A simple analysis for an M/GI/1/N queue with vacation time and exhaustive service discipline

Author

Frey, Andreas ; Takahashi, Yoshitaka

Author_Institution

NTT Multimedia Network Lab., Tokyo, Japan

Volume

4

fYear

1996

fDate

14-17 Oct 1996

Firstpage

3057

Abstract

We consider an M/GI/1/N queue with vacation time and exhaustive service discipline, the same queue as presented by Lee (1984). Focusing only on the service completion epochs (as opposed to both service completion epochs and vacation completion epochs by Lee), we present a simple analysis for the queue length distribution at an arbitrary time as well as the waiting time distribution. We consider the limiting behaviours of these distributions and provide some rigorous proofs for a more general setting (including a G/GI/1/N queue with a general vacation policy) by means of the rate conservation law

Keywords

Markov processes; probability; queueing theory; M/GI/1/N queue; Markov chain; exhaustive service discipline; probability; queue length distribution; queueing theory; rate conservation law; service completion epochs; vacation time; waiting time distribution; Capacity planning; Distribution functions; Laboratories; Length measurement; Queueing analysis; Random variables; Stochastic processes; Time division multiple access; Time measurement;

fLanguage

English

Publisher

ieee

Conference_Titel

Systems, Man, and Cybernetics, 1996., IEEE International Conference on

Conference_Location

Beijing

ISSN

1062-922X

Print_ISBN

0-7803-3280-6

Type

conf

DOI

10.1109/ICSMC.1996.561472

Filename

561472