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Phase type distributions are widely applicable modeling and statistical tools for non-negative random quantities. They are built on Markov chains, which provide a simple, intuitive stochastic interpretation for their use. Phase Type Distribution starts from the Markov chain-based definition of phase type distributions and presents many interesting properties, which follow from the basic definition. As a general family of non-negative distributions with nice analytical properties, phase type distributions can be used for approximating experimental distributions by fitting or by moments matching; and, for discrete event simulation of real word systems with stochastic timing, such as production systems, service operations, communication networks, etc. This book summarizes the up-to-date fitting, matching and simulation methods, and presents the limits of flexibility of phase type distributions of a given order. Additionally, this book lists numerical examples that support the intuitive understanding of the analytical descriptions and software tools that handle phase type distributions.

The book is the extended and revised version of the 1st edition and is composed of two main parts: mathematical background and queueing systems with applications. The mathematical background is a self-containing introduction to the stochastic processes of the later studied queueing systems. It starts with a quick introduction to probability theory and stochastic processes and continues with chapters on Markov chains and regenerative processes. More recent advances of queueing systems are based on phase type distributions, Markov arrival processes and quasy birth death processes, which are introduced in the last chapter of the first part.The second part is devoted to queueing models and their applications. After the introduction of the basic Markovian (from M/M/1 to M/M/1//N) and non-Markovian (M/G/1, G/M/1) queueing systems, a chapter presents the analysis of queues with  phase type distributions, Markov arrival processes (from PH/M/1 to MAP/PH/1/K). Thenext chapter presents the classical queueing network results and the rest of this part is devoted to the application examples. There are queueing models for bandwidth charing with different traffic classes, slotted multiplexers, media access protocols like Aloha and IEEE 802.11b, priority systems and retrial systems.An appendix supplements the technical content with Laplace and z transformation rules, Bessel functions and a list of notations. The book contains examples and exercises throughout and could be used for graduate students in engineering, mathematics and sciences.Reviews of first edition:"The organization of the book is such that queueing models are viewed as special cases of more general stochastic processes, such as birth-death or semi-Markov processes. … this book is a valuable addition to the queuing literature and provides instructors with a viable alternative for a textbook to be used in a one- or two-semester course on queueing models, at the upper undergraduate or beginning graduate levels."Charles Knessl, SIAM Review, Vol. 56 (1), March, 2014

The book is the extended and revised version of the 1st edition and is composed of two main parts: mathematical background and queueing systems with applications. The mathematical background is a self-containing introduction to the stochastic processes of the later studied queueing systems. It starts with a quick introduction to probability theory and stochastic processes and continues with chapters on Markov chains and regenerative processes. More recent advances of queueing systems are based on phase type distributions, Markov arrival processes and quasy birth death processes, which are introduced in the last chapter of the first part.The second part is devoted to queueing models and their applications. After the introduction of the basic Markovian (from M/M/1 to M/M/1//N) and non-Markovian (M/G/1, G/M/1) queueing systems, a chapter presents the analysis of queues with  phase type distributions, Markov arrival processes (from PH/M/1 to MAP/PH/1/K). Thenext chapter presents the classical queueing network results and the rest of this part is devoted to the application examples. There are queueing models for bandwidth charing with different traffic classes, slotted multiplexers, media access protocols like Aloha and IEEE 802.11b, priority systems and retrial systems.An appendix supplements the technical content with Laplace and z transformation rules, Bessel functions and a list of notations. The book contains examples and exercises throughout and could be used for graduate students in engineering, mathematics and sciences.Reviews of first edition:"The organization of the book is such that queueing models are viewed as special cases of more general stochastic processes, such as birth-death or semi-Markov processes. … this book is a valuable addition to the queuing literature and provides instructors with a viable alternative for a textbook to be used in a one- or two-semester course on queueing models, at the upper undergraduate or beginning graduate levels."Charles Knessl, SIAM Review, Vol. 56 (1), March, 2014

The book is the extended and revised version of the 1st edition and is composed of two main parts: mathematical background and queueing systems with applications. The mathematical background is a self-containing introduction to the stochastic processes of the later studied queueing systems. It starts with a quick introduction to probability theory and stochastic processes and continues with chapters on Markov chains and regenerative processes. More recent advances of queueing systems are based on phase type distributions, Markov arrival processes and quasy birth death processes, which are introduced in the last chapter of the first part.The second part is devoted to queueing models and their applications. After the introduction of the basic Markovian (from M/M/1 to M/M/1//N) and non-Markovian (M/G/1, G/M/1) queueing systems, a chapter presents the analysis of queues with  phase type distributions, Markov arrival processes (from PH/M/1 to MAP/PH/1/K). Thenext chapter presents the classical queueing network results and the rest of this part is devoted to the application examples. There are queueing models for bandwidth charing with different traffic classes, slotted multiplexers, media access protocols like Aloha and IEEE 802.11b, priority systems and retrial systems.An appendix supplements the technical content with Laplace and z transformation rules, Bessel functions and a list of notations. The book contains examples and exercises throughout and could be used for graduate students in engineering, mathematics and sciences.Reviews of first edition:"The organization of the book is such that queueing models are viewed as special cases of more general stochastic processes, such as birth-death or semi-Markov processes. … this book is a valuable addition to the queuing literature and provides instructors with a viable alternative for a textbook to be used in a one- or two-semester course on queueing models, at the upper undergraduate or beginning graduate levels."Charles Knessl, SIAM Review, Vol. 56 (1), March, 2014

The idea to establish a European forum for academic and industrial researchers working on various aspects of performance modeling and analysis of manuf- toring and information systems gave rise to an annual series of workshops, - ferred to as European Performance Engineering Workshop (EPEW). The ?rst two EPEW workshops were held in Toledo, Spain, October 1-2, 2004, and V- sailles,France,September 1-3,2005.Thisvolumecontainstheproceedingsofthe third EPEW workshop held at the Technical University of Budapest, Budapest, Hungary, June 21-22, 2006. These proceedings comprise the 16 accepted contributed papers of EPEW 2006.Toensurethehigh-qualityevaluationofthesubmittedpapersweextended the ProgramCommittee of EPEW 2006with international experts from all over the world. Each submitted papers went through a rigorous review by at least three international reviewers. Based on the reviews, the subsequent discussions ofreviewerswithdi?erentjudgementandanInternet-basedProgramCommittee meeting held on March 30, 2006, we selected 40% of the submitted papers. We therefore owe special thanks to all members of the Program Committee and to all external referees for the excellent work they did for the proper evaluation of the papers. The ?nal workshop program, as well as this volume, are made up of ?ve thematic sessions: – Stochastic process algebra – Workloads and benchmarks – Theory of stochastic processes – Formal dependability and performance evaluation – Queues, theory and practice These sessions cover a wide range of performance evaluation methods and c- pose an overview of the current research directions in performance evaluation.

The idea to establish a European forum for academic and industrial researchers working on various aspects of performance modeling and analysis of manuf- toring and information systems gave rise to an annual series of workshops, - ferred to as European Performance Engineering Workshop (EPEW). The ?rst two EPEW workshops were held in Toledo, Spain, October 1-2, 2004, and V- sailles,France,September 1-3,2005.Thisvolumecontainstheproceedingsofthe third EPEW workshop held at the Technical University of Budapest, Budapest, Hungary, June 21-22, 2006. These proceedings comprise the 16 accepted contributed papers of EPEW 2006.Toensurethehigh-qualityevaluationofthesubmittedpapersweextended the ProgramCommittee of EPEW 2006with international experts from all over the world. Each submitted papers went through a rigorous review by at least three international reviewers. Based on the reviews, the subsequent discussions ofreviewerswithdi?erentjudgementandanInternet-basedProgramCommittee meeting held on March 30, 2006, we selected 40% of the submitted papers. We therefore owe special thanks to all members of the Program Committee and to all external referees for the excellent work they did for the proper evaluation of the papers. The ?nal workshop program, as well as this volume, are made up of ?ve thematic sessions: – Stochastic process algebra – Workloads and benchmarks – Theory of stochastic processes – Formal dependability and performance evaluation – Queues, theory and practice These sessions cover a wide range of performance evaluation methods and c- pose an overview of the current research directions in performance evaluation.

Itisourgreatpleasuretopresenttheproceedingsofthe15thInternationalConf- ence on Analytical and Stochastic Modelling Techniques and Applications (ASMTA2008)thattookplaceonthebeautifulislandofCyprusforthe?rsttime. The conference has become an important annual event in the ?elds of - alytical modelling and performance evaluation in Europe and internationally. Nevertheless, e?orts have been made year after year to raise the standard and the quality of the programme.This yearthe proceedings are published as partof Springer's prestigiousLecture Notes in Computer Science (LNCS) series. This is another sign of the growing con?dence in the quality standards and procedures followed in the reviewing process and the programme compilation. The conference was honored to have a distinguished keynote speaker in the personofRaymondMariefromIRISA/INRIA,France,whoisaprominent?gure ofthe analyticalmodellingcommunity inEuropeandworldwide.The conference had a high-qualityprogrammewith anacceptanceratio of 40%.The programme comprised 22 high-quality papers organized into 7 sessions. Almost every paper was peer reviewed by three reviewers from the International Programme C- mittee.The reviewers were truly wonderful this year, as well, and in most cases the reviewsprovidedvaluable comments thatcontributedto increasingthe qu- ity of the ?nal versions of the papers. In many cases, discussion panels were also organized when the reviews were not decisive. We would therefore like to give a special thanks to all the members of the International Programme Committee for the excellent work in the reviewing process and the subsequent discussion panels during the selection process.

It is our great pleasure to present the proceedings of the Third International Workshop on Multiple Access Communications (MACOM) that was held in Barcelona during September 13–14, 2010. In 1961, Claude Shannon established the foundation for the discipline now known as “multi-user information theory” in his pioneering paper “Two-way Communication Channels,” and later Norman Abramson published his paper “The Aloha System—Another Alternative for Computer Communications” in 1970 which introduced the concept of multiple access using a shared common channel. Thereafter, for more than 40 years of study, numerous elegant theories and algorithms have been developed for multiple-access communications. During the 1980s and 1990s the evolution of multiple-access techniques p- ceeded in conjunction with the evolution of wireless networks. Novel multiple access techniques like code division multiple access (CDMA) and orthogonal frequency division multiple access (OFDMA) provided increased spectral - ?ciency, dynamicity and ?exibility in radio resource allocation with intrinsic anti-multipath and anti-interference features. In this ?rst decade of the 21st century,multiple-accesstechniques,derivedfromadvancedwirelesstransmission methodologiesbasedonthediversityconcept(e. g. ,MC-CDMA,MIMO-OFDMA and SC-FDMA), opened the road to a renewed idea of multiple access. Today multiple-access communications involve many challenging aspects not only l- ited (like in the past) to physical layer design. Medium access control (MAC) techniques play a crucial role in managing the radio resources that users will exploit to transmit their data streams. Recent developments in software radios and cognitive radios have led to a signi?cant impact also on spectrum m- agement andaccess paradigms.

It is our great pleasure to present the proceedings of the Third International Workshop on Multiple Access Communications (MACOM) that was held in Barcelona during September 13–14, 2010. In 1961, Claude Shannon established the foundation for the discipline now known as “multi-user information theory” in his pioneering paper “Two-way Communication Channels,” and later Norman Abramson published his paper “The Aloha System—Another Alternative for Computer Communications” in 1970 which introduced the concept of multiple access using a shared common channel. Thereafter, for more than 40 years of study, numerous elegant theories and algorithms have been developed for multiple-access communications. During the 1980s and 1990s the evolution of multiple-access techniques p- ceeded in conjunction with the evolution of wireless networks. Novel multiple access techniques like code division multiple access (CDMA) and orthogonal frequency division multiple access (OFDMA) provided increased spectral - ?ciency, dynamicity and ?exibility in radio resource allocation with intrinsic anti-multipath and anti-interference features. In this ?rst decade of the 21st century,multiple-accesstechniques,derivedfromadvancedwirelesstransmission methodologiesbasedonthediversityconcept(e. g. ,MC-CDMA,MIMO-OFDMA and SC-FDMA), opened the road to a renewed idea of multiple access. Today multiple-access communications involve many challenging aspects not only l- ited (like in the past) to physical layer design. Medium access control (MAC) techniques play a crucial role in managing the radio resources that users will exploit to transmit their data streams. Recent developments in software radios and cognitive radios have led to a signi?cant impact also on spectrum m- agement andaccess paradigms.