Sojourn times in feedback queues

J.L. Berg, van den; O.J. Boxma

doi:10.1007/978-3-642-73778-7_119

Sojourn times in feedback queues

J.L. Berg, van den, O.J. Boxma

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

Abstract

In many modern computer-communication systems, a job may be processed in several phases, or a job may generate new tasks. Such phenomena can be modeled by service systems with feedback. In the queueing literature, attention has been mainly devoted to single-service queues with so-called Bernoulli feedback: when a customer (task) completes his service, he departs from the system with probability l-p and is fed back with probability p. In the present study a more general feedback mechanism is allowed: when a customer completes his i-th service, he departs from the system with probability l-p(i) and is fed back with probability p(i). We mainly restrict ourselves to the case of a Poisson external arrival process and identically, negative exponentially, distributed service times at each service. The resulting queueing model has the property that the joint queue-length distribution of type-i customers, i=1,2,⋯, is of product-form type. This property is exploited to analyse the sojourn-time process.

Original language	English
Title of host publication	DGOR/NSOR
Subtitle of host publication	Papers of the 16th Annual Meeting of DGOR in Cooperation with NSOR/Vorträge der 16. Jahrestagung der DGOR zusammen mit der NSOR
Editors	H. Schellhaas, P. van Beek, H. Isermann
Place of Publication	Berlin
Publisher	Springer
Pages	478-478
ISBN (Electronic)	978-3-642-73778-7
ISBN (Print)	978-3-540-19365-4
DOIs	https://doi.org/10.1007/978-3-642-73778-7_119
Publication status	Published - 1989
Event	16th Annual Meeting of DGOR - Veldhoven, Netherlands Duration: 23 Sep 1987 → 25 Sep 1987

Publication series

Name	Operations Research Proceedings (ORP)
Volume	1987

Conference

Conference	16th Annual Meeting of DGOR
Country/Territory	Netherlands
City	Veldhoven
Period	23/09/87 → 25/09/87

Access to Document

10.1007/978-3-642-73778-7_119

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Berg, van den, J. L., & Boxma, O. J. (1989). Sojourn times in feedback queues. In H. Schellhaas, P. van Beek, & H. Isermann (Eds.), DGOR/NSOR: Papers of the 16th Annual Meeting of DGOR in Cooperation with NSOR/Vorträge der 16. Jahrestagung der DGOR zusammen mit der NSOR (pp. 478-478). (Operations Research Proceedings (ORP); Vol. 1987). Springer. https://doi.org/10.1007/978-3-642-73778-7_119

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title = "Sojourn times in feedback queues",

abstract = "In many modern computer-communication systems, a job may be processed in several phases, or a job may generate new tasks. Such phenomena can be modeled by service systems with feedback. In the queueing literature, attention has been mainly devoted to single-service queues with so-called Bernoulli feedback: when a customer (task) completes his service, he departs from the system with probability l-p and is fed back with probability p. In the present study a more general feedback mechanism is allowed: when a customer completes his i-th service, he departs from the system with probability l-p(i) and is fed back with probability p(i). We mainly restrict ourselves to the case of a Poisson external arrival process and identically, negative exponentially, distributed service times at each service. The resulting queueing model has the property that the joint queue-length distribution of type-i customers, i=1,2,⋯, is of product-form type. This property is exploited to analyse the sojourn-time process.",

author = "{Berg, van den}, J.L. and O.J. Boxma",

year = "1989",

doi = "10.1007/978-3-642-73778-7_119",

language = "English",

isbn = "978-3-540-19365-4",

series = "Operations Research Proceedings (ORP)",

publisher = "Springer",

pages = "478--478",

editor = "H. Schellhaas and {van Beek}, P. and H. Isermann",

booktitle = "DGOR/NSOR",

address = "Germany",

note = "16th Annual Meeting of DGOR ; Conference date: 23-09-1987 Through 25-09-1987",

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Berg, van den, JL & Boxma, OJ 1989, Sojourn times in feedback queues. in H Schellhaas, P van Beek & H Isermann (eds), DGOR/NSOR: Papers of the 16th Annual Meeting of DGOR in Cooperation with NSOR/Vorträge der 16. Jahrestagung der DGOR zusammen mit der NSOR. Operations Research Proceedings (ORP), vol. 1987, Springer, Berlin, pp. 478-478, 16th Annual Meeting of DGOR, Veldhoven, Netherlands, 23/09/87. https://doi.org/10.1007/978-3-642-73778-7_119

Sojourn times in feedback queues. / Berg, van den, J.L.; Boxma, O.J.

DGOR/NSOR: Papers of the 16th Annual Meeting of DGOR in Cooperation with NSOR/Vorträge der 16. Jahrestagung der DGOR zusammen mit der NSOR. ed. / H. Schellhaas; P. van Beek; H. Isermann. Berlin : Springer, 1989. p. 478-478 (Operations Research Proceedings (ORP); Vol. 1987).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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AU - Boxma, O.J.

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N2 - In many modern computer-communication systems, a job may be processed in several phases, or a job may generate new tasks. Such phenomena can be modeled by service systems with feedback. In the queueing literature, attention has been mainly devoted to single-service queues with so-called Bernoulli feedback: when a customer (task) completes his service, he departs from the system with probability l-p and is fed back with probability p. In the present study a more general feedback mechanism is allowed: when a customer completes his i-th service, he departs from the system with probability l-p(i) and is fed back with probability p(i). We mainly restrict ourselves to the case of a Poisson external arrival process and identically, negative exponentially, distributed service times at each service. The resulting queueing model has the property that the joint queue-length distribution of type-i customers, i=1,2,⋯, is of product-form type. This property is exploited to analyse the sojourn-time process.

AB - In many modern computer-communication systems, a job may be processed in several phases, or a job may generate new tasks. Such phenomena can be modeled by service systems with feedback. In the queueing literature, attention has been mainly devoted to single-service queues with so-called Bernoulli feedback: when a customer (task) completes his service, he departs from the system with probability l-p and is fed back with probability p. In the present study a more general feedback mechanism is allowed: when a customer completes his i-th service, he departs from the system with probability l-p(i) and is fed back with probability p(i). We mainly restrict ourselves to the case of a Poisson external arrival process and identically, negative exponentially, distributed service times at each service. The resulting queueing model has the property that the joint queue-length distribution of type-i customers, i=1,2,⋯, is of product-form type. This property is exploited to analyse the sojourn-time process.

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DO - 10.1007/978-3-642-73778-7_119

M3 - Conference contribution

SN - 978-3-540-19365-4

T3 - Operations Research Proceedings (ORP)

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EP - 478

BT - DGOR/NSOR

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Berg, van den JL, Boxma OJ. Sojourn times in feedback queues. In Schellhaas H, van Beek P, Isermann H, editors, DGOR/NSOR: Papers of the 16th Annual Meeting of DGOR in Cooperation with NSOR/Vorträge der 16. Jahrestagung der DGOR zusammen mit der NSOR. Berlin: Springer. 1989. p. 478-478. (Operations Research Proceedings (ORP)). https://doi.org/10.1007/978-3-642-73778-7_119

Sojourn times in feedback queues

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