Stochastic Monotonicity and Queueing Applications of Birth-Death Processes (Paperback)

Erik van Doorn

ISBN 10: 0387905472 / ISBN 13: 9780387905471

Editore: Springer-Verlag New York Inc., New York, NY, 1981

Riguardo questo articolo

Paperback. A stochastic process {X(t): 0 S t i}, i E S, are increasing (decreasing) with t on T. Stochastic monotonicity is a basic structural property for process behaviour. It gives rise to meaningful bounds for various quantities such as the moments of the process, and provides the mathematical groundwork for approximation algorithms. Obviously, stochastic monotonicity becomes a more tractable subject for analysis if the processes under consideration are such that stochastic mono tonicity on an inter val 0 i}, i E S, are increasing (decreasing) with t on T. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Codice articolo 9780387905471

Dati bibliografici

• Titolo: Stochastic Monotonicity and Queueing Applications of Birth-Death Processes (Paperback)
• Editore: Springer-Verlag New York Inc., New York, NY
• Data di pubblicazione: 1981
• Lingua: Inglese
• ISBN 10: 0387905472
• ISBN 13: 9780387905471
• Rilegatura: Paperback
• Condizione: new

Descrizione articolo

Riassunto

A stochastic process {X(t): 0 S t < =} with discrete state space S c ~ is said to be stochastically increasing (decreasing) on an interval T if the probabilities Pr{X(t) > i}, i E S, are increasing (decreasing) with t on T.

Contenuti

1 : Preliminaries.- 1.1 Markov processes.- 1.2 Stochastic monotonicity.- 1.3 Birth-death processes.- 1.4 Some notation and terminology.- 2 : Natural Birth-Death Processes.- 2.1 Some basic properties.- 2.2 The spectral representation.- 2.3 Exponential ergodicity.- 2.4 The moment problem and related topics.- 3 : Dual Birth-Death Processes.- 3.1 Introduction.- 3.2 Duality relations.- 3.3 Ergodic properties.- 4 : Stochastic Monotonicity: General Results.- 4.1 The case ?0 = 0.- 4.2 The case ?0 > 0.- 4.3 Properties of E(t).- 5 : Stochastic Monotonicity: Dependence on the Initial State Distribution.- 5.1 Introduction to the case of a fixed initial state.- 5.2 The transient and null recurrent process.- 5.3 The positive recurrent process.- 5.4 The case of an initial state distribution with finite support.- 6 : The M/M/S Queue Length Process.- 6.1 Introduction.- 6.2 The spectral function.- 6.3 Stochastic monotonicity.- 6.4 Exponential ergodicity.- 7 : A Queueing Model Where Potential Customers are Discouraged by Queue Length.- 7.1 Introduction.- 7.2 The spectral representation.- 7.3 Stochastic monotonicity and exponential ergodicity.- 8 : Linear Growth Birth-Death Processes.- 8.1 Introduction.- 8.2 Stochastic monotonicity.- 9 : The Mean of Birth-Death Processes.- 9.1 Introduction.- 9.2 Representations.- 9.3 Sufficient conditions for finiteness.- 9.4 Behaviour of the mean in special cases.- 10 : The Truncated Birth-Death Process.- 10.1 Introduction.- 10.2 Preliminaries.- 10.3 The sign structure of P’(t).- 10.4 Stochastic monotonicity.- Appendix 1 : Proof of the Sign Variation Diminishing Property of Strictly Totally Positive Matrices.- Appendix 2: On Products of Infinite Matrices.- Appendix 3: On the Sign of Certain Quantities.- Appendix 4: Proof of Theorem 10.2.8.- References.- Notation Index.- Author Index.