Author | Doorn, E. A. van. author |
---|---|
Title | Stochastic Monotonicity and Queueing Applications of Birth-Death Processes [electronic resource] / by E. A. van Doorn |
Imprint | New York, NY : Springer New York, 1981 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-5883-4 |
Descript | VI, 118 p. online resource |
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 Pโ(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