CoSIGN: A Parallel Algorithm for Coordinated Traffic Signal Control

Abstract

Abstract-The problem of finding optimal coordinated signal timing plans for a large number of traffic signals is a challenging problem because of the exponential growth in the number of joint timing plans that need to be explored as the network size grows. In this paper, we employ the game-theoretic paradigm of fictitious play to iteratively search for a coordinated signal timing plan that improves a system-wide performance criterion for a traffic network. The algorithm is robustly scalable to realistic-size networks modelled with high fidelity simulations. We report results of a case study for the the city of Troy, Michigan, where there are 75 signalized intersections. Under normal traffic conditions, savings in average travel time of more than 20 percent are experienced against a static timing plan, and even against an aggressively tuned automatic signal re-timing algorithm, savings of more than 10 percent are achieved. The efficiency of the algorithm stems from its parallel nature. With a thousand parallel CPUs available, our algorithm finds the plan above in under 10 minutes, while a version of a hill-climbing algorithm makes virtually no progress in the same amount of wall-clock computational time.

Platoon-based self-scheduling for real-time traffic signal control

“…It is modified from the automatic signal retiming (ASR) method in [13]. At the end of each cycle, the new cycle length and green time splits are adjusted using critical ratios between estimated and saturation flow rates, based on classical Webster's model.…”

“…The problem is quite challenging. On one hand, the number of joint timing plans and traffic conditions is huge for even an individual intersection [11], [12], and grows exponentially with the size of the traffic network [13]. On the other, the non-linear dynamics of a switched network [14] and unpredictable human driving behaviors make reliable prediction possible only over a limited time horizon and forces continual change to computed solutions.…”

Sampled fictitious play for approximate dynamic programming

“…Stochastic search methods rooted in game theory have recently been applied to large-scale discrete optimization problems, with special focus on cases where the objective function is available only through computationally expensive simulations [2,10,14,15,16,20,21,22]. Consequently, the hope is to at least find local optima, as stronger forms of optimality are nearly impossible to attain, and very difficult to check.…”

“…Consequently, the hope is to at least find local optima, as stronger forms of optimality are nearly impossible to attain, and very difficult to check. These techniques have been numerically tested with encouraging results on problems in transportation [10,14,22], power management in sensor networks [16], network optimization [15], and manufacturing systems [2].…”

“…However, efficacy of the original version of SFP for optimization problems has the following significant limitations: (i) the fictitious play property guarantees convergence to only an equilibrium solution rather than an optimal solution, (ii) SFP may converge to a mixed strategy equilibrium, whereas in many applications, and especially in optimization, a pure strategy equilibrium is desirable, (iii) the best response computation becomes increasingly expensive as the sample size grows without bound with iterations, (iv) it is computationally very expensive to force every player in large-scale problems to perform a best reply computation in every iteration, and, finally, (v) problem form (1) excludes optimization problems with constraints across variables. Thus, practical implementations of SFP [2,10,21] have attempted ad-hoc variations of the original version. Unfortunately, the original convergence results for SFP in [20] do not hold for these ad-hoc variants.…”