Algorithmic Computation of the Time-Dependent Solution of Structured Markov Chains and Its Application to Queues

ABSTRACT This paper considers spatially inhomogeneous bivariate Markov chains with the skip free to one direction (i.e., the left or right) property. For Markov chains of each type, we develop a numerically feasible algorithm to compute the approximation to the whole time-dependent solution, whose absolute error can be set in advance. To demonstrate the applicability of the proposed algorithms, we provide some numerical results for the time-dependent queue length distribution in BMAP/PH/1 queues with and without balking. As you will see, the proposed algorithms are applicable not only to the positive recurrent case, but also to null recurrent and transient cases.