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A single server general bulk service finite source loss model has been studied. For this model the system steady state probabilities and waiting time distributions are obtained. Some performance measures are also calculated. Particular model is deduced and some numerical examples are also given. [ABSTRACT FROM AUTHOR]

A reduced system is a smaller system derived in the process of analyzing a larger system. In solving for steady state probabilities of a Markov chain, generally the solution can be found by first solving a reduced system of equations which is obtained by appropriately partitioning the transition probability (or rate) matrix. Following Lal (1981), a Markov chain can be categorized as standard or nonstandard depending on the location of an invertible submatrix necessary for an efficient solution in a transition probability (or rate) matrix. In this paper, algorithms for the determination of steady state probabilities are developed by using (i) a backward recursion which is efficient for standard systems and (ii) a forward recursion which is efficient for nonstandard systems. It is also shown that the backward recursion can be used for finding the first passage time distribution and its mean and variance. [ABSTRACT FROM AUTHOR]