Stochastic Storage Processes

1 A Class of Stochastic Models.- 2 Problems Arising from the Models.- 3 The Scope of this Book.- 4 Further Remarks.- Problems.- Selected Bibliography.- I The Single Server Queue.- 1 The Queue G/G/1 and the Associated Random Walk.- 1 Orientation.- 2 Ladder Processes.- 3 Two Renewal Functions.- 4 Maximum and Minimum.- 5 Application to the Queue G/G/1.- 6 The Queue M/M/1.- 7 The Queues G/M/1 and M/G/1.- 8 Application to Queue Length.- 9 Further Remarks.- Problems.- 2 Further Results for the Queue G/G/1.- 1 Transforms.- 2 Further Applications to the Queue G/G/1.- 3 The Queues G/M/1 and M/G/1.- 4 The Queue G/Ek/1.- 5 The Queue Ek/G/1.- Problems.- References.- II Continuous Time Storage Models.- 3 The Basic Storage Model.- 1 Orientation.- 2 Lvy Processes.- 3 A Generalized Storage Model.- 4 A First Passage Time.- 5 Insurance Risk: Two Special Cases.- 6 The Ladder Epochs {Tk*}.- 7 Limit Theorems for the Storage Model.- 8 A Second Storage Model.- 9 The Queue G/M/1.- 10 Queues with Static Priorities.- 11 Queues with Dynamic Priorities.- Problems.- 4 More Storage Models.- 1 Introduction.- 2 Ladder Points for a Two-Dimensional Random Walk.- 3 Ladder Points for Processes of Class ? +.- 4 Properties of Processes of Class ? + ? ? ?.- 5 The Insurance Risk Problem: General Case.- 6 The Queue M/M/1.- 7 A Storage Model with Random Output.- 8 Further Remarks.- Problems.- References.