A Note on the Convexity of the Probability of a Full
نویسنده
چکیده
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 nite-buuer, 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 traac intensity (arrival rate) for values of the traac intensity below a certain value (K) and is concave for values of the traac intensity larger than (K). We establish several useful properties of (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.
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