Sojourn-time approximations in queueing networks with feedback

B.M.M. Gijsen, R.D. van der Mei, Hans Leo van den Berg, K.M.C. van Wingerden

Research output: Contribution to journalArticleAcademicpeer-review

5 Citations (Scopus)
52 Downloads (Pure)

Abstract

This paper is motivated by the response-time analysis of distributed information systems, where transactions are handled by a sequence of front-end server and back-end server actions. We study sojourn times in an open queueing network with a single Processor Sharing (PS) node and an arbitrary number of M multi-server First-Come-First-Served (FCFS) nodes. Customers arrive at the PS according to a Poisson process. After departing from the PS node a customer jumps to FCFS node k with probability pk, and departs from the system with probability 1 - p, where p = Σk-1M pk (0 < p < 1). After receiving service at a FCFS node, a customer jumps back to the PS node. For this model, we focus on the mean and the variability of the sojourn time of an arbitrary customer in the system. The model is a product-form network, which immediately leads to a closed-form expression for the mean sojourn times. The variance of the sojourn times, however, does not admit an exact expression; the complexity is caused by the possibility of overtaking. To this end, we propose a new methodology for deriving closed-form approximations for the variance of sojourn times in queueing networks with feedback. Numerical results from extensive experimentation with simulations demonstrates that the approximations are highly accurate for a wide range of parameter values.
Original languageUndefined
Article number10.1016/j.peva.2005.08.002
Pages (from-to)743-758
Number of pages16
JournalPerformance evaluation
Volume63
Issue numberA219/8
DOIs
Publication statusPublished - Aug 2006

Keywords

  • EWI-9130
  • IR-63928
  • METIS-237929

Cite this

Gijsen, B. M. M., van der Mei, R. D., van den Berg, H. L., & van Wingerden, K. M. C. (2006). Sojourn-time approximations in queueing networks with feedback. Performance evaluation, 63(A219/8), 743-758. [10.1016/j.peva.2005.08.002]. https://doi.org/10.1016/j.peva.2005.08.002
Gijsen, B.M.M. ; van der Mei, R.D. ; van den Berg, Hans Leo ; van Wingerden, K.M.C. / Sojourn-time approximations in queueing networks with feedback. In: Performance evaluation. 2006 ; Vol. 63, No. A219/8. pp. 743-758.
@article{b36a46c94b3e4de8ad2bef5f475418cb,
title = "Sojourn-time approximations in queueing networks with feedback",
abstract = "This paper is motivated by the response-time analysis of distributed information systems, where transactions are handled by a sequence of front-end server and back-end server actions. We study sojourn times in an open queueing network with a single Processor Sharing (PS) node and an arbitrary number of M multi-server First-Come-First-Served (FCFS) nodes. Customers arrive at the PS according to a Poisson process. After departing from the PS node a customer jumps to FCFS node k with probability pk, and departs from the system with probability 1 - p, where p = Σk-1M pk (0 < p < 1). After receiving service at a FCFS node, a customer jumps back to the PS node. For this model, we focus on the mean and the variability of the sojourn time of an arbitrary customer in the system. The model is a product-form network, which immediately leads to a closed-form expression for the mean sojourn times. The variance of the sojourn times, however, does not admit an exact expression; the complexity is caused by the possibility of overtaking. To this end, we propose a new methodology for deriving closed-form approximations for the variance of sojourn times in queueing networks with feedback. Numerical results from extensive experimentation with simulations demonstrates that the approximations are highly accurate for a wide range of parameter values.",
keywords = "EWI-9130, IR-63928, METIS-237929",
author = "B.M.M. Gijsen and {van der Mei}, R.D. and {van den Berg}, {Hans Leo} and {van Wingerden}, K.M.C.",
note = "10.1016/j.peva.2005.08.002",
year = "2006",
month = "8",
doi = "10.1016/j.peva.2005.08.002",
language = "Undefined",
volume = "63",
pages = "743--758",
journal = "Performance evaluation",
issn = "0166-5316",
publisher = "Elsevier",
number = "A219/8",

}

Gijsen, BMM, van der Mei, RD, van den Berg, HL & van Wingerden, KMC 2006, 'Sojourn-time approximations in queueing networks with feedback' Performance evaluation, vol. 63, no. A219/8, 10.1016/j.peva.2005.08.002, pp. 743-758. https://doi.org/10.1016/j.peva.2005.08.002

Sojourn-time approximations in queueing networks with feedback. / Gijsen, B.M.M.; van der Mei, R.D.; van den Berg, Hans Leo; van Wingerden, K.M.C.

In: Performance evaluation, Vol. 63, No. A219/8, 10.1016/j.peva.2005.08.002, 08.2006, p. 743-758.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Sojourn-time approximations in queueing networks with feedback

AU - Gijsen, B.M.M.

AU - van der Mei, R.D.

AU - van den Berg, Hans Leo

AU - van Wingerden, K.M.C.

N1 - 10.1016/j.peva.2005.08.002

PY - 2006/8

Y1 - 2006/8

N2 - This paper is motivated by the response-time analysis of distributed information systems, where transactions are handled by a sequence of front-end server and back-end server actions. We study sojourn times in an open queueing network with a single Processor Sharing (PS) node and an arbitrary number of M multi-server First-Come-First-Served (FCFS) nodes. Customers arrive at the PS according to a Poisson process. After departing from the PS node a customer jumps to FCFS node k with probability pk, and departs from the system with probability 1 - p, where p = Σk-1M pk (0 < p < 1). After receiving service at a FCFS node, a customer jumps back to the PS node. For this model, we focus on the mean and the variability of the sojourn time of an arbitrary customer in the system. The model is a product-form network, which immediately leads to a closed-form expression for the mean sojourn times. The variance of the sojourn times, however, does not admit an exact expression; the complexity is caused by the possibility of overtaking. To this end, we propose a new methodology for deriving closed-form approximations for the variance of sojourn times in queueing networks with feedback. Numerical results from extensive experimentation with simulations demonstrates that the approximations are highly accurate for a wide range of parameter values.

AB - This paper is motivated by the response-time analysis of distributed information systems, where transactions are handled by a sequence of front-end server and back-end server actions. We study sojourn times in an open queueing network with a single Processor Sharing (PS) node and an arbitrary number of M multi-server First-Come-First-Served (FCFS) nodes. Customers arrive at the PS according to a Poisson process. After departing from the PS node a customer jumps to FCFS node k with probability pk, and departs from the system with probability 1 - p, where p = Σk-1M pk (0 < p < 1). After receiving service at a FCFS node, a customer jumps back to the PS node. For this model, we focus on the mean and the variability of the sojourn time of an arbitrary customer in the system. The model is a product-form network, which immediately leads to a closed-form expression for the mean sojourn times. The variance of the sojourn times, however, does not admit an exact expression; the complexity is caused by the possibility of overtaking. To this end, we propose a new methodology for deriving closed-form approximations for the variance of sojourn times in queueing networks with feedback. Numerical results from extensive experimentation with simulations demonstrates that the approximations are highly accurate for a wide range of parameter values.

KW - EWI-9130

KW - IR-63928

KW - METIS-237929

U2 - 10.1016/j.peva.2005.08.002

DO - 10.1016/j.peva.2005.08.002

M3 - Article

VL - 63

SP - 743

EP - 758

JO - Performance evaluation

JF - Performance evaluation

SN - 0166-5316

IS - A219/8

M1 - 10.1016/j.peva.2005.08.002

ER -

Gijsen BMM, van der Mei RD, van den Berg HL, van Wingerden KMC. Sojourn-time approximations in queueing networks with feedback. Performance evaluation. 2006 Aug;63(A219/8):743-758. 10.1016/j.peva.2005.08.002. https://doi.org/10.1016/j.peva.2005.08.002