×

zbMATH — the first resource for mathematics

A queueing model with dependence between service and interarrival times. (English) Zbl 0996.90034
Summary: We consider a storage model that can be either interpreted as a certain queueing model with dependence between a service request and the subsequent interarrival time, or as a fluid production/inventory model with a two-state random environment. We establish a direct link between the workload distributions of the queueing model and the production/inventory model, and we present a detailed analysis of the workload and waiting time process of the queueing system.

MSC:
90B22 Queues and service in operations research
90B30 Production models
60K25 Queueing theory (aspects of probability theory)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Beichelt, F., A unifying treatment of replacement policies with minimal repair, Naval research logistics quarterly, 40, 51-67, (1993) · Zbl 0778.90011
[2] Borst, S.C.; Boxma, O.J.; Combé, M.B., An M/G/1 queue with customer collection, Stochastic models, 9, 341-371, (1993) · Zbl 0777.60086
[3] O.J. Boxma, D. Perry, F.A. van der Duyn Schouten, Fluid queues and mountain processes, Probability in the Engineering and Informational Sciences 13 (1999) 407-427 · Zbl 0972.60092
[4] Chen, H.; Yao, D.D., A fluid model for systems with random disruptions, Operations research, 40, S239-S247, (1992) · Zbl 0754.60107
[5] Cidon, I.; Guérin, R.; Khamisy, A.; Sidi, M., On queues with inter-arrival times proportional to service times, Tech. rep. technion EE PUB, 811, (1991)
[6] J.W. Cohen, The Single Server Queue, revised edition, North-Holland, Amsterdam, 1982 · Zbl 0481.60003
[7] Doshi, B.T., Level-crossing analysis of queues, (), 3-33 · Zbl 0783.60093
[8] Kaspi, H.; Kella, O.; Perry, D., Dam processes with state dependent batch sizes and intermittent production processes with state dependent rates, Queueing systems, 24, 37-57, (1996) · Zbl 0874.90075
[9] Kella, O.; Whitt, W., A storage model with a two-state random environment, Operations research, 40, S257-S262, (1992) · Zbl 0825.90344
[10] Lindley, D.V., The theory of queues with a single server, Proceedings of the Cambridge philosophical society, 48, 277-289, (1952) · Zbl 0046.35501
[11] Meyer, R.R.; Rothkopf, M.H.; Smith, S.A., Reliability and inventory in a production-storage system, Management science, 25, 799-807, (1979) · Zbl 0435.90055
[12] Meyer, R.R.; Rothkopf, M.H.; Smith, S.A., Erratum to reliability and inventory in a production-storage system, Management science, 29, 1346, (1983)
[13] D. Perry, M.J.M. Posner, A correlated M/G/1-type queue with randomized server repair and maintenance modes. Operations Research Letters 26 (3) (2000) 137-147 · Zbl 0978.90031
[14] Tákacs, L., Introduction to the theory of queues, (1962), Oxford University Press New York · Zbl 0118.13503
[15] Vanneste, S.G.; van der Duyn Schouten, F.A., Maintenance optimization of a production system with buffer capacity, European journal of operational research, 82, 323-338, (1995) · Zbl 0910.90148
[16] Voldes-Flores, C.; Feldman, R.M., A survey of preventive maintenance models for stochastically deteriorating single-unit systems, Naval research logistics quarterly, 36, 419-446, (1989) · Zbl 0671.90028
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.