Abstract This paper considers a FIFO single-server queue with service interruptions and multiple batch Markovian arrival streams. The server state (on and off), the type of arriving customers and their batch size are assumed to be governed by a continuous-time Markov chain with finite states. To put it more concretely, the marginal process of the server state is a phase-type alternating Markov ...

We propose a traffic measurement system which uses trap and polling methods. To obtain its performance we consider a queueing model with a single server and evaluate a packet delay. In our multi-cast traffic, packets are modeled as a batch with a batch size distribution {gk}. The batch arrival process is observed as two processes on the basis of batch size. For a batch whose size is more than o...

We address the batch arrival  systems with finite capacity under partial batch acceptance strategy where service times or rates oscillate between two forms according to the evolution of the number of customers in the system. Applying the theory of Markov regenerative processes and resorting to Markov chain embedding, we present a new algorithm for computing limit distributions of the number cus...

In this paper a study on the buffer overflow period in a finite-buffer queue is presented. A special attention is paid to the autocorrelation and batch arrivals, which are supposed to mimic the properties of real arrival processes. Using the batch Markovian arrival process, formulas for the duration of the first, subsequent and stationary overflow periods, as well as formulas for the distributi...

Previously, we derived the two-dimensional transforms of the emptiness function, the transient workload and queue-length distributions in the single-server queue with general service times and a batch Markovian arrival process (BMAP). This arrival process includes the familiar phase-type renewal process and the Markov modulated Poisson process as special cases, as well as superpositions of thes...