The distribution of delays of dispersed messages in an M/M/1 queue

Author

Altman, Eitan ; Jean-Marie, Alain

Author_Institution

Inst. Nat. de Recherche en Inf. et Autom., Sophia Antipolis, France

fYear

1995

fDate

2-6 Apr 1995

Firstpage

338

Abstract

We analyze the distribution of the delay of messages in an infinite capacity M/M/1 queue. A message is composed of n packets, and the arrival of the packets to the queue is Poisson. Our calculations are based on recursive schemes. We obtain explicit expressions for the Laplace-Stieltjes transform (LST) of the delays, which enables to obtain exact expressions for the moments of the delay in a complexity smaller than the one obtained by using recursive schemes. We repeat the above calculations for the case that messages are dispersed, i.e. packets from several sources arrive to an M/M/1 queue and are served according to the FIFO discipline. Hence, several packets of other messages may arrive between consecutive packets of a given message

Keywords

Laplace transforms; delays; message switching; packet switching; queueing theory; stochastic processes; FIFO discipline; Laplace-Stieltjes transform; M/M/1 queue; Poisson arrival; delay distribution; dispersed messages; infinite capacity queue; packets; recursive schemes; Delay effects; Protocols; Queueing analysis; Random variables; Steady-state; Tail;

fLanguage

English

Publisher

ieee

Conference_Titel

INFOCOM '95. Fourteenth Annual Joint Conference of the IEEE Computer and Communications Societies. Bringing Information to People. Proceedings. IEEE

Conference_Location

Boston, MA

ISSN

0743-166X

Print_ISBN

0-8186-6990-X

Type

conf

DOI

10.1109/INFCOM.1995.515893

Filename

515893