Sojourn Times in Markov Queueing Networks: Little's Formula Revisited.
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 and/or 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 Little's 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1980
- Accession Number
- ADA089658
Entities
People
- Frederick J. Beutler
Organizations
- University of Michigan