The Resource Introduction to Stochastic Networks, by Richard Serfozo, (electronic resource)

Introduction to Stochastic Networks, by Richard Serfozo, (electronic resource)

Label
Introduction to Stochastic Networks
Title
Introduction to Stochastic Networks
Statement of responsibility
by Richard Serfozo
Creator
Author
Author
Subject
Language
  • eng
  • eng
Summary
In a stochastic network, such as those in computer/telecommunications and manufacturing, discrete units move among a network of stations where they are processed or served. Randomness may occur in the servicing and routing of units, and there may be queueing for services. This book describes several basic stochastic network processes, beginning with Jackson networks and ending with spatial queueing systems in which units, such as cellular phones, move in a space or region where they are served. The focus is on network processes that have tractable (closed-form) expressions for the equilibrium probability distribution of the numbers of units at the stations. These distributions yield network performance parameters such as expectations of throughputs, delays, costs, and travel times. The book is intended for graduate students and researchers in engineering, science and mathematics interested in the basics of stochastic networks that have been developed over the last twenty years. Assuming a graduate course in stochastic processes without measure theory, the emphasis is on multi-dimensional Markov processes. There is also some self-contained material on point processes involving real analysis. The book also contains rather complete introductions to reversible Markov processes, Palm probabilities for stationary systems, Little laws for queueing systems and space-time Poisson processes. This material is used in describing reversible networks, waiting times at stations, travel times and space-time flows in networks. Richard Serfozo received the Ph.D. degree in Industrial Engineering and Management Sciences at Northwestern University in 1969 and is currently Professor of Industrial and Systems Engineering at Georgia Institute of Technology. Prior to that he held positions in the Boeing Company, Syracuse University, and Bell Laboratories. He has held
Member of
http://library.link/vocab/creatorName
Serfozo, Richard
Dewey number
519.2
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
at4gsxYaWTo
Image bit depth
0
Language note
English
LC call number
  • QA273.A1-274.9
  • QA274-274.9
Literary form
non fiction
Nature of contents
dictionaries
Series statement
Stochastic Modelling and Applied Probability,
Series volume
44
http://library.link/vocab/subjectName
  • Distribution (Probability theory
  • Statistics
  • Operations research
  • Probability Theory and Stochastic Processes
  • Statistics, general
  • Operations Research/Decision Theory
Label
Introduction to Stochastic Networks, by Richard Serfozo, (electronic resource)
Instantiates
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Color
not applicable
Content category
text
Content type code
  • txt
Contents
1 Jackson and Whittle Networks -- 1.1 Preliminaries on Networks and Markov Processes -- 1.2 Tandem Network -- 1.3 Definitions of Jackson and Whittle Processes -- 1.4 Properties of Service and Routing Rates -- 1.5 Equilibrium behavior -- 1.6 Production-Maintenance Network -- 1.7 Networks with Special Structures -- 1.8 Properties of Jackson Equilibrium Distributions -- 1.9 Convolutions for Single-Server Nodes -- 1.10 Throughputs and Expected Sojourn Times -- 1.11 Algorithms for Performance Parameters -- 1.12 Monte Carlo Estimation of Network Parameters -- 1.13 Properties of Whittle Networks -- 1.14 Exercises -- 1.15 Bibliographical Notes -- 2 Reversible Processes -- 2.1 Reversibility -- 2.2 Time Reversal -- 2.3 Invariant Measures -- 2.4 Construction of Reversible Processes -- 2.5 More Birth-Death Processes -- 2.6 Reversible Network Processes -- 2.7 Examples of Reversible Networks -- 2.8 Partition-Reversible Processes -- 2.9 Examples of Partition-Reversible Processes -- 2.10 Exercises -- 2.11 Bibliographical Notes -- 3 Miscellaneous Networks -- 3.1 Networks with Multiple Types of Units -- 3.2 Kelly Networks: Route-dependent Services -- 3.3 BCMP Networks: Class-Node Service Dependencies -- 3.4 Networks with Cox and General Service Times -- 3.5 Networks with Constraints -- 3.6 Networks with Blocking and Rerouting -- 3.7 Bottlenecks in Closed Jackson Networks -- 3.8 Modeling Whittle Networks by Locations of the Units -- 3.9 Partially Balanced Networks -- 3.10 Exercises -- 3.11 Bibliographical Notes -- 4 Network Flows and Travel Times -- 4.1 Point Process Notation -- 4.2 Extended Lévy Formula for Markov Processes -- 4.3 Poisson Functionals of Markov Processes -- 4.4 Multivariate Compound Poisson Processes -- 4.5 Poisson Flows in Jackson and Whittle Networks -- 4.6 Palm Probabilities for Markov Processes -- 4.7 Sojourn and Travel Times of Markov Processes -- 4.8 Palm Probabilities of Jackson and Whittle Networks -- 4.9 Travel Times on Overtake-Free Routes -- 4.10 Exercises -- 4.11 Bibliographical Notes -- 5 Little Laws -- 5.1 Little Laws for Markovian Systems -- 5.2 Little Laws for General Queueing Systems -- 5.3 Preliminary Laws of Large Numbers -- 5.4 Utility Processes -- 5.5 Omnibus Little Laws -- 5.6 Little Laws for Regenerative Systems -- 5.7 Exercises -- 5.8 Bibliographical Notes -- 6 Stationary Systems -- 6.1 Preliminaries on Stationary Processes -- 6.2 Palm Probabilities -- 6.3 Campbell-Mecke Formulas for Palm Probabilities -- 6.4 Little Laws for Stationary Systems -- 6.5 Sojourn Times and Related Functionals -- 6.6 Travel Times for Stochastic Processes -- 6.7 Sojourn and Travel Times in Networks -- 6.8 Exercises -- 6.9 Bibliographical Notes -- 7 Networks with String Transitions -- 7.1 Definition of a String-Net -- 7.2 Invariant Measures of String-Nets -- 7.3 Traffic Equations, Partial Balance, and Throughputs -- 7.4 String-Nets with Unit-Vector Transitions -- 7.5 Networks with One-Stage Batch Transitions -- 7.6 Networks with Compound-Rate String Transitions -- 7.7 Networks with Multiple, Compound-Rate String Transitions -- 7.8 String-Nets with Two-Node Batch Transitions -- 7.9 Single Service Station With String Transitions -- 7.10 Bibliographical Notes -- 8 Quasi-Reversible Networks and Product Form Distributions -- 8.1 Quasi-Reversibility -- 8.2 Network to be Studied -- 8.3 Characterization of Product Form Distributions -- 8.4 Quasi-Reversibility and Biased Local Balance -- 8.5 Networks with Reversible Routing -- 8.6 Queueing Networks -- 8.7 Time-Reversals and Departure—Arrival Reversals -- 8.8 Networks with Multiclass Transitions -- 8.9 Exercises -- 8.10 Bibliographical Notes -- 9 Space—Time Poisson Models -- 9.1 Introductory Examples -- 9.2 Laplace Functionals of Point Processes -- 9.3 Transformations of Poisson Processes -- 9.4 Translations, Partitions, and Clusters -- 9.5 Service Systems with No Queueing -- 9.6 Network of M/G/? Service Stations -- 9.7 Particle Systems -- 9.8 Poisson Convergence of Space-Time Processes -- 9.9 Transformations into Large Spaces -- 9.10 Particle Flows in Large Spaces -- 9.11 Exercises -- 9.12 Bibliographical Notes -- 10 Spatial Queueing Systems -- 10.1 Preliminaries -- 10.2 Stationary Distributions and Ergodicity -- 10.3 Properties of Stationary Distributions and Examples -- 10.4 Throughputs and Expected Sojourn Times -- 10.5 Poisson Flows in Open Systems -- 10.6 Systems with Multiclass Units -- 10.7 Bibliographical Notes -- References
Dimensions
unknown
Edition
1st ed. 1999.
Extent
1 online resource (XIV, 301 p.)
File format
multiple file formats
Form of item
online
Isbn
9781461214823
Level of compression
uncompressed
Media category
computer
Media type code
  • c
Other control number
10.1007/978-1-4612-1482-3
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000089564
  • (SSID)ssj0001297266
  • (PQKBManifestationID)11847552
  • (PQKBTitleCode)TC0001297266
  • (PQKBWorkID)11354712
  • (PQKB)10291470
  • (DE-He213)978-1-4612-1482-3
  • (MiAaPQ)EBC3074488
  • (EXLCZ)993400000000089564
Label
Introduction to Stochastic Networks, by Richard Serfozo, (electronic resource)
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Color
not applicable
Content category
text
Content type code
  • txt
Contents
1 Jackson and Whittle Networks -- 1.1 Preliminaries on Networks and Markov Processes -- 1.2 Tandem Network -- 1.3 Definitions of Jackson and Whittle Processes -- 1.4 Properties of Service and Routing Rates -- 1.5 Equilibrium behavior -- 1.6 Production-Maintenance Network -- 1.7 Networks with Special Structures -- 1.8 Properties of Jackson Equilibrium Distributions -- 1.9 Convolutions for Single-Server Nodes -- 1.10 Throughputs and Expected Sojourn Times -- 1.11 Algorithms for Performance Parameters -- 1.12 Monte Carlo Estimation of Network Parameters -- 1.13 Properties of Whittle Networks -- 1.14 Exercises -- 1.15 Bibliographical Notes -- 2 Reversible Processes -- 2.1 Reversibility -- 2.2 Time Reversal -- 2.3 Invariant Measures -- 2.4 Construction of Reversible Processes -- 2.5 More Birth-Death Processes -- 2.6 Reversible Network Processes -- 2.7 Examples of Reversible Networks -- 2.8 Partition-Reversible Processes -- 2.9 Examples of Partition-Reversible Processes -- 2.10 Exercises -- 2.11 Bibliographical Notes -- 3 Miscellaneous Networks -- 3.1 Networks with Multiple Types of Units -- 3.2 Kelly Networks: Route-dependent Services -- 3.3 BCMP Networks: Class-Node Service Dependencies -- 3.4 Networks with Cox and General Service Times -- 3.5 Networks with Constraints -- 3.6 Networks with Blocking and Rerouting -- 3.7 Bottlenecks in Closed Jackson Networks -- 3.8 Modeling Whittle Networks by Locations of the Units -- 3.9 Partially Balanced Networks -- 3.10 Exercises -- 3.11 Bibliographical Notes -- 4 Network Flows and Travel Times -- 4.1 Point Process Notation -- 4.2 Extended Lévy Formula for Markov Processes -- 4.3 Poisson Functionals of Markov Processes -- 4.4 Multivariate Compound Poisson Processes -- 4.5 Poisson Flows in Jackson and Whittle Networks -- 4.6 Palm Probabilities for Markov Processes -- 4.7 Sojourn and Travel Times of Markov Processes -- 4.8 Palm Probabilities of Jackson and Whittle Networks -- 4.9 Travel Times on Overtake-Free Routes -- 4.10 Exercises -- 4.11 Bibliographical Notes -- 5 Little Laws -- 5.1 Little Laws for Markovian Systems -- 5.2 Little Laws for General Queueing Systems -- 5.3 Preliminary Laws of Large Numbers -- 5.4 Utility Processes -- 5.5 Omnibus Little Laws -- 5.6 Little Laws for Regenerative Systems -- 5.7 Exercises -- 5.8 Bibliographical Notes -- 6 Stationary Systems -- 6.1 Preliminaries on Stationary Processes -- 6.2 Palm Probabilities -- 6.3 Campbell-Mecke Formulas for Palm Probabilities -- 6.4 Little Laws for Stationary Systems -- 6.5 Sojourn Times and Related Functionals -- 6.6 Travel Times for Stochastic Processes -- 6.7 Sojourn and Travel Times in Networks -- 6.8 Exercises -- 6.9 Bibliographical Notes -- 7 Networks with String Transitions -- 7.1 Definition of a String-Net -- 7.2 Invariant Measures of String-Nets -- 7.3 Traffic Equations, Partial Balance, and Throughputs -- 7.4 String-Nets with Unit-Vector Transitions -- 7.5 Networks with One-Stage Batch Transitions -- 7.6 Networks with Compound-Rate String Transitions -- 7.7 Networks with Multiple, Compound-Rate String Transitions -- 7.8 String-Nets with Two-Node Batch Transitions -- 7.9 Single Service Station With String Transitions -- 7.10 Bibliographical Notes -- 8 Quasi-Reversible Networks and Product Form Distributions -- 8.1 Quasi-Reversibility -- 8.2 Network to be Studied -- 8.3 Characterization of Product Form Distributions -- 8.4 Quasi-Reversibility and Biased Local Balance -- 8.5 Networks with Reversible Routing -- 8.6 Queueing Networks -- 8.7 Time-Reversals and Departure—Arrival Reversals -- 8.8 Networks with Multiclass Transitions -- 8.9 Exercises -- 8.10 Bibliographical Notes -- 9 Space—Time Poisson Models -- 9.1 Introductory Examples -- 9.2 Laplace Functionals of Point Processes -- 9.3 Transformations of Poisson Processes -- 9.4 Translations, Partitions, and Clusters -- 9.5 Service Systems with No Queueing -- 9.6 Network of M/G/? Service Stations -- 9.7 Particle Systems -- 9.8 Poisson Convergence of Space-Time Processes -- 9.9 Transformations into Large Spaces -- 9.10 Particle Flows in Large Spaces -- 9.11 Exercises -- 9.12 Bibliographical Notes -- 10 Spatial Queueing Systems -- 10.1 Preliminaries -- 10.2 Stationary Distributions and Ergodicity -- 10.3 Properties of Stationary Distributions and Examples -- 10.4 Throughputs and Expected Sojourn Times -- 10.5 Poisson Flows in Open Systems -- 10.6 Systems with Multiclass Units -- 10.7 Bibliographical Notes -- References
Dimensions
unknown
Edition
1st ed. 1999.
Extent
1 online resource (XIV, 301 p.)
File format
multiple file formats
Form of item
online
Isbn
9781461214823
Level of compression
uncompressed
Media category
computer
Media type code
  • c
Other control number
10.1007/978-1-4612-1482-3
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000089564
  • (SSID)ssj0001297266
  • (PQKBManifestationID)11847552
  • (PQKBTitleCode)TC0001297266
  • (PQKBWorkID)11354712
  • (PQKB)10291470
  • (DE-He213)978-1-4612-1482-3
  • (MiAaPQ)EBC3074488
  • (EXLCZ)993400000000089564

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