A Note on the Convexity of the Probability of a Full Buffer in the M/M/1/K Queue (1992)
| Venue: | IEEE J.Select.Areas Commun |
| Citations: | 3 - 1 self |
BibTeX
@TECHREPORT{Nagarajan92anote,
author = {Ramesh Nagarajan and Don Towsley},
title = {A Note on the Convexity of the Probability of a Full Buffer in the M/M/1/K Queue},
institution = {IEEE J.Select.Areas Commun},
year = {1992}
}
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Abstract
The loss probability in queueing systems is a very useful metric in the design and analysis of high-speed communication networks. In this paper, we investigate the convexity properties of this metric for the finite-buffer, single server M=M=1=K queue. We demonstrate that the loss probability in the M=M=1=K queue is convex with respect to the traffic intensity (arrival rate) for values of the traffic intensity below a certain value ae (K) and is concave for values of the traffic intensity larger than ae (K). We establish several useful properties of ae (K). Second, we show that the loss probability is convex with respect to the service rate. Last, we show that the throughput is jointly concave in the arrival and service rates while the loss rate is jointly convex with respect to the same. KEYWORDS: M=M=1=K QUEUE; CONVEXITY OF PERFORMANCE MEASURES; LOSS SYSTEM. 1 This work is supported in part by the National Science Foundation under grant NCR-9116183 2 Dept. of Elect. and C...
