Queue - Networks

The purpose of this tutorial is to survey queueing networks, a class of stochastic models extensively applied to represent and analyze resource sharing systems such as communication and computer systems. Queueing networks (QNs) have been proved to be a powerful and versatile tool for system performance evaluation and prediction. First we briefly survey QNs that consist of a single service center, i.e., the basic queueing systems defined under various hypotheses, and we discuss their analysis to evaluate a set of performance indices, such as resource utilization and throughput and customer response time. Their solution is based on the introduction of an underlying stochastic Markov process. Then, we introduce QNs that consist of a set of service centers representing the system resources that provide service to a collection of customers that represent the users. Various types of customers define the customers classes in the network that are gathered in chains. We consider various analytical methods to analyze QNs with single-class and multiple-class. We mostly focus on product-form QNs that have a simple closed form expression of the stationary state distribution that allows to define efficient algorithms to evaluate average performance measures. We review the basic results, stating from the BCMP theorem that defines a large class of product-form QNs, and we present the main solution algorithms for single-class e multiple-class QNs. We discuss some interesting properties of QNs including the arrival theorem, exact aggregation and insensitivity. Finally, we discuss some particular models of product-form QNs that allow to represent special system features such as state-dependent routing, negative customers, customers batch arrivals and departures and finite capacity queues. The class of QN models is illustrated through some application examples of to analyze computer and communication systems.