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Field name	Details
Dewey Class	519.2
Title	Stationary Random Processes Associated with Point Processes ([EBook] /) / by Tomasz Rolski.
Author	Rolski, Tomasz
Other name(s)	SpringerLink (Online service)
Publication	New York, NY : : Springer US, , 1981.
Physical Details	139 p. : online resource.
Series	Lecture Notes in Statistics 0930-0325 ; ; 5
ISBN	9781468462685
Summary Note	In this set of notes we study a notion of a random process assoc- ted with a point process. The presented theory was inSpired by q- ueing problems. However it seems to be of interest in other branches of applied probability, as for example reliability or dam theory. Using developed tools, we work out known, aswell as new results from queueing or dam theory. Particularly queues which cannot be treated by standard techniques serve as illustrations of the theory. In Chapter 1 the preliminaries are given. We acquaint the reader with the main ideas of these notes, introduce some useful notations, concepts and abbreviations. He also recall basic facts from ergodic theory, an important mathematical tool employed in these notes. Finally some basic notions from queues are reviewed. Chapter 2 deals with discrete time theory. It serves two purposes. The first one is to let the reader get acquainted with the main lines of the theory needed in continuous time without being bothered by tech nical details. However the discrete time theory also seems to be of interest itself. There are examples which have no counte~ in continuous time. Chapter 3 deals with continuous time theory. It also contains many basic results from queueing or dam theory. Three applications of the continuous time theory are given in Chapter 4. We show how to use the theory in order to get some useful bounds for the stationary distribution of a random process.:
Contents note	1 Preliminaries -- 1 Introduction -- 2 Some notations and conventions -- 3 Ergodic theory — discrete parameter -- 4 Ergodic theory — continuous parameter -- 5 Stationary random elements -- 6 Loynes’ lemma -- 7 Queues -- Notes -- 2 Discrete time r.p.@ p.p. -- 1 Basic concepts -- 2 Construction of stationary processes -- 3 First and second type relations -- 4 Applications in queueing theory -- Notes -- 3 Continuous time r.p.@ m.p.p. -- 1 Random process associated with marked point process -- 2 Construction of stationary r.p.@ m.p.p.’s -- 3 Ergodic theorems -- 4 Relations of the first and second type -- 5 A rate conservative principle approach -- Notes -- 4 Miscellaneous examples -- 1 Inequalities and identities -- 2 Kopoci?ska’s model -- 3 Equivalence of distributions of embedded chains in the queue size process -- Notes -- 5 Application to single server queues -- 1 Introductory remarks -- 2 Single server queue with periodic input -- 3 Fagging queueing systems -- 4 $$\overrightarrow G /\overrightarrow G /1$$ queue with work-conserving normal discipline -- 5 Takács relation in G/G/1; FIFO. queues -- 6 Takács relation in GI/GI/1; FIFO queues -- Notes -- References.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-1-4684-6268-5
Links to Related Works	Subject References: Mathematics . Probabilities . Probability theory and stochastic processes . Authors: Rolski, Tomasz . Corporate Authors: SpringerLink (Online service) . Series: Lecture Notes in Statistics . Classification: 519.2 .

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Stationary Random Processes Associated with Point Processes

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