Single-Server Queues with Impatient Customers
We consider a single-server queueing system in which a customer gives up whenever his waiting time is larger than a random threshold, his patience time. In the case of a GI/GI/1 queue with i.i.d. patience times, we establish the extensions of the classical GI/GI/1 formulae concerning the stability c...
Veröffentlicht in: | Advances in Applied Probability. - Applied Probability Trust. - 16(1984), 4, Seite 887-905 |
---|---|
1. Verfasser: | |
Weitere Verfasser: | , |
Format: | Online-Aufsatz |
Sprache: | English |
Veröffentlicht: |
1984
|
Zugriff auf das übergeordnete Werk: | Advances in Applied Probability |
Schlagworte: | Queueing theory Limited waiting times Ergodic Markov chain Actual waiting times Virtual waiting times Regenerative processes Invariant measure Functional equation Mathematics Applied sciences mehr... |
Zusammenfassung: | We consider a single-server queueing system in which a customer gives up whenever his waiting time is larger than a random threshold, his patience time. In the case of a GI/GI/1 queue with i.i.d. patience times, we establish the extensions of the classical GI/GI/1 formulae concerning the stability condition and the relation between actual and virtual waiting-time distribution functions. We also prove that these last two distribution functions coincide in the case of a Poisson input process and determine their common law. |
---|---|
ISSN: | 00018678 |
DOI: | 10.2307/1427345 |