PAM-a noniterative approximate solution method for closed multichain queueing networks

Abstract

Approximate MVA algorithms for separable queueing networks are based upon an iterative solution of a set of modified MVA formulas. Although each iteration has a computational time requirement of O(MK 2) or less, many iterations are typically needed for convergence to a solution. (M denotes the number of queues and K the number of closed chains or customer classes.) We present some faster approximate solution algorithms that are noniterative. They are suitable for the analysis and design of communication networks which may require tens to hundreds, perhaps thousands, of closed chains to model flow-controlled virtual channels. Three PAM algorithms of increasing accuracy are presented. Two of them have time and space requirements of O(MK). The third algorithm has a time requirement of O(MK 2) and a space requirement of O(MK).

Product Form Queueing Networks

“…Various bounding methods such as Balanced Job Bounds, Proportional Bound and Performance Bound Hierarchies (PBH) techniques [67,25,32,33] provide bounds on the average performance measures. Some techniques are based on the MVA equations, such that the PBH method that provides increasingly tighter bounds at the expense of increasing computation cost.…”