The n-network model with upgrades

  • Authors:

  • Douglas g. Down;Mark e. Lewis

  • Affiliations:

  • Department of computing and software, mcmaster university, hamilton, on l8s 4l7, canadae-mail: downd@mcmaster.ca;School of operations research and information engineering, cornell university, 226 rhodes hall, ithaca, ny 14853 e-mail: mark.lewis@cornell.edu

  • Venue:
  • Probability in the Engineering and Informational Sciences
  • Year:
  • 2010

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Abstract

In this article we introduce a new method of mitigating the problem of long wait times for low-priority customers in a two-class queuing system. To this end, we allow class 1 customers to be upgraded to class 2 after they have been in queue for some time. We assume that there are ci servers at station i, i=1, 2. The servers at station 1 are flexible in the sense that they can work at either station, whereas the servers at station 2 are dedicated. Holding costs at rate hi are accrued per customer per unit time at station i, i=1, 2. This study yields several surprising results. First, we show that stability analysis requires a condition on the order of the service rates. This is unexpected since no such condition is required when the system does not have upgrades. This condition continues to play a role when control is considered. We provide structural results that include a c-μ rule when an inequality holds and a threshold policy when the inequality is reversed. A numerical study verifies that the optimal control policy significantly reduces holding costs over the policy that assigns the flexible server to station 1. At the same time, in most cases the optimal control policy reduces waiting times of both customer classes.