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An efficient algorithm for semi-homogeneous queueing network models

The class of product-form semi-homogeneous queueing networks is introduced as a generalization of the class of homogeneous networks, which has been considered by Balbo et al for the performance modeling of local area networks. In semi-homogeneous networks, the relative traffic intensity at the various shared resources may depend on the routing chain to which a customer belongs. We develop an efficient algorithm for the exact analysis of this class of networks. It is based on the equations which form the foundation of RECAL, a general purpose exact algorithm for multiple-chain closed queueing networks. The complexity of the algorithm is shown to be of order less than exponential in (P-1)1/2, where P is the number of processors (workstations) in the network. It is therefore, in general, more efficient than a direct application of either convolution, MVA or RECAL to the class of semi-homogeneous queueing networks. The algorithm presented here may be situated between the algorithms of Balbo et al and the general purpose algorithms, both in terms of its generality and efficiency.