Busy period analysis for M/G/1 and G/M/1 type queues with restricted accessibility
Autor(en): | Perry, D Stadje, W Zacks, S |
Stichwörter: | busy period; compound Poisson process; elapsed waiting time; G/M/1; linear boundary; M/G/1; Operations Research & Management Science; restricted accessibility; stopping time; virtual waiting time | Erscheinungsdatum: | 2000 | Herausgeber: | ELSEVIER SCIENCE BV | Journal: | OPERATIONS RESEARCH LETTERS | Volumen: | 27 | Ausgabe: | 4 | Startseite: | 163 | Seitenende: | 174 | Zusammenfassung: | We consider two models of M/G/1 and G/M/1 type queueing systems with restricted accessibility. Let(V(t))(t greater than or equal to0) be the virtual waiting time process, let S-n be the time required for a full service of the nth customer and let tau (n) be his arrival time. Tn both models there is a capacity bound nu* is an element of (0, infinity). In Model I the amount of service given to the nth customer is equal to min[S-n,nu* - V(tau (n)-)], i.e. the full currently free workload is assigned to the new customer. In Model II the customer is rejected iff the currently used workload V(tau (n)-) exceeds nu*, but the service times of admitted customers are not censored. We obtain closed-form expressions for the Laplace transforms of the lengths of the busy periods. (C) 2000 Elsevier Science B.V. All rights reserved. |
ISSN: | 01676377 | DOI: | 10.1016/S0167-6377(00)00043-2 |
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