Public transport network model

abstract:

The 29th Olympic Games will be held in Beijing next August. By then, a large number of spectators will go to the scene to watch the Olympic Games, which will have a great impact on Beijing's traffic. According to the given bus lines in Beijing, aiming at the transfer problem of the bus network, a bus network model is constructed. The solutions to the three problems are as follows:

(1) In order to solve the problem of 1, this paper first reads out the bus lines with MATLAB programming and finds out the adjacency matrix between stations. Calculate the adjacency matrix according to the adjacency matrix. Processing the obtained adjacency matrix; Judge whether there is a direct route between the starting point and the end point, and if there is, determine it as the optimal route. If not, the program will find a suitable value (marked as m) as a limit (that is, find out the part with the most adjacent points in the site) and find out the sites that exceed this value.

The next step is to find a transit station. By comparing the obtained stations with the required start and end points, a loop is established to modify the values of the start and end points one by one, and the route through each station can be found, and then the route through the obtained station is compared with the route through the start and end points to find the same route. If it exists, this station can be used as a transit station for a given starting point and ending point (but according to people's habit of taking a bus, it is assumed that the number of transit times is no more than two). If there is no transfer station in the station, adjust the value of m until a feasible bus route is found.

According to the obtained feasible bus routes, according to the functional relationship between traffic, cost and time, and according to the principle of less absorption and transfer times, the routes with less cost and less time are calculated, and finally the optimal bus scheme is obtained.

(2) For question 2, the transfer to subway station and bus station is regarded as equivalent, which is similar to question 1, and the best route is found in the same way, but the situation is more complicated than question 1, especially the transfer between subway and subway, which needs to be considered separately. At this time, the functions of station number, cost and time have changed, so the optimal path is obtained by solving and comparing with the new function expression.

(3) For question 3, when considering walking, we can first find out the shortest path between any two stations by Floyd algorithm in graph theory, and then find out the time required to walk this path. On the basis of the second question, add a threshold value t to the time. When calculating the shortest walking time between two points

The algorithm considered in this paper can query the optimal ride path between any two stations.

Keywords: MATLAB program, bus transfer, constraint solving, Freudian algorithm, optimal path

I. Restatement of the problem

Beijing's successful bid for the Olympic Games has put forward higher requirements for Beijing's transportation system. According to the experience and lessons of hosting the Olympic Games abroad, whether the traffic conditions are good and whether the traffic management is efficient during the Olympic Games is one of the decisive conditions for the successful hosting of the Olympic Games. Therefore, on the basis of comprehensive investigation, feasible traffic planning and management strategies must be formulated to ensure the success of the Olympic Games.

In the traffic behavior of the audience, the transfer of track stations, peripheral parking lots and special cars is an important link in the whole traffic chain. Once there is a traffic bottleneck, the blocking wave (or traffic disturbance) fed back to the upstream will be traced back to the source, and the impact will be intensified, which will eventually lead to the delay of evacuation of the main venue, the reduction of the service level of traffic facilities, and some chaotic and immeasurable economic losses and negative social impacts. Therefore, the transfer system planning should consider the whole system to ensure the smooth whole process of the audience's travel.

Second, the model hypothesis.

1. Passengers can get on the bus or subway directly at the departure station, that is, the waiting time at the departure station is not counted.

2. In the actual process, buses (including buses and subways) may have to change more than twice, and users can't stand it any more, so it is considered as unreachable. Because if they transfer between them, the cost will increase a lot, which people don't want to see, and it is generally impossible to reach the terminal only by subway, so we will not consider changing to other means because there are too many transfers.

3. Average travel time of adjacent subway stations (including stopping time): 2.5 minutes.

4. Average running time of adjacent bus stops (including stopping time): 3 minutes.

5. The average transfer time from bus to bus: 5 minutes (including 2 minutes on foot).

6. The average time to transfer from subway to subway: 4 minutes (including 2 minutes on foot).

7. The average time to transfer from subway to bus: 7 minutes (including 4 minutes on foot).

8. It takes an average time to transfer from bus to subway: 6 minutes (including 4 minutes on foot).

9. Bus fare: divided into single fare and segmented pricing, marked behind the line; Among them, the sectional fare is: 0 ~ 20 stops: 1 yuan; 2 1 ~ 40 station: 2 yuan; More than 40 stops: 3 yuan.

10. Subway fare: 3 yuan (regardless of whether there is a transfer between subway lines).

1 1. The walking time between all stations is known.

12. Any two bus stops corresponding to the same subway station can transfer through this subway station (no subway fee is required).

13, the interval between bus stops in suburban counties and busy areas is roughly the same.

Third, the symbol description

1, indicating the total time taken from the starting station to the terminal in the first question.

2. Say the first question from the starting point to the end point.

3, m represents the limit value of finding the local optimal solution.

T is the threshold for judging whether to take the bus or walk, but this value varies from person to person.

Fourth, the analysis of the problem.

Literature [2] studies the travel psychology of bus passengers, and the results show that "transfer times" is the first factor that most bus passengers consider when choosing travel routes, followed by travel time and distance. Travel time is closely related to transfer times, waiting time and distance. Therefore, for travel time and distance, it is transformed into the shortest travel distance problem on the basis of the least number of transfers. Implement the problem of bus transfer

Research, first of all, is to solve how to express the bus network model reasonably; Secondly, the train of thought to solve the problem of bus transfer.

Public transportation network is different from ordinary road transportation network. In many books and documents, the characteristics of public transportation network are expounded, such as the connectivity of the network is different from that of ordinary road networks, the nodes have their spatial location characteristics and one-to-many properties, and the characteristics of arc segments and directed lines are analyzed. I won't go into details about the characteristics of the public transport network.

In GIS network analysis, public transportation network can be mapped into directed graph. According to the characteristics of public transport network, the public transport network model is mapped as, where G is a directed weighted graph; V represents the collection of all nodes on the network, that is, the bus stop, and a bus stop may be the boarding and alighting stop of multiple bus lines; Represents a set of network edges (arcs connecting two bus stops on a bus line). If Station A and bilibili are adjacent boarding and disembarking stations with n lines, there are at most 2n connecting edges between Station A and bilibili: r stands for the set of bus lines connecting all nodes between the starting point and the target point on the network; Is the non-negative weight of the node; Is the nonnegative weight of edge [4]. The optimal travel path refers to the shortest road section and the set of bus lines with the least transfer, which is composed of a series of connecting nodes selected by passengers from the starting point to the target point. [3]