Queue lengths and waiting times for multiserver queues with abandonment and retrials

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

Research output: Contribution to journalArticlepeer-review

50 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)149-171
Number of pages23
JournalTelecommunication Systems
Issue number2-4
StatePublished - 2002

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering


  • Call centers
  • Diffusion approximations
  • Fluid approximations
  • Multiserver queues
  • Nonstationary queues
  • Queues with abandonment
  • Queues with retrials
  • Virtual waiting time


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