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 Sept 1987 → 25 Sept 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

Cite this

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.

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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)

A2 - Schellhaas, H.

A2 - Beek, van, P.

A2 - Isermann, H.

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 -

Sojourn times in feedback queues

Abstract

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