Analyzing and optimizing pedestrian flow through a topological network based on M/G/C/C and network flow approaches

Abstract

Summary An M/G/C/C state dependent queuing network measures the performance of a system whose service rate decreases with the increasing number of residing entities. However, the performance in terms of throughputs, levels of congestions, the expected number of entities, and the expected service time is typically analyzed based on a series of arrival rates without any further discussion on the optimal arrival rate. This paper derives the optimal arrival rates of corridors in a topological network using calculus and numerical analysis approaches. These optimal rates are then used as capacity parameters in the network's flow model to obtain the optimal arrival rates that maximize its total throughput. To ease the construction and performance evaluation of the network, we design and construct an M/G/C/C framework based on the Object‐Oriented Programming approach that integrates the lingo software as an optimization tool. The framework is then tested on virtual and real networks. This framework can be used to develop a more advanced traffic management tool for studying and managing traffic flow through a complex network. Copyright © 2015 John Wiley & Sons, Ltd.

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