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

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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) .

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