The Omni-Transform in Single-Channel Queues.
Abstract
The method of omni-equations along with the conservation method is well-suited to the treatment of the process 'unfinished work'--or 'backlog' for terseness--in the model M/G/1. Since some partial results have also been obtained for the more general model G/G/1 we shall start with G/g/1 under steady-state conditions. Throughout this paper linear omni-equations will be subject to the omni-convention, i.e., it will be understood that the expectation is taken of each side of the omni-equation with respect to each random variable. An analogy was pointed out between the process 'waiting time in M/G/1' and the process 'toss a coin till 'heads' show up' where the tossing time is a random variable. The omni-calculus also sheds some light on the model G/G/1. Keywords include: Backlog, Omni-transform, Single-channel queue, Free-copy, Removal equations, Mixtures, Residual time, Omni-equation.
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1985
- Accession Number
- ADA151019
Entities
People
- M. Krakowski
Organizations
- University of Virginia