System Size in Some Variants of M/G/1.
Abstract
For some queueing models with Poisson input and the first-in-first-out property (this includes the model M/D/c) the size probabilities for the queue and the system can be formulated in terms of (1) the transit equation which relates the size of the system, as seen by a departing customer, to the size of the queue lift behind by this customer upon entering the service station; and (2) the static equation which relates the queue size to system size at a random instant. When the solutions are stated in matrix form the matrices are stochastic; this assures the convergence of an iterative algorithm for computing the state probabilities. The method presented in this paper are direct methods, that is these are obtained without recourse to, or specialization of, the equations for the process waiting for service or time spent in the system. The indirect methods based on these processes can be very effective, especially when one is interested in both waiting for service and queue size. For some vacation models the indirect methods are the simpler ones. However, the author will deal with these indirect techniques in a future report. Keywords: computer networks.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1986
- Accession Number
- ADA175611
Entities
People
- Martin Krakowski
Organizations
- George Mason University