Analysis of Worst Case Stochastic Link Capacity Degradation to Aid Assessment of Transportation Network Reliability

AbstractWhile link capacities of urban transportation networks possess inherent randomness due to varying reasons, conventional models assume that the designed link capacities prevail. The recent developments in reliable network design require the link capacities to be treated as stochastic. It is, however, laborious to collect data to explicitly model stochastic nature of link capacities. It is also hard to relate the link-level randomness and system-level performance. A smarter alternative is to treat link capacities as random variables and search for probability distributions over such random variables which would effect in a worst case scenario. One can then assess the performance of the network at this worst case and comment on the reliability of the network. This paper formulates and solves a worst case stochastic link capacity degradation problem. The randomness involved has been modeled as the mixed strategy profile of a player in a fictitious game. The players of the game – a friend who plays for the network and a foe who plays against the network – compete each other to minimize and maximize the expected system travel time (ESTT). The foe has been modeled as an intelligent player, who knows that the network users would settle to probabilistic user equilibrium (PUE). The foe is also cautious of the friend's presence who would try to assign flows system-optimally, thereby minimizing the ESTT. The game has been formulated as a multi-level optimization equation. Different algorithms which can use the results from this methodology as inputs to establish most probable worst case states of the network have been discussed. A planner can input the results from this problem into some of the existing algorithms to identify the most probable worst case states, and the probabilities associated with these states, thus defining the reliability of the network