The M/G/c queue in light traffic

Authors:
Chia-li Wang;Ronald W. Wolff
Affiliations:
Department of Applied Mathematics, National Dong Hwa University, Hualien, Taiwan, ROC;Department of Industrial Engineering and Operations Research, University of California, Berkeley, CA 94720, USA, and Faculty of Economics, Tokyo Metropolitan University, Tokyo 192-03, Japan
Venue:
Queueing Systems: Theory and Applications
Year:
1998

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Abstract

Under light traffic, we investigate the quality of a well-known approximation for first-moment performance measures for an M/G/c queue, and, in particular, conditions under which the approximation is either an upper or a lower bound. The approach is to combine known relationships between quantities such as average delay and time-average work in system with direct sample-path comparisons of system operation under two modes of operation: conventional FIFO and a version of preemptive LIFO. We then use light traffic limit theorems to show an inequality between time-average work of the M/G/c queue and that of the approximation. In the process, we obtain new and improved approximations.