On the analytical approximation of joint aggregate queue-length distributions for traffic networks: A stationary finite capacity Markovian network approach

This paper is motivated by recent results in the design of signal plans for Manhattan that highlight the importance of providing signal control algorithms with an analytical description of between-link dependencies. This is particularly important for congested networks prone to the occurrence of spillbacks. This paper formulates a probabilistic network model that proposes an aggregate description of the queue-length, and then approximates the joint aggregate queue-length distribution of subnetworks. The goal is to model between-queue dependencies beyond first-order moments, yet to do so in a tractable manner such that these techniques can be used for optimization purposes.