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Extensions and computational aspects of an iterative method

The so-called iterative methods are among a class of methods that have recently been applied to obtain approximate solutions to general queueing networks. In this paper it is shown that if the network contains feedback loops, then it is more advantageous to incorporate these loops into the analysis of the station itself rather than into the analysis of the complement of the station. We show how this analysis may be performed for a simple two-phase Coxian server. Additionally, it is shown that the number of iterations required to achieve a specified degree of accuracy may be considerably reduced by using a continuous updating procedure in which the computed throughputs are incorporated as soon as they are available, rather than at the end of an iteration. An efficient computational scheme is presented to accompany this continuous updating. Finally a number of examples are provided to illustrate these features.