Discrete-Time Single-Server System with Requests of Several Types

The authors analyze a discrete-time single-server $\mathrm{Geom}_k|\mathrm{Geom}_k|1|R|f_0$ queuing system (QS) with several types of incoming requests. The time intervals between arrivals and the servicing durations are independent and distributed geometrically (the discrete analog of the exponential distribution). Scalar and matrix relations are obtained for the distribution of the stationary state probabilities of the Markov chain describing the QS. It is shown that, as the discretization unit $h$ tends to zero, the solution for an $M_k|M_k|1|R|f_0$ QS is obtained. A numerical example is given.