1. Introduction
1.1 Background
Within the rational planning framework, transportation forecasting is important to transportation management. It followed the sequential four-step model or urban transportation planning (UTP) procedure. The four steps of the classical urban planning system model includes Trip Generation, Trip Distribution, Modal Split process, and Traffic Assignment.
Traffic Assignment Problem(TAP) is a multicommodity flow problem which arises when users (or commodities) must share a common resource, the street network.
It is to assign flows by various modes in given link to paths in transportation networks.
It describe how road-users to choose the optimal route between an origin-destination (OD) pairs, and can be used for analyzing and forecasting traffic flows on every link or route furthermore. However, each user’s choice is dependent upon other users’
choices as well, because the travel time on each street depends on the total number of cars on that street: more congestion means longer travel times. Meyer and Miller (2001) introduced several traffic assignment techniques as follows:
(1) Static assignment model
Network flows will not vary with time in the above approaches. In static assignment techniques, these procedures assume that each vehicle is
simultaneously located on every link on its chosen path and assign all flow simultaneously to all links on the chosen paths. The commonly static assignment technique as follows:
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All-or-nothing assignment: It is the simplest approach involving the selection and loading between each origin and destination. It makes a previous assumption that road capacity is unlimited, and link cost is fixed.
For each OD pair, find the shortest path and assign all the travel demand into it. The method ignores the limitations imposed by restriction on the capacity of the network. Links may be allocated far greater flows than they are capable of carrying.
Equilibrium assignment: The idea of equilibrium in the analysis of
transportation networks arises from the dependence of the link travel time on the link flows. Travelers will strive to find the shortest path (least resistance) path from origin to destination, and network equilibrium occurs when no traveler can decrease travel effort by shifting to a new path. In this situation, no user can changing travel path unilaterally to reduce the travel cost or time.
Stochastic assignment: The second assignment technique is also called deterministic user equilibrium, because it assumes all travelers obtain perfect information on travel costs on any given path are perfect, resulting in making rational route choices. However, in real world, traveler cannot always obtain the whole network information. This leads to development of stochastic assignment, in which link travel time function is viewed as random variables varying with users’ preferences, perception and experience.
(2) Dynamic assignment
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In real world, the static representation of network performance is not sufficiently accurate. A dynamic representation of route choice behavior and resulting network performance is required in which the movements of vehicles along their chosen paths is explicitly simulated through time. Dynamic assignment models may be either probabilistic in terms of the simulation of users’ route choices and/or determination of vehicles’ travel times along given links, or they can be deterministic.
It is unrealistic assumption obviously, but for many regional transportation
planning applications, static assignment assumption is acceptable and can yield useful results. The research use the game theory to analyze the equilibrium assignment which is classified in static assignment.
1.2 Research Objective
Game theory aims to help people understand situations in which decision-makers interact. It had been applied in transportation in many different aspects. Fisk (1983) discuss some transportation problem as the game theory models, include Nash non-cooperative and Stackelberg games. The discussion serves to underline differences between two categories of transportation problems and introduces the game theory literature as a potential source of solution algorithms. The purpose of research is to demonstrate why the n-person assignment problem can be regard as a two-person game. The research construct a n-person non-cooperation game, use the technique of game theory to consider the assignment problem. Then prove the equivalent between the constructed n-person concave game to a two-person zero sum
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game. The research use the idea proposed by Zukhovitshii et al. (1973), demonstrate the theory step by step.
1.3 Research Procedure
Figure 1.3-1 is the procedure of the research
Figure 1.3-1 The research flow chart
Network equilibrium model Review
Game theory Review
Model Formulation
Demonstration process
Conclusion Problem definition
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The research was divided in following part:
(1) Problem definition:
This paper tends to make a completely proof that the network traffic assignment problem can be represented in a n-person concave game, which is equivalent to a two-person zero-sum game. It can help us analyze the problem in different way.
(2) Review:
Before we start to discuss the traffic assignment game, we first review the existed assignment model. Chapter 2 review the article about network
equilibrium, include the development of the equilibrium model and their foundation concept. Because of changing our view to the game based side, Chapter 3 reviews the basic theory of game, and introduces the application of game theory to the traffic side.
(3) Model Construction and Demonstration:
In Chapter 4, we first construct a network game, and use several mathematic theorems to demonstrate the element of the game, include the existence and uniqueness to the equilibrium point. Then make the demonstration to prove the equivalent to the n-person game with two person game.
(4) Conclusion and contribution
Finally, this paper presented some conclusions of this literature and the contribution for the traffic field.
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