Asymptotically Optimal Idling in the GI/GI/N+GI Queue

TL;DR

This paper develops an asymptotic control policy for large-scale GI/GI/N+GI queues, balancing operational costs and server utilization, and demonstrates its asymptotic optimality.

Contribution

It introduces a novel admission control policy for GI/GI/N+GI queues that ensures sufficient server idling and proves its asymptotic optimality.

Findings

The proposed policy achieves asymptotic optimality in large-scale queues.

Non-idling service disciplines are not always optimal without admission control.

Turning away some arrivals can improve long-term operational costs.

Abstract

We formulate a control problem for a GI/GI/N+GI queue, whose objective is to trade off the long-run average operational costs (i.e., abandonment costs and holding costs) with server utilization costs. To solve the control problem, we consider an asymptotic regime in which the arrival rate and the number of servers grow large. The solution to an associated fluid control problem motivates that non-idling service disciplines are not in general optimal, unless some arrivals are turned away. We propose an admission control policy designed to ensure servers have sufficient idle time that we show is asymptotically optimal.