Large deviations for the total queue size in non-Markovian tandem queues

Anne Buijsrogge; Pieter-Tjerk de Boer; K.A. Rosen Esquivel; Willem R.W. Scheinhardt

doi:10.1007/s11134-016-9512-z

Large deviations for the total queue size in non-Markovian tandem queues

Anne Buijsrogge, Pieter-Tjerk de Boer, K.A. Rosen Esquivel, Willem R.W. Scheinhardt

Stochastic Operations Research

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

10 Citations (Scopus)

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Abstract

We consider a $d$-node tandem queue with arrival process and light-tailed service processes at all queues i.i.d. and independent of each other. We consider three variations of the probability that the number of customers in the system reaches some high level $N$, namely during a busy cycle, in steady state, and upon arrival of a new customer. We show that their decay rates for large $N$ have the same value and give an expression for this value.

Original language	English
Pages (from-to)	305-312
Number of pages	8
Journal	Queueing systems
Volume	85
Issue number	3-4
DOIs	https://doi.org/10.1007/s11134-016-9512-z
Publication status	Published - 1 Apr 2017

Keywords

MSC-60K25
MSC-60F10
EWI-27679
IR-104020
Tandem queue
Decay rate
GG1 queue
Large deviations

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10.1007/s11134-016-9512-z

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title = "Large deviations for the total queue size in non-Markovian tandem queues",

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AU - de Boer, Pieter-Tjerk

AU - Rosen Esquivel, K.A.

AU - Scheinhardt, Willem R.W.

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N2 - We consider a $d$-node tandem queue with arrival process and light-tailed service processes at all queues i.i.d. and independent of each other. We consider three variations of the probability that the number of customers in the system reaches some high level $N$, namely during a busy cycle, in steady state, and upon arrival of a new customer. We show that their decay rates for large $N$ have the same value and give an expression for this value.

AB - We consider a $d$-node tandem queue with arrival process and light-tailed service processes at all queues i.i.d. and independent of each other. We consider three variations of the probability that the number of customers in the system reaches some high level $N$, namely during a busy cycle, in steady state, and upon arrival of a new customer. We show that their decay rates for large $N$ have the same value and give an expression for this value.

KW - MSC-60K25

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KW - EWI-27679

KW - IR-104020

KW - Tandem queue

KW - Decay rate

KW - GG1 queue

KW - Large deviations

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DO - 10.1007/s11134-016-9512-z

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SP - 305

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JO - Queueing systems

JF - Queueing systems

IS - 3-4

ER -

Large deviations for the total queue size in non-Markovian tandem queues

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Keywords

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