A single-server queueing system with a batch Markovian arrival process (BMAP) and MAP-input of disasters causing all customers to leave the system instantaneously is considered. The system has two operation modes, which depend on the current queue length. The embedded and arbitrary time stationary queue length distribution has been derived and the optimal control threshold strategy has been det...

The simplest (stationary) queueing models with catastrophes have been studied some years ago, see for instance [1–6, 9]. Namely, when the queue is not empty, catastrophes may occur with the respective rates. The effect of each catastrophe is to make the queue instantly empty. Simultaneously, the system becomes ready to accept new customers. Nonstationary Markovian queueing models (birthdeath pr...

A new queue, referred to here as the HetSigma queue, in the Markovian framework, is proposed in order to model nodes in modern telecommunication networks. The queue has many of the necessary ingredients, such as joint (or individual) Markov modulation of the arrival and service processes, superposition of K CPP (compound Poisson process) streams of (positive) customer arrivals, and a CPP of neg...

We consider a finite buffer fluid queue receiving its input from the output of a Markovian queue with finite or infinite waiting room. The input flow into the fluid queue is thus characterized by a Markov modulated input rate process and we derive, for a wide class of such input processes, a procedure for the computation of the stationary buffer content of the fluid queue and the stationary ove...

This paper presents a discrete-time single-server finite buffer N threshold policy queue with renewal input and discrete Markovian service process. The server terminates service whenever the system becomes empty, and recommences service as soon as the number of waiting customers in the queue is N . We obtain the system-length distributions at prearrival and arbitrary epochs using the supplement...

We consider a uid queue receiving its input from the output of a Marko-vian queue with nite or innnite waiting room. The input rate of the uid queue is characterized by a Markov modulated rate process. We derive a new approach for the computation of the stationary buuer content. This approach leads to a numerically stable algorithm for which the precision of the result can be given in advance. ...

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...

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...

We show that, for the M/M/∞ queue in a Markovian random environment, the joint probability distribution function (pdf) of the two variables: random phase and number of customers in the system, is equal to the product of the corresponding marginal pdfs if and only if the ratio of arrival rate to service rate is the same for all phases. We explicitly derive this joint pdf. Furthermore, for the ge...