Abstract. In this paper a queuing system with an in nite number of servers is considered. Customers arrive in the system according to a Markovian Arrival Process. Each customer carries a random quantity of work (capacity of the customer). In this study service time does not depend on the customers' capacities; the latter are used just to x some additional features of the system evolution. It is...

We treat a single–server vacation queue with queue–length dependent vacation schedules. This subsumes the single–server vacation queue with exhaustive service discipline and the vacation queue with Bernoulli schedule as special cases. The lengths of vacation times depend on the number of customers in the system at the beginning of a vacation. The arrival process is a batch–Markovian arrival pro...

In this paper we introduce and analyze a model of a multiplexer queue with a batch Markovian arrival process and a special, timer based, non-work-conserving service discipline. We show that the embedded process at departures is an M/G/1 type process with proper state partitioning, which can be efficiently analyzed by matrix geometric methods. We derive the expressions to compute the distributio...

We derive in this paper the transient queue length and the busy period distributions of a single server queue with phase-type (PH) service times and a batch Markovian arrival process (BMAP). These distributions are obtained by the uniformization technique which gives simple recurrence relations. The main advantage of this technique is that it leads to stable algorithms for which the precision o...

In this paper, we consider a discrete time queueing system fed by a superposition of an ON and OFF source with heavy tail ON periods and geometric OFF periods and a D-BMAP (Discrete Batch Markovian Arrival Process). We study the tail behavior of the queue length distribution and both infinite and finite buffer systems are considered. In the infinite buffer case, we show that the asymptotic tail...