The Value of Service Rate Flexibility in an M/M/1 Queue with Admission Control

TL;DR

This paper analyzes a queueing system with dynamic service rate switching and admission control, demonstrating how flexibility benefits system performance especially under high congestion, with threshold-based optimal policies.

Contribution

It introduces a Markov Decision Process model for joint admission and service control with flexible rates, revealing threshold structures and conditions for the benefits of service rate flexibility.

Findings

Flexibility benefit increases with system congestion.

Optimal policies have a threshold structure.

Service flexibility improves admission thresholds under certain conditions.

Abstract

We consider a single server queueing system with admission control and the possibility to switch dynamically between a low and a high service rate, and examine the benefit of this service rate flexibility. We formulate a discounted Markov Decision Process model for the problem of joint admission and service control, and show that the optimal policy has a threshold structure for both controls. Regarding the benefit due to flexibility, we show that it is increasing in system congestion, and that its effect on the admission policy is to increase the admission threshold. We also derive a simple approximate condition between the admission reward and the relative cost of service rate increase, so that the service rate flexibility is beneficial. We finally show that the results extend to the expected average reward case.