Study on mean-standard deviation shortest path problem in stochastic and time-dependent networks: A stochastic dominance based approach

Xing Wu

Transportation Research Part B: Methodological, 2015, vol. 80, issue C, 275-290

Abstract: This paper studies a mean-standard deviation shortest path model, also called travel time budget (TTB) model. A route’s TTB is defined as this route’s mean travel time plus a travel time margin, which is the route travel time’s standard deviation multiplied with a factor. The TTB model violates the Bellman’s Principle of Optimality (BPO), making it difficult to solve it in any large stochastic and time-dependent network. Moreover, it is found that if path travel time distributions are skewed, the conventional TTB model cannot reflect travelers’ heterogeneous risk-taking behavior in route choice. This paper proposes to use the upper or lower semi-standard deviation to replace the standard deviation in the conventional TTB model (the new models are called derived TTB models), because these derived TTB models can well capture such heterogeneous risk-taking behavior when the path travel time distributions are skewed. More importantly, this paper shows that the optimal solutions of these two derived TTB models must be non-dominated paths under some specific stochastic dominance (SD) rules. These finding opens the door to solve these derived TTB models efficiently in large stochastic and time-dependent networks. Numerical examples are presented to illustrate these findings.

Keywords: Mean-standard deviation; Stochastic dominance (SD); Semi-standard deviation; Time-dependent networks; Travel time budget (TTB) (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (11)

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DOI: 10.1016/j.trb.2015.07.009

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