An M/G/1 Queue with Adaptable Service Speed

Abstract

We consider a queueing system where feedback information about the level of congestion is given right after arrival instants. When the amount of work right after arrival is at most (respectively, larger than) K, then the server works at speed r ₁ (respectively, r ₂) until the next arrival instant. We derive the distribution of the workload right after and right before arrivals, as well as in steady state. In addition, we consider the generalization to the N-step service rule.

Keywords:

• Production systems
• Sojourn times
• State-dependent rates
• Workload

AMS Subject Classification:

• Primary 60K25
• Secondary 90B22

ACKNOWLEDGMENTS

The authors are indebted to Johan van Leeuwaarden for interesting discussions and to Prof. Ton de Kok for posing the problem.

A preliminary version of this paper was presented in a Korea-Netherlands workshop in Seoul ^[4] ; the second author gratefully acknowledges the hospitality of Prof. B. D. Choi.

The research was conducted while the first author was affiliated with Eindhoven University of Technology, Eindhoven, The Netherlands. The first author was financially supported by a research grant from Philips Research. The research of the second author fits into the BRICKS project. Part of the research was conducted in the framework of Euro-NGI.