SOME INEQUALITIES FOR SINGLE SERVER QUEUES
Abstract
The expected wait in the Gl/G/1 queue is related to the mean and variance of the idle time. For arrival distributions which are IFR or have man residual life bounded by 1/lambda, simple bounds are obtained which give, for example, the expected number in queue to within at most one customer. By equating input with output, relations between random variables are used to obtain expressions for the moments of the waiting time in terms of moments of the inter-arrival, service, and idle time distributions. By bounding the idle time moments, bounds are obtained on the mean and variance of the waiting time, the mean length of a busy period, and the probability an arrival finds the system empty. Bounds on the mean wait lead to bounds on the expected virtual wait. Similar results are obtained for some generalizations of the G1/G/1 queue, including batch arrivals, batch service and priority queues. Queues where the first customer in each busy period has some added delay are also considered. Some preliminary results for tandem queues are given.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1966
- Accession Number
- AD0639168
Entities
People
- Kneale T. Marshall
Organizations
- University of California, Berkeley