A General Decomposition Algorithm for Parallel Queues with Correlated Arrivals

Authors:
S. M. R. Iravani;K. L. Luangkesorn;D. Simchi-Levi
Affiliations:
Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, IL 60208, USA;Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, IL 60208, USA;Department of Engineering Systems, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Venue:
Queueing Systems: Theory and Applications
Year:
2004

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Abstract

Queueing with correlated arrivals occurs when customers arrive at a set of queues simultaneously. The difficulty in analyzing systems with correlated arrivals is due to the fact that the individual queueing systems are stochastically dependent. Exact methods for analyzing these systems are computationally intensive and are limited to only a few special cases. In this paper, we consider a system of parallel queues with bulk service and correlated arrivals. We show how the matrix-geometric approach can be used to obtain the performance measures of the system. We also develop an algorithm for large systems that efficiently approximates the performance measures by decomposing it into individual queueing systems. Finally, we describe how the principles of our decomposition algorithm can be extended to analyze a variety of different parallel queueing systems with correlated arrivals. We then evaluate the accuracy of our algorithm through a numerical study.