On the Accuracy of Fluid Models for Capacity Sizing in Queueing Systems with Impatient Customers

  • Authors:

  • Achal Bassamboo;Ramandeep S. Randhawa

  • Affiliations:

  • Kellogg School of Management, Northwestern University, Evanston, Illinois 60208;Marshall School of Business, University of Southern California, Los Angeles, California 90089

  • Venue:
  • Operations Research
  • Year:
  • 2010

Quantified Score

Hi-index 0.00

Visualization

Abstract

We consider queueing systems in which customers arrive according to a Poisson process and have exponentially distributed service requirements. The customers are impatient and may abandon the system while waiting for service after a generally distributed amount of time. The system incurs customer-related costs that consist of waiting and abandonment penalty costs. We study capacity sizing in such systems to minimize the sum of the long-term average customer-related costs and capacity costs. We use fluid models to derive prescriptions that are asymptotically optimal for large customer arrival rates. Although these prescriptions are easy to characterize, they depend intricately upon the distribution of the customers' time to abandon and may prescribe operating in a regime with offered load (the ratio of the arrival rate to the capacity) greater than 1. In such cases, we demonstrate that the fluid prescription is optimal up to O(1). That is, as the customer arrival rate increases, the optimality gap of the prescription remains bounded.