A heavy-traffic expansion for asymptotic decay rates of tail probabilities in multichannel queues

The authors establish a heavy-traffc asymptotic expansion (in powers of one minus the traffic intensity) for the asymptotic decay rates of queue-length and workload tail probabilities in stable infinite-capacity multichannel queues. The specific model has multiple independent heterogeneous servers, each with i.i.d. service times, that are independent of the arrival process, which is the superposition of independent nonidentical renewal processes. Customers are assigned to the first available server in the order of arrival. The heavy-traffic expansion yields relatively simple approximations for the tails of steady-state distributions and higher percentiles, yielding insight into the impact of the first three moments of the defining distributions.