Monotonicity Properties For Multiserver Queues With Reneging And Finite Waiting Lines
Probability in the Engineering and Informational Sciences
The effect of transmission error on audio quality for simple FEC schemes
CCNC'09 Proceedings of the 6th IEEE Conference on Consumer Communications and Networking Conference
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The loss of probability in queueing systems is a very useful metric in the design and analysis of high-speed 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 p*(K) and is concave for the values of the traffic intensity larger than p*(K). We establish several useful properties of p*(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.