A Markovian bridge is a probability measure taken from a disintegration of the law of an initial part of the path of a Markov process given its terminal value. As such, Markovian bridges admit a natural parameterization in terms of the state space of the process. In the context of Feller processes with continuous transition densities, we construct by weak convergence considerations the only ver...

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 define a non-Markovian extension of Value Passing CCS, based on PHdistributions. The approach consists in describing the execution time of each action with a PH-distribution, i.e. by associating a finite CTMC with a terminal, absorbing, state to each action of a process. Such CTMC characterises a random variable, namely the time needed to go from the initial state to the final one. It is wel...

Abstract Priority queueing models have been commonly used in telecommunication systems. The development of analytically tractable models to determine their performance is vitally important. The discrete time batch Markovian arrival process (DBMAP ) has been widely used to model the source behavior of data traffic, while phase-type (PH) distribution has been extensively applied to model the serv...

We consider in this paper a class of vector valued processes that have the form Yn+1 = An(Yn)+ Bn. Bn is assumed to be stationary ergodic and An is assumed to have a divisibility property. This class includes linear stochastic difference equations as well as multi-type branching processes (with a discrete or with a continuous state space). We derive explicit expressions for the probability dist...

Vacation time queues with Markovian arrival process (MAP) are mainly useful in modeling and performance analysis of telecommunication networks based on asynchronous transfer mode (ATM) environment. This paper analyzes a single-server finite capacity queue wherein service is performed in batches of maximum size “b” with a minimum threshold “a” and arrivals are governed by MAP. The server takes a...

Abstract. Queueing systems with batch service have been investigated extensively during the past decades. However, nearly all the studied models share the common feature that an uncorrelated arrival process is considered, which is unrealistic in several real-life situations. In this paper, we study a discrete-time queueing model, with a server that only initiates service when the amount of cust...

In this paper we examine an existing model of composable internet switches from which statistical guarantees of service can be obtained. We then present some small analysis to show how the model can be implemented so that its assumptions, in this case about Markovian traffic streams, are in fact properties of the implementation. In order to achieve this we need to construct a box which makes th...

This paper presents a general framework for optimal task reallocation in heterogeneous distributed computing systems (DCSs). The framework relies on a rigorous analytical model for the stochastic execution time of a workload. The model takes into account the heterogeneity and randomness of both service times and communication delays, an arbitrary task-reallocation policy as well as the stochast...

Avi Mandelbaum , William A. Massey b and Martin I. Reiman c Davidson Faculty of Industrial Engineering and Management, Technion Institute, Haifa 32000, Israel E-mail: [email protected] b Bell Laboratories, Lucent Technologies, Office 2C-320, Murray Hill, NJ 07974, USA E-mail: [email protected] c Bell Laboratories, Lucent Technologies, Office 2C-315, Murray Hill, NJ 07974, USA E-m...