System Size and Remaining Service in M/G/1
Abstract
Wishart and Takacs derived the joint distribution of the size N and residual service R as encountered by a new arrival into a regular M/G/1. Wishart obtained the following expression for the generating function pi(z,x) = Sum from 0 to infinity (Pi sub j(x)z to the j power), where pi sub j = over d Pr(R is < or = to x, N = j): pi(z,x) = ((1 - rho) lambda z (1 - z)/(eta(lambda-z lambda)- z) Integral from 0 to infinity exp(-lambda (1 - z) xi) (H(xi + x) - H(xi))d xi. We exploit the fact that the system size N is known and find the conditional r. v.'s R sub j = residual service seen while N = j. Our method seems better suited to numerical work and we extend it to some variants of M/G/1: M/G/1/K, and then M/G/1 and M/G/1/K with state dependent service and arrival rates.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 14, 1989
- Accession Number
- ADA211718
Entities
People
- Martin Krakowski
Organizations
- George Mason University