A public transit network differs from a general road network. The passenger flow of bus stops and the limited capacity of buses have a greater effect than road traffic flow on the running time of buses. As a result, conventional public transit assignment models that adopt the econometric road network path concept have numerous limitations. Based on the analysis, the generalized bus trip time chain is analyzed, and the concept of a congestion function is proposed to describe the relationship between trip resistance and flow in the current paper. On the premise of this study, the transit network resistance function is formed and the multiroute probit-based loading model is established. With using STOCH or Dial's algorithm, the process of distribution is proposed. Finally, the model is applied to the transit network assignment of Deqing Town in Zhejiang Province. The result indicates that the model can be applied to practical operations with high-precision results.
Public transit passenger flow distribution is the core of public transit network planning. A great deal of research has been conducted on this subject over the past 30 years. Daganzo and Sheffi proposed the probit-based distribution model [
The conventional models of public transit assignment adopt the road impedance function to reflect the relationship between traffic flow and road impedance, which is called road impedance renovation. However, the route congestion effects of the public transit network are primarily reflected in bus stops, that is, the trip time between the two stops has little correlation with the variety of the route flow [
The detailed choosing behavior of passengers then progresses as follows: if the first expected bus is overly crowded, the next bus or another route will be selected. Based on this premise, the congestion function is proposed. Integrating with the study of the public transit trip time chain, the multiroute probit-based loading model is established, and the algorithm is analyzed.
To address the aforementioned issues, the present study focuses on the following: analyze bus trip time chain and propose congestion function based on bus stop; establish multiroute probit-based loading model and analyze the algorithm; Investigate the operational performance of the model through five bus routes assignments of Deqing Town in Zhejiang Province.
The most important step in public transit assignment is to confirm the selected path’s traffic impedance. Public transit network impedance refers to the comprehensive expense guideline for trip time (including out-vehicle time), fees, and convenience (transfer rate) in a given public transit network, which is the rationale behind passenger selection of public transport.
As shown in Figure
Sketch map of generalized public transit network between sections
In the course of the bus trip, generalized trip time
Given that different parts of the bus trip chain have different values,
Walking time
The bus route
Sketch map of bus trip route
In reviewing the single bus route
Based on the analysis of the sectional passenger flow
Therefore, considering single route
The selection behavior of passengers is a variable factor. Passengers typically prefer the optimal route in terms of service frequency, service quality, and service costs. Considering the vehicle and passenger arrival distribution and economical situation based on probability, the route with the higher service frequency can attract more passengers. On the other hand, the degree of congestion in the vehicle affects the passengers’ choice of trip route. Thus, the user (passenger) equilibrium concept in the bus route differs from the user (vehicle) equilibrium concept. The latter reflects the equilibrium in travel time, given that travel time varies with the degree of road congestion. The former reflects the equilibrium of congestion degree in the vehicle aside from the equilibrium of travel time, given that the degree of congestion has less influence on travel time.
The multiroute probit-based loading model is proposed based on the following premises: assuming that a group of passengers is sent out from point of origin
The chosen bus multiroute probit-based distribution model is constructed in the following:
In the process of distribution, the capacity constrained distribution model of capacity constrained-increment loading is integrated as a contributing factor. The former OD table is initially decomposed into
Multi-route probit-based loading model flow chart.
After the calculations, little difference is found between the calculated and experience values
This paper takes several parts of the urban area of Deqing Town in Zhejiang Province as an example to investigate the operational performance of the model. The sketch map and the five bus routes are shown in Figure
Sketch map of computation example.
Take the Route 1 bus passenger flow as an example to explain the model application. Route 1 has the length 10.2 km, with a total of 17 stops, respectively, for the Guangming Road, Shishan Road, Lijin Hotel, Xixin Bridge, Ruijin Hospital, Southern Mall, Cooperation
The surveyed public transit OD data based on stops of Route 1.
OD | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 0 | 0 | 1 | 2 | 1 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
2 | 0 | 0 | 3 | 3 | 2 | 4 | 1 | 2 | 2 | 1 | 1 | 2 | 1 | 1 | 1 | 0 | 0 |
3 | 0 | 0 | 2 | 2 | 6 | 5 | 11 | 3 | 4 | 2 | 2 | 5 | 4 | 3 | 2 | 0 | 1 |
4 | 0 | 0 | 0 | 0 | 2 | 1 | 3 | 1 | 2 | 1 | 2 | 4 | 4 | 3 | 3 | 1 | 1 |
5 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 1 | 1 | 1 | 1 | 3 | 3 | 4 | 3 | 1 | 1 |
6 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 4 | 5 | 6 | 6 | 2 | 3 |
7 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 2 | 8 | 12 | 14 | 14 | 7 | 6 |
8 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 3 | 3 | 7 | 7 | 5 | 7 |
9 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 3 | 4 | 7 | 4 | 7 |
10 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 3 | 6 | 10 | 7 | 12 |
11 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 2 | 2 | 4 |
12 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 2 | 3 | 2 | 7 |
13 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 3 | 2 | 3 |
14 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 1 | 5 |
15 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
16 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
17 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
The route section flow of assignments results and surveyed data of Route 1.
Stop code | Stop name | Route section flow of assignments results | Surveyed section flow |
---|---|---|---|
1 | Guangming Road | 1 | 1 |
2 | Shishan Road | 5 | 6 |
3 | Lijin Hotel | 13 | 16 |
4 | Xixin Bridge | 17 | 19 |
5 | Ruijin Hospital | 19 | 21 |
6 | Southern Mall | 22 | 24 |
7 | Cooperation Bank | 29 | 28 |
8 | Dianzi Village | 33 | 34 |
9 | Telecom Building | 35 | 36 |
10 | Lanling Hotel | 40 | 41 |
11 | Pudong New Village | 40 | 42 |
12 | Qinliag Village | 37 | 38 |
13 | Nanping Street | 32 | 30 |
14 | Zhiyuan Road | 25 | 26 |
15 | Changhong Street | 15 | 14 |
16 | Changan Road | 9 | 8 |
Comparison among the assignments results and field data of Route 1.
From the comparisons shown in Table As the section flow increases, the assignments results will fluctuate within a certain range from the filed survey data, which is more or less related to the stochastic nature of public transit flow. However, the general tendencies of field data and calculation results are all the same, showing that assignments results can reflect the change of the section flow. When the section flow is between bus stops 10 and 11, the section flow has the maximal value and assignments results also get the maximal value. The assignments results are good representative of actual filed data.
Maximal route section flow is an effective index to evaluate the OD assignment results. After loading the OD table onto the public transit network, the maximal route section flow assignments results can be obtained. The comparison of maximal route section flow among the assignments results and field survey data is shown in Table
Comparison of maximal route section flow.
Route | Maximal route section flow of assignments results | Actual maximal section route flow | Discrepancy percentage |
---|---|---|---|
1 | 7379 | 7580 | 2.7% |
2 | 17048 | 18344 | 7.1% |
3 | 30220 | 32821 | 7.9% |
4 | 15440 | 14374 | 7.4% |
5 | 37880 | 36743 | 3.1% |
According to the field survey data and computation results, the model is capable of estimating the maximum route section flow based on the OD table. The percentage of the difference between the maximal route section flow of assignments results and actual section route flow is less than 10%.
This paper highlights the limitations of the equilibrium assignment model in practical applications based on an analysis of the conventional equilibrium assignment model of the public transit network. The multiroute probit-based distribution model is established, and the multiroute capacity-constrained nonequilibrium algorithm is analyzed. The model was applied to the transit network assignment of Deqing with satisfactory results.
The current work is supported by the Zhejiang Provincial Natural Science Foundation of China (no. LY12E08020) and the National High-Tech Research and Development Program (863 Program) (no. 2011AA110302).