A HEAVY-TRAFFIC EXPANSION FOR ASYMPTOTIC DECAY-RATES OF TAIL PROBABILITIES IN MULTICHANNEL QUEUES

We establish a heavy-traffic asymptotic expansion (in powers of one mi nus the traffic intensity) for the asymptotic decay rates of queue-len gth and workload tail probabilities in stable infinite-capacity multic hannel queues. The specific model has multiple independent heterogeneo us servers, each with i.i.d. service times, that are independent of th e arrival process, which is the superposition of independent nonidenti cal renewal processes. Customers are assigned to the first available s erver in the order of arrival. The heavy-traffic expansion yields rela tively simple approximations for the tails of steady-state distributio ns and higher percentiles, yielding insight into the impact of the fir st three moments of the defining distributions.