Impacts of Correlations on Reliable Shortest Path Finding

Abstract

This paper examines how correlations in link travel times affect reliable path finding in a stochastic network. The reliable path is defined as the path that requires the lowest travel time budget to ensure a given probability of on-time arrival. Such a path can be found by solving the shortest path problem considering on-time arrival reliability (SPOTAR). SPOTAR is solved approximately by using an approach based on Monte Carlo simulation. A major advantage of the simulation-based algorithm is its ability to deal with correlated link travel times. Through the use of a real-world network, the simulation-based algorithm is first validated by comparing it with a label-correcting algorithm that can solve the uncorrelated case exactly; the impacts of the correlations on link travel times are then examined. The results of the numerical experiments indicate that correlations affect the optimal SPOTAR solutions significantly. However, larger correlations do not always lead to larger errors in the reliable route choices that ignore them.

Using temporal detrending to observe the spatial correlation of traffic

“…Traffic analysts have utilized the spatial dependency of road segments to solve three typical problems in a traffic network: (1) short-term traffic forecasting [1, 2, 5, 6], (2) reliable path problem [7], and (3) missing data estimation [8]. …”

An iterative learning approach for network contraction: Path finding problem in stochastic time‐varying networks

“…The approach of the mentioned study is considered as the benchmark in this study, since it accounts for link travel correlations and heterogeneous users in terms of reliability valuation. The optimality and solution time of the benchmark approach are already compared and validated (Zockaie et al., ; Zockaie et al., ) by comparing the solutions with the results of an outer approximation algorithm, which considers link travel time correlations (Shahabi et al., ), and a label correcting algorithm to solve SPOTAR problem (Nie & Wu, ). All approaches are implemented for the Chicago downtown network using a realistic joint time‐dependent travel time distribution for the SPOTAR and MTTBP problems.…”

“…Several studies are conducted in the literature to develop algorithms for solving the SPOTAR and MTTBP problems (Chen, Lam, Sumalee, & Li, ; Fan, Kalaba, & Moore, ; Lo, Luo, & Siu, ; Sen, Pillai, Joshi, & Rathi, ). Specifically, a Monte‐Carlo simulation (MCS)‐based approach is presented to solve these path finding problems for static (Zockaie et al., ; Zockaie, Nie, & Mahmassani, ) and time‐varying (Zockaie, Mahmassani, & Nie, ) stochastic networks. The main advantages of this approach are its ability to deal with network‐wide correlated link travel times, considering heterogeneous users in terms of reliability, and the applicability to dynamic networks.…”

“…After a certain number of realizations (iterations), candidate paths are processed to obtain their travel time distributions, from which the solution to the SPOTAR and MTTBP problems can be determined. The optimality of this approach is validated by comparing the solutions with other existing algorithms in the literature (Shahabi, Unnikrishnan, & Boyles, ; Zockaie et al., ; Zockaie et al., ). However, the major computational burden of this approach is associated with the deterministic dynamic shortest path finding for each realization.…”

A Strategic User Equilibrium for Independently Distributed Origin‐Destination Demands

“…Under the framework, the correlation between links is considered hence path travel time is nonadditive (Fan et al, 2005;Dong and Mahmassani, 2009). Path travel time can be derived from link travel time covariance matrix (Sen et al, 2001;Xing and Zhou, 2011;Shahabi et al, 2013), temporal and spatial correlations (Miller-Hooks and Mahmassani, 2003;Gao and Chabini, 2006), or simulation-based approaches (Ji et al, 2011;Huang and Gao, 2012;Zockaie et al, 2013;Zockaie et al, 2014). Some research also focuses on the penalties due to late arrival and the corresponding route choice (Watling, 2006;Chen and Zhou, 2010).…”