A game theory based traffic assignment using queueing networks

As the last process of traditional four processes management method, traffic assignment plays an important role both in theory and practice. User Equilibrium (UE) traffic assignment is a basic problem in the field of urban traffic equilibrium assignment and many studies focus on it. Ant colony algorithm is a new simulating evolution algorithm which has solved many typical combinatorial optimization problems. This paper tries to solve UE traffic assignment problem with ant colony algorithm and improve the goal function value and the formula of transition probability according to the character of UE traffic assignment. The algorithm may get brush-fire optimum result and stop earlier in large scale problems. To solve this problem, this paper optimizes the formula of trail pheromone increment and use max-min ant system to limit the concentration of path pheromone into a scope. Finally, a numerical example is given to prove the feasibility and validity of this algorithm; the result is also compared with the one gotten by traditional algorithm.

User-equilibrium (UE) traffic assignment is widely used in travel forecasting models. Analyses of assignment results often require detailed information about route flows. For a given UE model, total link flows are uniquely determined, but there can be many route flow solutions. Our goal is to evaluate the potential disagreement between different route flow solutions for the same UE model. We considered a case study of a UE model for the Chicago region. We examined 1,000 different UE route flow solutions. Out of 127,248 routes used by UE solutions, 53,134 have alternatives. For 51,748 routes (97%) the flow is completely undetermined, meaning that it is zero in one UE solution and equal to the total origin-destination (O-D) flow in another UE solution. Significant differences were also found in the distribution of users of a given link among O-D pairs (“select link analysis”). We conclude that in analyses that require route flows, it is important to make a proper choice of a specific route flow solution, such as the maximum entropy user equilibrium route flow solution.

A Trade-off between User-Equilibrium and System Optimal Traffic Assignments for Congestion Mitigation in City Networks

In this chapter we are concerned with two schemes for allocating traffic to the arcs of congested road networks: system optimal traffic assignment and user equilibrium traffic assignment. We begin with some cautionary remarks concerning terminology. Techniques for determining Nash equilibria of road networks are frequently collectively referred to by transportation engineers as traffic assignment . In some ways this choice of terminology is unfortunate since other branches of engineering tend to reserve the word “assignment” for normative , value-laden judgments informed by some measure of performance or social welfare. However, to transportation engineers, traffic assignment is the behavior-based allocation of origin-destination specific, forecasted travel demands to the arcs of a real physical road network. As such, traffic assignment involves foresight and is intrinsically a descriptive or positive modeling exercise. Furthermore, because traffic assignment allocates origin-destination specific travel demands to paths of the network of interest in order to determine arc flows, traffic assignment is fundamentally a problem of route selection .

Turn‐delays in intersections contribute significantly to travel times and thus route choices in urban networks. However, turns are difficult to handle in traffic assignment models due to the asymmetric Jacobian in the cost functions. The paper describes a model where turn delays have been included in the solution algorithm of Stochastic User Equilibrium (SUE) traffic assignment. When the Jacobian is symmetric, SUE minimises the road users' ‘perceived travel resistances’. This is a probit‐model where the links cost‐functions of the links are traffic dependent. Hereby, overlapping routes are handled in a consistent way. However, no theoretical proof of convergence has been given if the Jacobian is asymmetric, although convergence can be shown probable for model data representing realistic road‐networks. However, according to the authors knowledge SUE with intersection delays have not been tested earlier on a full‐scale network. Therefore, an essential part of the paper presents practical tests of convergence. Both geometric delays and delays caused by other turns are considered for each turn. Signalised and non‐signalised intersections are handled in different ways, as are roundabouts. In signalised intersections a separate model handles queues longer than one green‐period. Green‐waves can also be taken into consideration. The model has been tested on a large‐scale network for Copenhagen with good results. To make it possible to establish the comprehensive data, a GIS‐based ‘expert system’ was implemented (see Nielsen, O.A., Frederiksen, R. D. and Simonsen, N. (1997). Using expert system rules to establish data on intersections and turns in road networks. International Transactions in Operational Research, 5, 513–529.

Dynamic user optimal traffic assignment on congested multidestination networks

We propose two types of extended time-of-day user equilibrium assignment models for an urban road network including expressways in this paper. In time-of-day traffic assignment it is significant to modify traffic demand remained on route at the end of a study period. These models are able to modify the traffic demand in considering the toll load for expressway. In the models the user equilibrium conditions are also able to be held based on travel time forarterial road users but based on general travel time considering the toll load for expressway users. These new models are applied to the arterial road network and the results show good accuracy and practicability.

Tailpipe emissions in the road transportation system are a major source of air pollution and greenhouse gases. One of the possible approaches is to influence drivers’ routing decisions such that the emissions and fuel consumption is minimized. In order to evaluate such condition, we develop environmental traffic assignment (E-TA) models based on user equilibrium (UE) and system optimal (SO) behavioral principles. Extending the traditional travel time-based UE and SO principles to E-TA is not straightforward because, unlike travel time, the rate of emissions increases with the increase in vehicle speed beyond a certain point. The results of various TA models show a network-wide traffic control strategy in which vehicles are routed according to SO-based E-TA, can reduce system-wide emissions. However, a system in which drivers make routing decisions to minimize their own emissions (E-UE system) results in a paradoxical situation of increased individual as well as system-wide emissions.

The stochastic user equilibrium (SUE) traffic assignment model integrates the concepts of random assignment and Wardrop equilibrium, and it makes the assignment results more reasonable. The conventional Logit-based SUE model is explicitly built upon path flow variables, which encumbers its large-scale applications and further theoretical analyses. In this paper, a link-based SUE traffic assignment model with link capacity constraints is developed by using the network equilibrium modeling approach. The solution equivalence and uniqueness of the proposed model are rigorously proved. An efficient solution algorithm is also proposed to obtain the equilibrium solution. Numerical results indicate that the proposed link-based SUE model can reflect the real route choice behavior of travelers more reasonable and also facilitate the algorithmic development and further theoretical analyses.

This paper addresses a general stochastic user equilibrium (SUE) traffic assignment problem with link capacity constraints. It first proposes a novel linearly constrained minimization model in terms of path flows and then shows that any of its local minimums satisfies the generalized SUE conditions. As the objective function of the proposed model involves path‐specific delay functions without explicit mathematical expressions, its Lagrangian dual formulation is analyzed. On the basis of the Lagrangian dual model, a convergent Lagrangian dual method with a predetermined step size sequence is developed. This solution method merely invokes a subroutine at each iteration to perform a conventional SUE traffic assignment excluding link capacity constraints. Finally, two numerical examples are used to illustrate the proposed model and solution method.

Stackelberg games and multiple equilibrium behaviors on networks

The simulation of travel management st;stem by vehicle emission consideration is using faur stepsmodeling. The congestion existed in cimahi city especially in peak periods c.aused btj the increasing thenumber of private c.ars. Based on the reasons, the study only considers private car passengers as modeof transportation that will be assigned in peak hour periods. To obtain the peak period result, the resultof traffic assignment should be multiplied btj 10.5% for collector road and 9% for arterial road. Thetechnique assignment is used user equilibrium and traffic assignment is run by using generalized cost.Generalized cost is c.alculated btj actual cost and -perceive cost (emission cost). CUBE software hasbeen employed for this research to analyze traffic performance. CUBE software applies existingcondition (base) and faur scenarios. The analysis will compare between the assignment with emissioncost and the assignment without emission cost.Cimahi CihJ is study case for transportation improvements c.ause changes in the existing trafficnetwork Therefore, The scenarios are built high side friction reduction on arterial road (scenario 1)and building ringroad (scenario 2). These changes analyzed is reduction of v/c ratio as well as lengthof congested links. The first analysis is v/c ratio reduction all of scenario which compared with basecondition. The scenario 1 result create only 9 congested links with is the v/c ratio reduction of scenariobtj assignment with emission cost is 29% and withour emission cost is 26%. and scenario 2 (26%).In additional , the second scenario result achieve the best scenario bec.ause the v/c ratio reductionwithout cost is 31 % with 6 congested links and assignment with emission cost is 26% with 2congested links The result of both scenarios shJw that assignment with consideration vehicle emissioncost more efektif because provide more v/c ratio reduction and number of congested link reductions.Key words: traffic assignment, private c.ar, peak hour, emission.

For travelers with continuously distributed value of time (VOT) in a general transportation network, the user equilibrium (UE) model and system optimization (SO) model can be depicted either in time units or cost units. Under the condition of road pricing, the equivalent conditions between the UE flow pattern and the SO flow pattern are given. Furthermore, we adopt a bi-objective minimization model with fixed travel demand, and identify the Pareto optimal frontier. Because users with different VOTs are observationally indistinguishable and differential tolls on links are difficult to implement in reality, we investigate a pricing scheme with anonymous link tolls to decentralize a Pareto system optimum into user equilibrium.

Joint routing and pricing control in congested mixed autonomy networks

A hybrid routing model for mitigating congestion in networks