parties is finally reached.
10. The inter-city railway ticket time-sharing pricing method based on the generalized cost function of claim 9, wherein the step S130 specifically comprises:
firstly, substituting initial fare of each time period, solving a passenger flow balanced distribution model by utilizing a frank-wolfe algorithm, and substituting the obtained passenger flow into a fare floating proportion model to solve by utilizing a particle swarm algorithm; the iteration times are set, repeated iteration is carried out to continuously approach the optimal solution, and the algorithm steps are as follows:
step S141: initializing a particle swarm; generating a population size N, a position X of each particleiAnd train speed ViSetting the maximum iteration times Gen, and making i equal to 0; xiRepresenting the fare of each time period of the intercity railway;
step S142: positioning the population at XiSubstituting into a passenger flow balanced distribution model, and solving by using Frank-wolfe algorithm to obtain the current optimal fare
Optimal solution Y ofi *；Yi *The passenger flow of different transportation modes in each time period is represented;
step S143, if i is larger than or equal to Gen, the algorithm is terminated and output
And Yi *(ii) a Otherwise, go to step S144;
step S144: will be provided with
And Yi *Substituting into the floating proportion model of the fare to calculate XiAnd recording the individual and global optimal positions so far;
step S145: successively updating the particle positions to obtain new generation particle positions, Xi＝Xi+1(ii) a Let i be i +1, go to step S142.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910918238.5A CN110807651A (en) | 2019-09-26 | 2019-09-26 | Intercity railway passenger ticket time-sharing pricing method based on generalized cost function |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910918238.5A CN110807651A (en) | 2019-09-26 | 2019-09-26 | Intercity railway passenger ticket time-sharing pricing method based on generalized cost function |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN110807651A true CN110807651A (en) | 2020-02-18 |
Family
ID=69487732
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201910918238.5A Pending CN110807651A (en) | 2019-09-26 | 2019-09-26 | Intercity railway passenger ticket time-sharing pricing method based on generalized cost function |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN110807651A (en) |
Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111582918A (en) * | 2020-04-24 | 2020-08-25 | 海南太美航空股份有限公司 | Flight profit prediction method and system |
| CN112529288A (en) * | 2020-12-10 | 2021-03-19 | 五邑大学 | Multi-train differential pricing strategy optimization method and system |
| CN112633940A (en) * | 2020-12-30 | 2021-04-09 | 北京交通大学 | Demand response type urban rail transit time-of-use fare formulation method |
| CN112950015A (en) * | 2021-02-25 | 2021-06-11 | 武汉大学 | Railway ticket amount pre-classifying method based on self-adaptive learning rate particle swarm optimization |
| CN113743987A (en) * | 2021-08-25 | 2021-12-03 | 东南大学 | Passenger transport mode shift and ticket price making method based on air-rail link |
| CN114923497A (en) * | 2022-04-21 | 2022-08-19 | 西南交通大学 | Method, device, equipment and storage medium for planning railway trip path |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108334996A (en) * | 2018-04-04 | 2018-07-27 | 深圳市创艺工业技术有限公司 | A kind of Passenger Flow analysis system based on big data |
| CN109409955A (en) * | 2018-10-24 | 2019-03-01 | 天津市市政工程设计研究院 | Timesharing customizes public transport fares formulating method by stages under changes in demand |
-
2019
- 2019-09-26 CN CN201910918238.5A patent/CN110807651A/en active Pending
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108334996A (en) * | 2018-04-04 | 2018-07-27 | 深圳市创艺工业技术有限公司 | A kind of Passenger Flow analysis system based on big data |
| CN109409955A (en) * | 2018-10-24 | 2019-03-01 | 天津市市政工程设计研究院 | Timesharing customizes public transport fares formulating method by stages under changes in demand |
Cited By (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111582918A (en) * | 2020-04-24 | 2020-08-25 | 海南太美航空股份有限公司 | Flight profit prediction method and system |
| CN111582918B (en) * | 2020-04-24 | 2023-07-25 | 海南太美航空股份有限公司 | Flight profit prediction method and system |
| CN112529288A (en) * | 2020-12-10 | 2021-03-19 | 五邑大学 | Multi-train differential pricing strategy optimization method and system |
| CN112529288B (en) * | 2020-12-10 | 2023-10-24 | 五邑大学 | Multi-train differentiated pricing strategy optimization method and system |
| CN112633940A (en) * | 2020-12-30 | 2021-04-09 | 北京交通大学 | Demand response type urban rail transit time-of-use fare formulation method |
| CN112950015A (en) * | 2021-02-25 | 2021-06-11 | 武汉大学 | Railway ticket amount pre-classifying method based on self-adaptive learning rate particle swarm optimization |
| CN112950015B (en) * | 2021-02-25 | 2022-06-14 | 武汉大学 | Railway ticket amount pre-classifying method based on self-adaptive learning rate particle swarm optimization |
| CN113743987A (en) * | 2021-08-25 | 2021-12-03 | 东南大学 | Passenger transport mode shift and ticket price making method based on air-rail link |
| CN114923497A (en) * | 2022-04-21 | 2022-08-19 | 西南交通大学 | Method, device, equipment and storage medium for planning railway trip path |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN110807651A (en) | Intercity railway passenger ticket time-sharing pricing method based on generalized cost function | |
| Li et al. | Fifty years of the bottleneck model: A bibliometric review and future research directions | |
| Downward et al. | Tourism transport and visitor spending: A study in the North York Moors National Park, UK | |
| Li et al. | Transit technology investment and selection under urban population volatility: A real option perspective | |
| Wilson et al. | The potential impact of automated data collection systems on urban public transport planning. | |
| CN105930914A (en) | City bus optimal charging structure charge determination method based on origin-destination distance | |
| Yang et al. | Multi-mode public transit OD prediction and scheduling model | |
| Liu et al. | A queuing network simulation optimization method for coordination control of passenger flow in urban rail transit stations | |
| Yin et al. | Optimum equilibrium passenger flow control strategies with delay penalty functions under oversaturated condition on urban rail transit | |
| Zheng et al. | Ticket fare optimization for China’s high-speed railway based on passenger choice behavior | |
| Niu et al. | An optimization to schedule train operations with phase-regular framework for intercity rail lines | |
| Hu et al. | Robust metro train scheduling integrated with skip-stop pattern and passenger flow control strategy under uncertain passenger demands | |
| Wei et al. | A two-layer network dynamic congestion pricing based on macroscopic fundamental diagram | |
| Wang et al. | A simulation-based metro train scheduling optimization incorporating multimodal coordination and flexible routing plans | |
| Lee et al. | A smart city transportation system of systems governance framework: a case study of Singapore | |
| Lu et al. | Demand-responsive transport for students in rural areas: A case study in vulkaneifel, germany | |
| CN112529288A (en) | Multi-train differential pricing strategy optimization method and system | |
| Dikas et al. | Scheduled paratransit transport enhanced by accessible taxis | |
| Luo et al. | Regression model for daily passenger volume of high-speed railway line under capacity constraint | |
| Rusca et al. | Algorithm for traffic allocation when are developed park and ride facilities | |
| Willumsen | Urban traffic modelling with limited data | |
| Kumazawa et al. | A novel train rescheduling algorithm for correcting disrupted train operations in a dense urban environment | |
| Hau et al. | An estimation of efficient time-varying tolls for cross harbor tunnels in Hong Kong | |
| Yong et al. | Capacity design and pareto improvement of highway toll plaza in a competitive transport system | |
| Mekky | Toll revenue and traffic study of highway 407 in Toronto |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| RJ01 | Rejection of invention patent application after publication |
Application publication date: 20200218 |
|
| RJ01 | Rejection of invention patent application after publication |