Karthik K Srinivasan

There is a growing interest in modeling travel time uncertainty in transportation networks in addition to optimizing the reliability of travel times at the path and network level. This paper focuses on the analysis and optimization of travel time (including stopped delays) Reliability on the Urban Road Network in Chennai. Specifically, two objectives are investigated. The first objective involves the quantification of travel time reliability at the link and path level. In particular, the distribution of link travel times is quantified for the Chennai Urban road network using empirical data. The results indicate that the shifted log-normal distribution (SLN) reasonably represents link travel time for all facility types and relevant facility wise distribution parameters are estimated. Further, the resulting path travel time distribution is approximated by a SLN distribution, which is computationally less expensive than traditional Monte-Carlo estimation techniques with an acceptable compromise on accuracy. The second objective addresses the optimal reliability path problem on a network with SLN link travel times with general correlation structure. For this problem, it is shown that the sub-path optimality property of shortest path problems does not hold making traditional label-setting/label correcting algorithms inapplicable. Consequently, a sufficient optimality condition based on reliability bounds is established and a new network optimization algorithm is proposed and proof of correctness is presented. The convergence rate of the algorithm was shown to increase at every iteration under some mild conditions. The computational performance of the proposed algorithm is investigated using synthetic and real-world networks and found to be reasonably accurate. © 2013 Elsevier Ltd.

This study addresses various formulations of the optimal reliability path problem on stochastic networks. Robust-Cost is adopted as the measure of reliability, which is defined as a weighted combination of the mean and standard deviation of travel time. The principal problem solved is the Minimum Robust-Cost Path (MRCP) problem in the presence of Correlated link travel times. It is shown that the subpath optimality and subpath non-dominance principles, which are conventionally adopted in the literature, cannot be used to solve this problem. In this light, this study proposes an algorithm based on the subpath pruning approach, which eliminates nonoptimal subpaths by using a pruning criterion. We construct the novel pruning criterion, which depends on only two independent objectives, by transforming the network and using efficient shortest path algorithms. The correctness of the algorithm is established, and its good practical performance is demonstrated on real-world networks. Furthermore, the pruning procedure is generalized with suitable modifications to solve three related problems: (i) the MRCP problem with independent link travel times, (ii) the K-best Robust-Cost Paths problem, and (iii) the MRCP problem with stochastic nondominance constraints. These extensions demonstrate the potential wider applications of the proposed solution approach.