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

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

doi:10.1023/A:1020921829517

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 journal › Article › peer-review

50 Scopus citations

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.

Original language	English (US)
Pages (from-to)	149-171
Number of pages	23
Journal	Telecommunication Systems
Volume	21
Issue number	2-4
DOIs	https://doi.org/10.1023/A:1020921829517
State	Published - 2002

All Science Journal Classification (ASJC) codes

Electrical and Electronic Engineering

Keywords

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

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10.1023/A:1020921829517

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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.",

keywords = "Call centers, Diffusion approximations, Fluid approximations, Multiserver queues, Nonstationary queues, Queues with abandonment, Queues with retrials, Virtual waiting time",

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AU - Mandelbaum, Avi

AU - Massey, William A.

AU - Reiman, Martin I.

AU - Stolyar, Alexander

AU - Rider, Brian

PY - 2002

Y1 - 2002

N2 - 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.

AB - 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.

KW - Call centers

KW - Diffusion approximations

KW - Fluid approximations

KW - Multiserver queues

KW - Nonstationary queues

KW - Queues with abandonment

KW - Queues with retrials

KW - Virtual waiting time

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EP - 171

JO - Telecommunication Systems

JF - Telecommunication Systems

IS - 2-4

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

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