Stochastic Decomposition in M/M/∞ Queues with Markov Modulated Service Rates

Authors:
Melike Baykal-Gursoy;Weihua Xiao
Affiliations:
Department of Industrial and Systems Engineering, Rutgers University, 96 Frelinghuysen Road, Piscataway, NJ 08854-8018, USA gursoy@rci.rutgers.edu;Department of Industrial and Systems Engineering, Rutgers University, 96 Frelinghuysen Road, Piscataway, NJ 08854-8018, USA xiao@rci.rutgers.edu
Venue:
Queueing Systems: Theory and Applications
Year:
2004

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Abstract

Motivated by the need to study transportation systems in which incidents cause traffic to slow down, we consider an M/M/∞ queueing system subject to random interruptions of exponentially distributed durations. System breakdowns, where none of the servers work, as well as partial failures, where all servers work with lower efficiency, are investigated. In both cases, it is shown that the number of customers present in the system in equilibrium is the sum of two independent random variables. One of these is the number of customers present in an ordinary M/M/∞ queue without interruptions.