[...]... theory to system design The primary objective is to provide the reader with basic information that can form the basis of thought about how queuing theory can be applied to telecommunications problems The chapter concludes with a brief summary 1.1 The Terminology of Queueing Systems In this section, we introduce the reader to the terminology of queueing theory and to some definitions from the theory of stochastic... the study of queueing systems as they apply to telecommunications networks and systems Our objective is to provide sufficient background to allow our readers to formulate and solve interesting queueing problems in the telecommunications area The book contains a selection of material that provides the reader with a sufficient background to read much of the queueing theory- based literature on telecommunications... been a trend towards ubiquitous service over packet- switched facilities, the primary motivation being cost reduction resulting from an increased capability to share resources The primary obstacle has been the development of mechanisms that assure quality of service at a competitive costs Queueing theory is one of the primary tools used to deal QUEUEING THEORY FOR TELECOMMUNICATIONS 2 with questions... integers Our goal is to review and reinforce a subset of the ideas and principles from the theory of stochastic processes that is needed for understanding queueing systems As an example, we review in detail the relationship between discretetime and discrete-parameter stochastic processes, which is very important to the understanding of queueing theory but often ignored in courses on stochastic processes... and then, under contract with the Government of the United States of America (USA), built the first telegraph system in 1843 Immediately, waiting lines began to form by those wanting to use the system Thus, queueing problems in telecommunications began virtually simultaneously with the advent of electrical telecommunications The world-wide telecommunications infrastructure of today consists largely of... same variables without tildes For example, denotes a random variable and denotes its value 4 QUEUEING THEORY FOR TELECOMMUNICATIONS Figure 1.3 Sequence of events for general customer DEFINITION 1.1 Stochastic process (Ross [1983]) A stochastic process (SP) is a collection of random variables, indexed on That is, for each is a random variable We now turn to a more formal definition of a queueing process... K denotes the number of customers allowed to wait Sometimes the 8 QUEUEING THEORY FOR TELECOMMUNICATIONS notation GI is used in place of G to emphasize independence, as, for example, in the notation GI/M/l/K to denote the queueing system having general and independent interarrivals, a single exponential server, and a finite waiting room of capacity K.2 Remark The induced queueing process is defined... The system is now in a busy state, and the amount of time required to satisfy the customer’s needs is dependent upon how many calls the customer makes, how long it takes to set up each call, and how long it takes the customer to conduct the business at hand Define the total amount of time the telephone system is occupied by this customer as the service-time requirement, or simply the service-time of... device led to a deployed electrical telecommunications system in 1843, waiting lines began to form by those wanting to use the system At this writing queueing is still a significant factor in designing and operating communications services, whether they are provided over the Internet or by other means, such as circuit switched networks This book is intended to provide an efficient introduction to the fundamental... 100 customers from (1.2) for can be obtained from and compute DEFINITION 1.6 Busy period With reference to Figure 1.4, it is seen that the unfinished work is 0 prior to and that the level of unfinished work returns Terminology and Examples 7 to zero after customer is served The period of time between a transition from zero to a positive level of unfinished work and a transition from a positive to zero . I attest to the accuracy and integrity of this document Date: 2005.05.26 21:14:08 +08'00' QUEUEING THEORY WITH APPLICATIONS TO PACKET TELECOMMUNICATION This. PACKET TELECOMMUNICATION This page intentionally left blank QUEUEING THEORY WITH APPLICATIONS TO PACKET TELECOMMUNICATION JOHN N. DAIGLE Prof. of Electrical Engineering The