A Game-Theoretic Framework for Medium Access Control

In this paper, we generalize the random access game model, and show that it provides a general game-theoretic framework for designing contention based medium access control. We extend the random access game model to the network with multiple contention measure signals, study the design of random access games, and analyze different distributed algorithms achieving their equilibria. As examples, a series of utility functions is proposed for games achieving the maximum throughput in a network of homogeneous nodes. In a network with n traffic classes, an N-signal game model is proposed which achieves the maximum throughput under the fairness constraint among different traffic classes. In addition, the convergence of different dynamic algorithms such as best response, gradient play and Jacobi play under propagation delay and estimation error is established. Simulation results show that game model based protocols can achieve superior performance over the standard IEEE 802.11 DCF, and comparable performance as existing protocols with the best performance in literature

A Differential Game Modeling Approach to Dynamic Traffic Assignment and Signal Control

This paper addresses a theoretical issue related to combined dynamic traffic assignment and signal control under conditions of congestion through a brief review of previous research and the discussion on interaction between dynamic traffic assignment and signal control. The dynamic characteristics of the interaction are approached using a differential game modeling approach here to formulate the decision-making process for solving the problem inherent in this combination. Specifically, the combined dynamic traffic assignment and signal control problem is formulated as a leader−follower differential game, where a leader and multiple followers engage interactively to finding optimal strategies under the assumption of an openloop information structure. Discretization in time is used to find a numerical solution for the proposed game model, and a simulated annealing algorithm is applied to obtain optimal strategies. Finally, a simulation study is conducted on a simple traffic network in which numerical results demonstrate the effectiveness of the proposed approach

A bi-level model of dynamic traffic signal control with continuum approximation

This paper proposes a bi-level model for traffic network signal control, which is formulated as a dynamic Stackelberg game and solved as a mathematical program with equilibrium constraints (MPEC). The lower-level problem is a dynamic user equilibrium (DUE) with embedded dynamic network loading (DNL) sub-problem based on the LWR model (Lighthill and Whitham, 1955; Richards, 1956). The upper-level decision variables are (time-varying) signal green splits with the objective of minimizing network-wide travel cost. Unlike most existing literature which mainly use an on-and-off (binary) representation of the signal controls, we employ a continuum signal model recently proposed and analyzed in Han et al. (2014), which aims at describing and predicting the aggregate behavior that exists at signalized intersections without relying on distinct signal phases. Advantages of this continuum signal model include fewer integer variables, less restrictive constraints on the time steps, and higher decision resolution. It simplifies the modeling representation of large-scale urban traffic networks with the benefit of improved computational efficiency in simulation or optimization. We present, for the LWR-based DNL model that explicitly captures vehicle spillback, an in-depth study on the implementation of the continuum signal model, as its approximation accuracy depends on a number of factors and may deteriorate greatly under certain conditions. The proposed MPEC is solved on two test networks with three metaheuristic methods. Parallel computing is employed to significantly accelerate the solution procedure

Comparison of Different Toll Policies in the Dynamic Second-best Optimal Toll Design Problem: Case study on a Three-link network

In this paper, the dynamic optimal toll design problem is considered as a one leader-many followers hierarchical non-cooperative game. On a given network the road authority as the leader tolls some links in order to reach its objective, while travelers as followers minimize their perceived travel costs. So far toll has always been considered either as constant or as time-varying. Inspired by the San Diego's Interstate 15 congestion pricing project, in which heuristics with toll proportional to traffic flow are applied on a real two-link highway network, we consider toll as proportional to traffic flows in the network. On a three-link network we investigate various toll schemes and their influence on the outcome of the game for the road authority. We show that the use of alternative toll schemes may improve system performance remarkably