The M/G/1 Queue with Instantaneous, Bernoulli Feedback.
Abstract
This paper is concerned with several random processes that occur within the class of M/G/1 queues with instantaneous feedback in which the feedback decision process is a Bernoulli process. Such systems in the case G=M are the simplest, non-trivial examples of Jackson networks. Indeed, they are so simple that they are usually dismissed from consideration in queueing network theory as being obvious. It will be shown that far from being obvious they exhibit some important, unexpected properties whose implications raise some interesting questions about Jackson networks and their application. In particular, Jackson observed that in his networks the vector valued queue length process behaved as if the component processes were independent, M/M/1 systems. Since those results appeared there has developed a mythology to explain them. These arguments usually rest on three sets of results that are well known in random point process theory: superposition, thinning, and stretching. By examining the network flow, it will be shown that the application of these results are inappropriate to queueing network with instantaneous, Bernoulli feedback. Their flows are considerably more complicated than one expects based on such arguments and one is left to ponder what the Jackson results mean to queueing network decomposition.
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1977
- Accession Number
- ADA040555
Entities
People
- Donald C. Mcnickle
- Ralph L. Disney
Organizations
- University of Michigan