Książka - szczegóły

CONTENTS

Introduction......................................................................................................................................... 5

1. n-Monotonic functions on (— ∞, ∞)........................................................................................... 6
2. Order relations in the set of probability distribution functions....................................................... 12
 2.1. Preliminary concepts............................................................................................................ 12
 2.2. Relations $≤_{1.n}, ≤_{2.n}$............................................................................................. 13
 2.3. Extremal probability distribution functions........................................................................ 17
 2.4. Relations $≤_{2.0}, ≤_{2.0}$............................................................................................. 18
 2.5. Isotonic operators................................................................................................................. 22
 2.6. Remarks about quasi-ordering relations in the set of random variables.................. 26
 3. Order relationship between queueing systems................................................................. 26
 3.1. Preliminary concepts, $GI^{(x)}/G^{(y)}/1$ queues.......................................................... 26
 3.2. $GI^{(x)}/G/1$ queues........................................................................................................... 27
 3.3. Order relationship between $GI^{(x)}/M^{(y)}/1$ and $M^{(x)}/G^{(y)}/1$ queues...... 30
 4. Bounds for $GI^{(x)}/G^{(y)}/1$ queues................................................................................ 32
 4.1. Introduction............................................................................................................................. 32
 4.2. Bounds for $GI^{(x)}/G^{(y)}/1$ queues ........................................................................... 33
 4.3. Bounds for $GI^{(x)}/M^{(y)}/1, M^{(x)}/G^{(y)}/1$ queues............................................... 36
 4.4. Application of the relations $≤_{1.n} ≤_{2.n}$ in queues............................................ 37
Appendix...................................................................................................................................................... 38
References.................................................................................................................................................. 46