We investigate the transient and stationary queue-length distributions of a class of service systems with correlated service times. The classical MX/G/1 queue with semi-Markov service times is the most prominent example in this class and serves as a vehicle to display our results. The sequence of service times is governed by a modulating process J(t). The state of J(·) at a service initiation t...

We consider a class of finite Markovian queueing models and obtain uniform approximation bounds of truncations. INTRODUCTION It is well known that explicit expressions for the probability characteristics of stochastic models can be found only in a few special cases, moreover, if we deal with an inhomogeneous Markovian model, then we must approximately calculate the limiting probability characte...

This dissertation is concerned with the study of non-Markovian queueing systems and networks, with applications to communication networks. The main contribution of the dissertation consists in deriving results for non-Markovian networks that have been obtained so far only for Markovian queueing networks. We study large closed client/server communication networks and losses in single-server queu...

this paper analyzes an m/m/2 queueing system with two heterogeneous servers. both servers goes on vacation when there is no customers waiting for service after this server 1 is always available but the other goes on vacation whenever server 2 is idle. the vacationing server however, returns to serve at a low rate as an arrival finds the other server busy. the system is analyzed in the steady st...

This paper provides an accurate model of the General Packet Radio Service (GPRS). GPRS is modeled as a single server queue in a Markovian environment. The queueing performance of data packets is evaluated by matrix geometric methods. The arrival process is assumed to follow a two state Markov modulated Poisson process (MMPP), and the service rate fluctuates based on voice loading. The analytica...

We consider a Markovian queue subject to Poisson generated catastrophes. Whenever a catastrophe occurs, all customers are forced to abandon the system, the server is rendered inoperative and an exponential repair time is set on. We assume that the arriving customers decide whether to join the system or balk, based on a natural reward-cost structure. We study the balking behavior of the customer...

We establish in a direct manner that the steady state distribution of Markovian fluid flow models can be obtained from a quasi birth and death queue. This is accomplished through the construction of the processes on a common probability space and the demonstration of a distributional coupling relation between them. The results here provide an interpretation for the quasi-birth-and-death process...

We consider a Markovian queue subject to Poisson generated catastrophes. Whenever a catastrophe occurs, all customers are forced to abandon the system, the server is rendered inoperative and an exponential repair time is set on. We assume that the arriving customers decide whether to join the system or balk, based on a natural reward-cost structure. We study the balking behavior of the customer...

The convex analytic approach which is dual, in some sense, to dynamic programming, is useful for the investigation of multicriteria control problems. It is well known for discrete time models, and the current paper presents similar results for the continuous time case. Namely, we define and study the space of occupation measures, and apply the abstract convex analysis to the study of constraine...

We consider finiteand infinite-capacity queues with discrete-time batch Markovian arrival processes (D-BMAP) under the assumption of the Late Arrival System with Delayed Access as well as the Early Arrival System. Using simple arguments such as the balance equation, “rate in = rate out,” we derive relationships among the stationary queue lengths at arrival, at departure, and at random epochs. S...