Derivation of Equilibrium and Time-Dependent Solutions to M/M/Infinity/ /N and M/M/Infinity Queueing Systems Using Entropy Maximization.

摘要

Conventional approaches to the solution of queueing and similar stochastic problems use differential equations in the probabilities or probability densities of appropriate system states. Although this approach has had widespread success, it has some conceptual difficulties. It is the author's opinion that work by R.T. Cox and E.T. Jaynes may offer a better conceptual foundation for the study of stochastic processes. The purpose of this report is to support that opinion by illustrating the application of the Cox-Jaynes approach to the analysis of M/M/infinity/ /N and M/M/infinity queueing systems. Both equilibrium and time-dependent distributions are derived.