Accession Number:

ADA089658

Title:

Sojourn Times in Markov Queueing Networks: Little's Formula Revisited.

Descriptive Note:

Interim rept.,

Corporate Author:

MICHIGAN UNIV ANN ARBOR COMPUTER INFORMATION AND CONTROL ENGINEERING PROGRAM

Personal Author(s):

Report Date:

1980-06-01

Pagination or Media Count:

37.0

Abstract:

It is commonly supposed that L lambda W applies to almost any queueing system, with lambda the mean customer entrance rate, L the asymptotic expectation of the number of customers in the system, and W the asymptotic sojourn time expectation. We study the formula for irreducible positive recurrent Markov queueing systems whose state vector Z consists of entries representing queue lengths at the respective service stations such a model permits blocking, finite capacities, jockeying, state-dependent or random routing, bulk andor Erlang service, and variable arrival and service rates. To define waiting times under various queueing disciplines, Z is augmented by a customer location process to yield the new Markov process Y Z,U. It is shown that the standard regenerative process proof of Littles equality fails in the absence of further hypotheses however, additional assumptions assure the validity of L lambda W for a broad variety of queueing disciplines.

Subject Categories:

  • Statistics and Probability

Distribution Statement:

APPROVED FOR PUBLIC RELEASE