Fluid models have for some time been used to approximate stochastic networks with discrete state. These range from traditional ‘heavy traffic’ approximations to the recent advances in bio-chemical system models. Here we present a simple approximate compositional method for analysing a network of fluid queues with Markovmodulated input processes at equilibrium. The idea is to approximate the on/...

This paper examines a discrete-time queuing system with applications to telecommunications traffic. The arrival process is a particular Markov modulated process which belongs to the class of discrete batched Markovian arrival processes. The server process is a single server deterministic queue. A closed form exact solution is given for the expected queue length and delay. A simple system of equ...

A finite-buffered banyan network analysis technique designed to model networks at high traffic loads is presented. The technique specially models two states of the network queues: queue empty and queue congested (roughly, zero or one slots free). A congested queue tends to stay congested because packets bound for the queue accumulate in the previous stage. The expected duration of this state is...

Queueing network models have proven to be very useful in the analysis of communication systems. The departure process of a queue in a queueing network is of special interest because it is the arrival process to other queues in the network. For high speed networks, correlation and burstiness are very important factors for system performance and thus the smooth Bernoulli process is no longer a go...

Abstract: We consider a discrete-time 1 X Geo G retrial queue with general retrial times, and introduce working vacations and vacation interruption policy into the retrial queue. Firstly, we analyze the stationary condition for the embedded Markov chain at the departure epochs. Secondly, using supplementary variable method, we obtain the stationary probability distribution and some performance ...

We consider the stationary distribution of the M/GI/1 type queue when background states are countable. We are interested in its tail behavior. To this end, we derive a Markov renewal equation for characterizing the stationary distribution using a Markov additive process that describes the number of customers in system when the system is not empty. Variants of this Markov renewal equation are al...

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...

In this paper, we focus on queues with a superposition of periodic and bursty sources where the initial states of the sources are randomly and independently selected. The dynamics of the queue are described as a reducible Markov chain. For such queues, we consider the tail probability of the queue length as the performance measure and try to estimate it by simulations. To do simulation efficien...

This paper studies a continuous time queueing system with multiple types of customers and a first-come-first-served service discipline. Customers arrive according to a semi-Markov arrival process and the service times of individual types of customers have PH -distributions. A GI /M /1 type Markov process for a generalized age process of batches of customers is constructed. The stationary distri...