目次
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.
