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

Stochastic Operations Research

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	Operations Research Proceedings 1987 (Papers of the 16th Annual Meeting of DGOR, in cooperation with NSOR, Veldhoven, The Netherlands, September 23-25, 1987)
Editors	H. Schellhaas, P. Beek, van, H. Isermann, R. Schmidt, M. Zijlstra
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

Conference

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

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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. Beek, van, H. Isermann, R. Schmidt, & M. Zijlstra (Eds.), Operations Research Proceedings 1987 (Papers of the 16th Annual Meeting of DGOR, in cooperation with NSOR, Veldhoven, The Netherlands, September 23-25, 1987) (pp. 478-478). 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",

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booktitle = "Operations Research Proceedings 1987 (Papers of the 16th Annual Meeting of DGOR, in cooperation with NSOR, Veldhoven, The Netherlands, September 23-25, 1987)",

publisher = "Springer",

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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 Beek, van, H Isermann, R Schmidt & M Zijlstra (eds), Operations Research Proceedings 1987 (Papers of the 16th Annual Meeting of DGOR, in cooperation with NSOR, Veldhoven, The Netherlands, September 23-25, 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.

Operations Research Proceedings 1987 (Papers of the 16th Annual Meeting of DGOR, in cooperation with NSOR, Veldhoven, The Netherlands, September 23-25, 1987). ed. / H. Schellhaas; P. Beek, van; H. Isermann; R. Schmidt; M. Zijlstra. Berlin : Springer, 1989. p. 478-478.

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

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AU - Boxma, O.J.

PY - 1989

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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

SP - 478

EP - 478

BT - Operations Research Proceedings 1987 (Papers of the 16th Annual Meeting of DGOR, in cooperation with NSOR, Veldhoven, The Netherlands, September 23-25, 1987)

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A2 - Schmidt, R.

A2 - Zijlstra, M.

PB - Springer

CY - Berlin

T2 - 16th Annual Meeting of DGOR

Y2 - 23 September 1987 through 25 September 1987

ER -

Berg, van den JL, Boxma OJ. Sojourn times in feedback queues. In Schellhaas H, Beek, van P, Isermann H, Schmidt R, Zijlstra M, editors, Operations Research Proceedings 1987 (Papers of the 16th Annual Meeting of DGOR, in cooperation with NSOR, Veldhoven, The Netherlands, September 23-25, 1987). Berlin: Springer. 1989. p. 478-478 https://doi.org/10.1007/978-3-642-73778-7_119

Sojourn times in feedback queues

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