On the exact asymptotics for the stationary sojourn time distribution in a tandem of queues with light-tailed service times

S. G. Foss

doi:10.1134/S0032946007040084

On the exact asymptotics for the stationary sojourn time distribution in a tandem of queues with light-tailed service times

S. G. Foss

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6 Citations (Scopus)

Abstract

We study the asymptotics of the stationary sojourn time Z of a "typical customer" in a tandem of single-server queues. It is shown that in a certain "intermediate" region of light-tailed service time distributions, Z may take a large value mostly due to a large value of a single service time of one of the customers. Arguments used in the paper also allow us to obtain an elementary proof of the logarithmic asymptotics for the tail distribution of the stationary sojourn time in the whole class of light-tailed distributions. © Pleiades Publishing, Inc. 2007.

Original language	English
Pages (from-to)	353-366
Number of pages	14
Journal	Problems of Information Transmission
Volume	43
Issue number	4
DOIs	https://doi.org/10.1134/S0032946007040084
Publication status	Published - Dec 2007

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title = "On the exact asymptotics for the stationary sojourn time distribution in a tandem of queues with light-tailed service times",

abstract = "We study the asymptotics of the stationary sojourn time Z of a {"}typical customer{"} in a tandem of single-server queues. It is shown that in a certain {"}intermediate{"} region of light-tailed service time distributions, Z may take a large value mostly due to a large value of a single service time of one of the customers. Arguments used in the paper also allow us to obtain an elementary proof of the logarithmic asymptotics for the tail distribution of the stationary sojourn time in the whole class of light-tailed distributions. {\textcopyright} Pleiades Publishing, Inc. 2007.",

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N2 - We study the asymptotics of the stationary sojourn time Z of a "typical customer" in a tandem of single-server queues. It is shown that in a certain "intermediate" region of light-tailed service time distributions, Z may take a large value mostly due to a large value of a single service time of one of the customers. Arguments used in the paper also allow us to obtain an elementary proof of the logarithmic asymptotics for the tail distribution of the stationary sojourn time in the whole class of light-tailed distributions. © Pleiades Publishing, Inc. 2007.

AB - We study the asymptotics of the stationary sojourn time Z of a "typical customer" in a tandem of single-server queues. It is shown that in a certain "intermediate" region of light-tailed service time distributions, Z may take a large value mostly due to a large value of a single service time of one of the customers. Arguments used in the paper also allow us to obtain an elementary proof of the logarithmic asymptotics for the tail distribution of the stationary sojourn time in the whole class of light-tailed distributions. © Pleiades Publishing, Inc. 2007.

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DO - 10.1134/S0032946007040084

M3 - Article

SN - 0032-9460

VL - 43

SP - 353

EP - 366

JO - Problems of Information Transmission

JF - Problems of Information Transmission

IS - 4

ER -

On the exact asymptotics for the stationary sojourn time distribution in a tandem of queues with light-tailed service times

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