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• # Książka - szczegóły

Tytuł książki

## Order relations in the set of probability distribution functions and their applications in queueing theory

### Seria

Rozprawy Matematyczne tom/nr w serii: 132 wydano: 1976

### Abstrakty

EN

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

Warszawa

### Seria

Rozprawy Matematyczne tom/nr w serii: 132

47

### Opis fizyczny

Dissertationes Mathematicae, Tom CXXXII

wydano
1976

autor

### Bibliografia

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