This paper analyses a multiple class single server M/M/1/K queue with finite capacity under weighted fair queuing (WFQ) discipline. The Poisson process has been used to model the multiple classes of arrival streams. The service times have exponential distribution. We assume each class is assigned a virtual queue and incoming jobs enter the virtual queue related to their class and served in FIFO...

An efficient yet accurate estimation of the tail distribution of the queue length has been considered as one of the most important issues in call admission and congestion controls in ATM networks. The arrival process in ATM networks is essentially a superposition of sources which are typically bursty and periodic either due to their origin or their periodic slot occupation after traffic shaping...

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. ...

In this paper, we study a finite capacity queue where the arrival process is special case of discrete time Markov modulated Poisson process, service times are generally distributed, and server takes repeated vacations when system empty. The buffer acceptance strategy based on generalized push-out scheme: full, an arriving customer pushes out Nth in queue, N values between 2 system, joins end qu...

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...

One of the classical, but yet unsolved queueing systems is the M/G/k queue with Poisson input, general service time distribution and serving facilities. In the present paper, this queue is analyzed as a piecewise–deterministic Markov process. First, an iteration formula for the transient distributions is derived. This formula is a new result for piecewise–deterministic Markov processes, too, si...

We present a non-equilibrium analysis and control approach for the Active Queue Management (AQM) problem in communication networks. Using simplified fluid models, we carry out a bifurcation study of the complex dynamic queue behavior to show that non-equilibrium methods are essential for analysis and optimization in the AQM problem. We investigate an ergodic theoretic framework for stochastic m...

This paper gives a natural definition of the relaxation time for general single server queues. First, we describe a GI/GI/I queue as a limit of GI/GPH/I queues. Each GI/GPH/I queue is transferred to some equivalent bulk arrival GIx/M/I queue, which is formulated by a spatially homogeneous Markov chain with reflecting barrior at zero. An upper bound, which is easy to calculate, of the relaxation...

Batch arrival and batch service queueing systems are of importance in the context telecommunication networks. None work reported so far consider dependence consecutive batches. Batch Markovian Arrival Process(\begin{document}$ BMAP $\end{document}) Service Process (\begin...