Approximation of the transient joint queue-length distribution in tandem networks

Abstract

This work considers an urban traffic network, and represents it as a Markovian queueing network. This work proposes an analytical approximation of the time-dependent joint queue-length distribution of the network. The challenge is to provide an accurate analytical description of between and within queue (i.e. link) dynamics, while deriving a tractable approach. In order to achieve this, we use an aggregate description of queue states (i.e. state space reduction). These are referred to as aggregate (queue-length) distributions. This reduces the dimensionality of the joint distribution. The proposed method is formulated over three different stages: we approximate the time-dependent aggregate distribution of 1) a single queue, 2) a tandem 3-queue network, 3) a tandem network of arbitrary size. The third stage decomposes the network into overlapping 3-queue sub-networks. The methods are validated versus simulation results. We then use the proposed tandem network model to solve an urban traffic signal control problem, and analyze the added value of accounting for time-dependent between queue dependency in traffic management problems for congested urban networks.