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Telecommunication Systems

, Volume 21, Issue 2–4, pp 149–171 | Cite as

Queue Lengths and Waiting Times for Multiserver Queues with Abandonment and Retrials

  • Avi Mandelbaum
  • William A. Massey
  • Martin I. Reiman
  • Alexander Stolyar
  • Brian Rider
Article

Abstract

We consider a Markovian multiserver queueing model with time dependent parameters where waiting customers may abandon and subsequently retry. We provide simple fluid and diffusion approximations to estimate the mean, variance, and density for both the queue length and virtual waiting time processes arising in this model. These approximations, which are generated by numerically integrating only 7 ordinary differential equations, are justified by limit theorems where the arrival rate and number of servers grow large. We compare our approximations to simulations, and they perform extremely well.

fluid approximations diffusion approximations multiserver queues queues with abandonment virtual waiting time queues with retrials nonstationary queues call centers 

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Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Avi Mandelbaum
    • 1
  • William A. Massey
    • 2
  • Martin I. Reiman
    • 2
  • Alexander Stolyar
    • 2
  • Brian Rider
    • 3
  1. 1.Technion InstituteHaifaIsrael
  2. 2.Bell LaboratoriesMurray HillUSA
  3. 3.Courant InstituteNew YorkUSA

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