On Homogeneity and On-Line-Off-Line Behavior in M/G/1 Queueing Systems.
Abstract
Operational analysis replaces certain classical queueing theory assumptions with the conditions of 'homogeneous service times' and 'on-line=off-line behavior.' In the general case, it has been conjectured that these conditions hold as t-->infinity only if the service times are exponentially distributed. In this paper, we show that this is correct for stable M/G/1 queueing systems. We also state dual results for inter-arrival times in G/M/1. Finally, we consider the relationship between the operational quantities S(n) and the mean service time in M/G/1. This relationship is shown to depend on the form of the service time distribution. It follows that using operational analysis to predict the performance of an M/G/1 queueing system will be most successful when the service time is exponential. Simulation evidence is presented which supports this claim. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1980
- Accession Number
- ADA083827
Entities
People
- Raymond M. Bryant
Organizations
- University of Wisconsin–Madison