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

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 <italic>O(MK<supscrpt>2</supscrpt>)</italic> or less, many iterations are typically needed for convergence to a solution. (<italic>M</italic> denotes the number of queues and <italic>K</italic> the number of closed chains or customer classes.) We present some faster approximate solution algorithms that are <italic>noniterative</italic>. 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 <italic>O(MK)</italic>. The third algorithm has a time requirement of <italic>O(MK<supscrpt>2</supscrpt>)</italic> and a space requirement of <italic>O(MK)</italic>.

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