Regularly varying tails in a queue with discrete autoregressive arrivals of order p

Jeongsim Kim; Bara Kim

doi:10.1007/s11134-007-9035-8

Regularly varying tails in a queue with discrete autoregressive arrivals of order p

Jeongsim Kim, Bara Kim

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

We consider a discrete time single server queueing system where the service time of a customer is one slot, and the arrival process is governed by a discrete autoregressive process of order p (DAR(p)). For this queueing system, we investigate the tail behavior of the queue size and the waiting time distributions. Specifically, we show that if the stationary distribution of DAR(p) input has a tail of regular variation with index -β-1, then the stationary distributions of the queue size and the waiting time have tails of regular variation with index -β.

Original language	English
Pages (from-to)	93-102
Number of pages	10
Journal	Queueing Systems
Volume	56
Issue number	2
DOIs	https://doi.org/10.1007/s11134-007-9035-8
Publication status	Published - 2007 Jun

Bibliographical note

Funding Information:
This research was supported by the MIC (Ministry of Information and Communication), Korea, under the ITRC (Information Technology Research Center) support program supervised by the IITA (Institute of Information Technology Assessment).

Keywords

Discrete autoregressive process
Discrete time queueing system
Regular variation

ASJC Scopus subject areas

Statistics and Probability
Computer Science Applications
Management Science and Operations Research
Computational Theory and Mathematics

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10.1007/s11134-007-9035-8

Cite this

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abstract = "We consider a discrete time single server queueing system where the service time of a customer is one slot, and the arrival process is governed by a discrete autoregressive process of order p (DAR(p)). For this queueing system, we investigate the tail behavior of the queue size and the waiting time distributions. Specifically, we show that if the stationary distribution of DAR(p) input has a tail of regular variation with index -β-1, then the stationary distributions of the queue size and the waiting time have tails of regular variation with index -β.",

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author = "Jeongsim Kim and Bara Kim",

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N2 - We consider a discrete time single server queueing system where the service time of a customer is one slot, and the arrival process is governed by a discrete autoregressive process of order p (DAR(p)). For this queueing system, we investigate the tail behavior of the queue size and the waiting time distributions. Specifically, we show that if the stationary distribution of DAR(p) input has a tail of regular variation with index -β-1, then the stationary distributions of the queue size and the waiting time have tails of regular variation with index -β.

AB - We consider a discrete time single server queueing system where the service time of a customer is one slot, and the arrival process is governed by a discrete autoregressive process of order p (DAR(p)). For this queueing system, we investigate the tail behavior of the queue size and the waiting time distributions. Specifically, we show that if the stationary distribution of DAR(p) input has a tail of regular variation with index -β-1, then the stationary distributions of the queue size and the waiting time have tails of regular variation with index -β.

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Regularly varying tails in a queue with discrete autoregressive arrivals of order p

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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