Regenerative Processes in the Theory of Queues, with Applications to the Alternating-Priority Queue
Using some well-known and some recently proved asymptotic properties of regenerative processes, we present a new proof in a general regenerative setting of the equivalence of the limiting distributions of a stochastic process at an arbitrary point in time and at the time of an event from an associat...
| Veröffentlicht in: | Advances in Applied Probability. - Applied Probability Trust. - 4(1972), 3, Seite 542-577 |
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| 1. Verfasser: | |
| Format: | Online-Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
1972
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| Zugriff auf das übergeordnete Werk: | Advances in Applied Probability |
| Schlagworte: | Queuing theory Priority queue Alternating-priority queue Zero switch rule Regenerative process Cumulative process Conservation equations Time averages and customer averages Virtual and actual waiting time Mathematics |
| Zusammenfassung: | Using some well-known and some recently proved asymptotic properties of regenerative processes, we present a new proof in a general regenerative setting of the equivalence of the limiting distributions of a stochastic process at an arbitrary point in time and at the time of an event from an associated Poisson process. From the same asymptotic properties, several conservation equations are derived that hold for a wide class of GI/G/1 priority queues. Finally, focussing our attention on the alternating-priority queue with Poisson arrivals, we use both types of result to give a new, simple derivation of the expected steady-state delay in the queue in each class. |
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| ISSN: | 00018678 |
| DOI: | 10.2307/1425993 |