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Most queuing analyses performed in the literature are based on characterization of queueing phenomena in continuous-time items. Recently in the telecommunication industries, BISDN (broadband integrated services digital network) has received considerable attention since it can provide a common interface for future communication needs including video, data, and speech. Since information in BISDN is transported by means of dicsrete units of 53-octet ATM (asynchronous transfer mode) cells, interests in discrete-time systems have increased.
Discrete-Time Models for Communication Systems Including ATM provides a general framework for queueing analyses of dicrete-time systems. After a brief look at past studies of discrete-time systems, a detailed description and analysis are presented for a generic discrete-time model with a single server, arbitrary service times and independent arrivals. The book then follows a less stringent approach and focuses more on the average statistics and on different queueing disciplines. Conventional first-in-out and last-in-first-out disciplines are discussed in terms of the average statistics. Systems with multiple classes of messages without class-dependent priorities are considered to establish a discrete-time conservation law. Multiple classes with priorities are also considered to derive performance measures of priority scheduling disciplines. Finally, a multi-queue system with cyclic service is analyzed in the context of round-robin service ordering.
This is followed by analyses of discrete-time queueing systems with `more complicate' input and output processes. Specifically, single-server systems are investigated whereby either the arrivals or the server is subject to random interruptions. Results are mainly obtained in terms of generating functions and mean values of the principal performance measures. The influence of the nature of the arrival correlation and the server interruptions on the queueing behavior is discussed. Finally, the book explores queueing models directly associated with ATM switches and multiplexers.
This book is a valuable reference and may be used as a text for and advanced course on the subject.



Chapter 1. Independent Arrivals

A discrete-time system is characterized by time-slotted and synchronous service. After a brief review of literature for discrete-time models, section 1.2 presents the definition and analysis of a general discrete-time model with a single server, arbitrary service times and independent arrivals.
Herwig Bruneel, Byung G. Kim

Chapter 2. Scheduling Disciplines

When more than one message (customer) is waiting in the buffer, the next message to be served is determined by the scheduling policy. Some scheduling disciplines are studied in this chapter. The primary performance measure of interest is the expected waiting time of messages. Section 2.1 considers a single class of messages. The performance results of the FIFO (First-In, First-Out) discipline from chapter 1 are presented in a different perspective. Those of the the LIFO (Last-In, First-Out) discipline are derived as well in the section. Queueing systems with multiple classes are considered in the next two sections. A work conservation property is established in section 2.2, whereas several priority disciplines are considered in section 2.3. Finally, in section 2.4, the cyclic service discipline is examined as it is applied to a system with multiple queues.
Herwig Bruneel, Byung G. Kim

Chapter 3. More Complicated Models

In the previous chapters, rather simple models have been adopted with respect to stochastic processes for inputs to and outputs from the buffer. Specifically, arrivals have been assumed to occur independently from one time slot to another, and the output channel, i.e., the server of the buffer queueing system, has been considered permanently available. Both these simplifying assumptions are not always realistic in real-life situations. For instance, in many applications the arrival process of units into the buffer is in some sense “correlated,” because users (or “data sources”) usually generate data in a “bursty” fashion, i.e., a user which is active in a given slot is very likely to generally remain inactive for a large number of consecutive slots. On the other hand, the output channel of a buffer system may be subject to (more or less) random interruptions, for various reasons: there may be failures of the channel, transmissions may be sometimes unreliable, the channel may have to be shared with other (higher priority) communication systems, etc. In order to be able to deal with these kinds of situations, more complicated queueing models than in the previous chapters are needed.
Herwig Bruneel, Byung G. Kim

Chapter 4. Applications to ATM

Broadband Integrated Services Digital Network (BISDN) is conceived as a universal digital network providing both integrated switching and services. Typical services include data, voice, video, high-resolution image, etc. [Spea 87]. Encouraged by developments of fast packet switches [Turn 85] and ATD experiments in France [Deva 88], a packet-oriented virtual circuit transfer mode, called ATM (Asynchronous Transfer Mode), has been adopted as the universal transport vehicle of BISDN services [Minz 89]. Data from various sources are segmented into fixed-size ATM cells and statistically multiplexed to high-speed transmission lines and switches. An ATM cells consists of a 5-octet header and a 48-octet payload fields. Unlike the conventional STM (Synchronous Transfer Mode) technique which switches data according to positions in recurrent structure (frame), ATM cells are switched by labels containing routing information in the headers. Label-based switching is believed to be flexible in integrating diverse traffic types, envisioned for BISDN environments.
Herwig Bruneel, Byung G. Kim


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