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 minus the traffic intensity) for the asymptotic decay rates of queue-length and workload tail probabilities in stable infinite-capacity multi-channel 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 non-identical 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.