In this paper we study a Geo/T-IPH/1 queue model, where T-IPH denotes the discrete time phase type distribution defined on a birth-and-death process with countably many states. The queue model can be described by a quasi-birth-anddeath (QBD) process with countably phases. Using the operator-geometric solution method, we first give the expression of the operator and the joint stationary distribu...

For the discrete D/G/1 queue, the stationary waiting time can be expressed in terms of infinite series that follow from Spitzer’s identity. These series involve convolutions of the probability distribution of a discrete random variable, which makes them suitable for computation. For practical purposes, though, the infinite series should be truncated. We therefore seek for some means to characte...

Priority scheduling for packets is a hot topic, as interactive (voice,video) services are being integrated in existing data networks. In this paper, we consider a discrete-time queueing system with nonpreemptive (or Head-Of-the-Line) priority scheduling and a general number of priority classes. Packets of variable length arrive in the queueing system. We derive expressions for the probability g...

Priority queueing systems come natural when customers with diversified delay requirements have to wait to get service. The customers that cannot tolerate but small delays get service priority over customers which are less delay-sensitive. In this contribution, we analyze a discretetime two-class preemptive repeat identical priority queue with infinite buffer space and generally distributed serv...

We analyze a discrete-time queue with variable service capacity, such that the total amount of work that can be performed during each time slot is a stochastic variable that is geometrically distributed. We study the buffer occupancy by constructing an analogous model with fixed service capacity. In contrast with classical discrete-time queueing models, however, the service times in the fixed-c...

In this paper, we present a transient analysis of the system contents in a two-class priority queue with single-slot service times. In particular, we derive an expression for the generating function of the transient system contents of both classes. Performance measures are calculated from this generating function. Finally, by means of a numerical example we investigate the impact of the traffic...

In this paper we compare the queue performances of three different traces with gaussian marginals generated using the discrete-time Fractional Gaussian Noise algorithm [1]. We have introduced some additional features in one out of the three traces generation process to have less dependence on very large time scale (as it is the case in video traffic). We highlight the issues at stake when we lo...

The information-theoretic capacity of continuous-time single-server queues has been analyzed recently by Anantharam and Verdu 1]. They observed that information is transmitted through a queue not only by the contents of the packets but also by the arrival times of these packets. The sequence of packet interarrival times can be used as a code to convey information to the receiver, who observes t...

This paper concentrates on the steady state analysis of the discrete-time batch arrival Geo/G/1 queue with vacations. In this model, after serving all customers in the system, the server will take a random maximum number of vacations before returning to the service mode. The distributions of busy period, vacation period and vacation cycle have been given. Meanwhile, the PGFs for the off-line pe...