State Dependent Models of Material Handling Systems in Closed Queueing Networks

J. MacGregor Smith, L. KERBACHE

International Journal of Production Research

January 2012, vol. 50, n°2, pp.461-484

Departments: Information Systems and Operations Management, GREGHEC (CNRS)

Keywords: materials handling; performance analysis; queueing networks

A comprehensive algorithmic analysis of finite state-dependent queueing models and exponentially distributed workstations is formulated and presented. The material handling system is modeled with finite statedependent queueing networkM/G/c/c models and the individual workstations are modeled with exponentially distributed single and multi-server M/M/c queueing models. The coupling of these queueing models is unique via the material handling structure. The performance modeling of the systems for series, merge, and split and other complex network topologies are included so as to demonstrate the type of topological network design that is possible with these incorporated material handling systems. Of some importance, it is shown that these integrated M/M/c and M/G/c/c networks have a product form when the population arriving at the M/G/c/c queues is controlled. Numerous experimental results demonstrate the efficacy of our approach for a variety of contexts and situations