System analysis is often needed with respect to both qualitative and quantitative aspects. In the last decades, several formalisms have been developed that attempt to combine these aspects in one description. Present emphasis is on Stochastic Petri Nets. Amongst others, one disadvantage of these formalisms lies with the diiculties when describing scheduling strategies with Petri Net elements. T...

Queueing network modeling of manufacturing systems has been addressed by a large number of researchers. The purpose of this paper is to provide a bibliography of material concerned with modeling of production and transfer lines using queueing networks. Both production and transfer lines have a product-flow layout and are used in mass manufacturing. We denote production lines as flow lines with ...

A class of queueing networks which consist of single-server fork-join nodes with infinite buffers is examined to derive a representation of the network dynamics in terms of max-plus algebra. For the networks, we present a common dynamic state equation which relates the departure epochs of customers from the network nodes in an explicit vector form determined by a state transition matrix. We sho...

We introduce Bayesian Expansion (BE), an approximate numerical technique for passage time distribution analysis in queueing networks. BE uses a class of Bayesian networks to approximate the exact joint probability density of the model by a product of conditional marginal probabilities that scales efficiently with the model size. We show that this naturally leads to decomposing a queueing networ...

This paper investigates geometric stability and L p-stability of discrete-time Markov chains associated with closed and open queueing networks with Markovian routing. By geometric stability (resp. L p-stability) we mean that the chain is re-generative in the Harris-recurrent sense and that the times between the successive regeneration points have a bounded moment generating function (resp. a bo...

This paper addresses the problem of constructing multidimensional Markov chains with product form steady state distribution. Product connection theorems are established which guarantee that the product ∏ ν π (ν) nν of steady state probabilities π (ν) nν related to ergodic Markov chains X (ν) = {X(ν)(t) : t ∈ T} represents the steady state probability p(n) = p(n1, n2, . . .) of an ergodic multid...

We introduce a new method to investigate stability of work-conserving policies in multiclass queueing networks. The method decomposes feasible trajectories and uses linear programming to test stability. We show that this linear program is a necessary and suucient condition for the stability of all work-conserving policies for multiclass uid queueing networks with two stations. Furthermore, we n...

Mean value analysis is an exact solution technique for infinite capacity queueing networks and enjoyed widespread popularity during recent years. It considers the behavior of the system by stepwise increasing the number of jobs in the entire network, thus it is well-suited for the analysis of queueing networks with blocking. In this work, an approximation is introduced for the mean value analys...

Abstract This paper is concerned with a class of multidimensional diffusion processes, variously known as reflected Brownian motions, regulated Brownian motions, or just RBM’s, that arise as approximate models of queueing networks. We develop an algorithm for numerical analysis of a semimartingale RBM with state space S Rd (the non-negative orthant of d-dimensional Euclidean space). This algori...

We introduce queueing network models for characterizing and modeling the performance of graph programs. We show that graph programs can be modelled as a queuing network whose behaviour can be mapped to a queueing network of the underlying architecture. Operational analysis of these queueing networks allows us to systematically analyze performance and identify performance bottlenecks. We demonst...