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

Tomasz Rolski

GDML_Books, (1976), p.

Résumé

CONTENTSIntroduction......................................................................................................................................... 51. n-Monotonic functions on (— ∞, ∞)........................................................................................... 62. 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............................................ 37Appendix...................................................................................................................................................... 38References.................................................................................................................................................. 46

Détail

Zbl 0357.60025

EUDML-ID : urn:eudml:doc:268532