Abstract
This paper presents an algorithmic approach to calculate the loss probability of customers in discrete time D-BMAP/PH/1/N queue, where the service time follows the discrete phase-type distribution. We give closed form expressions for the elements of the transition probability matrix of the underlying three-dimensional Markov chain. We use a matrix-analytic method to compute the steady-state distribution of the number of customers in the system. We compute the loss probability as a function of the system capacity using the steady-state distribution. We obtain the asymptotic behavior of the loss probability function. Numerical examples are provided to study the behavior of the loss probability function.
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