Second-order properties of the loss probability in M/M/s/s+c systems

Queueing Systems. Theory and Applications, 15(1-4) (1994), 289-308
http://dx.doi.org/10.1007/BF01189242

The Erlang loss function, which gives the steady state loss probability in anM/M/s/s system, has been extensively studied in the literature. In this paper, we look at the similar loss probability inM/M/s/s + c systems and an extension of it to nonintegral number of servers and queue capacity. We study its monotonicity properties. We show that the loss probability is convex in the queue capacity, and that it is convex in the traffic intensity ? if ? is below some ?* and concave if ? is greater that ?*, for a broad range of number of servers and queue capacities. We prove that the one-server loss system is the onlyM/M/s/s +c system for which the loss probability is concave in the traffic intensity in all its range.