Some light-traffic and heavy-traffic results for the GI/G/n/0 queue using the GM Heuristic

In this paper we carry out both light-traffic and heavy-traffic analyses for the calculation of steady-state loss probabilities in the general multi-server queuing loss system, the GI/G/n/0queue.The analysis makes use of a heuristic approach called the GM Heuristic, for which a detailed analysis in normal traffic has previously been published. Sufficient conditions are given for the GM Heuristic to be asymptotically exact in light traffic. The heuristic is also shown to be asymptotically exact in heavy-traffic when the number of servers n tends to infinity. These results are illustrated numerically using two-phase Coxian distributions for both the inter-arrival time and service time.