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Multiple class memory constrained queueing networks

Published: 30 August 1982 Publication History

Abstract

Most computer systems have a memory constraint: a limit on the number of requests that can actively compete for processing resources, imposed by finite memory resources. This characteristic violates the conditions required for queueing network performance models to be <i>separable,</i> i.e., amenable to efficient analysis by standard algorithms. Useful algorithms for analyzing models of memory constrained systems have been devised only for models with a single customer class.
In this paper we consider the multiple class case. We introduce and evaluate an algorithm for analyzing multiple class queueing networks in which the classes have independent memory constraints. We extend this algorithm to situations in which several classes share a memory constraint. We sketch a generalization to situations in which a subsystem within an overall system model has a population constraint.
Our algorithm is compatible with the extremely time- and space-efficient iterative approximate solution techniques for separable queueing networks. This level of efficiency is mandatory for modelling large systems.

References

[1]
{Bard 1979} Yonathan Bard; "Some Extensions to Multiclass Queueing Network Analysis"; Proc. IFIP W.G.7.3 International Symposium on Computer Performance Modelling, Measurement and Evaluation, Vienna, February 1979.
[2]
{Baskett et al. 1975} Forest Baskett, K. Mani Chandy, Richard R. Muntz and Fernando G. Palacios; "Open, Closed and Mixed Networks of Queues with Different Classes of Customers"; JACM 22, 2, April 1975, pp. 248--260.
[3]
{Brandwajn 1974} Alexandre Brandwajn; "A Model of a Time-Sharing System Solved Using Equivalence and Decomposition Methods"; Acta Informatica 4, 1, 1974, pp. 11--47.
[4]
{Brown et al. 1975} R. M. Brown, J. C. Browne and K. M. Chandy; "Memory Management and Response Time"; CACM 20, 3, March 1977, pp. 153--165.
[5]
{Bryant 1982} R. M. Bryant: "Maximum Processing Rates of Memory Bound Systems"; JACM 29, 2, April 1982, pp. 461--477.
[6]
{Chandy et al. 1975} K. M. Chandy, U. Herzog and L. Woo; "Parametric Analysis of Queueing Networks"; IBM J. Res. Develop. 19, 1, January 1975, pp. 36--42.
[7]
{Chandy & Neuse 1982} K. M. Chandy and D. Neuse; "Fast Accurate Heuristic Algorithms for Queueing Network Models of Computing Systems"; CACM 25, 2, February 1982.
[8]
{Chandy & Sauer 1978} K. Mani Chandy and Charles H. Sauer; "Approximate Methods for Analyzing Queueing Network Models of Computing Systems"; Computing Surveys 10, 8, September 1978, pp. 281--317.
[9]
{Courtois 1977} P. J. Courtois; Decomposability: Queueing and Computer System Applications; Academic Press, 1977.
[10]
{Jacobson & Lazowska 1982} Patricia A. Jacobson and Edward D. Lazowska; "The Method of Surrogates: Simultaneous Resource Possession in Queueing Network Models of Computer Systems"; CACM 25, 2, February 1982.
[11]
{Keller 1976} T. W. Keller; "Computer System Models with Passive Resources"; Ph.D. Thesis, University of Texas at Austin, 1976.
[12]
{Lam 1977} S. S. Lam; "Queuing Networks with Population Size Constraints"; IBM J. Res. Develop. 21, 4, July 1977, pp. 370--378.
[13]
{Menasce & Almeida 1981} Daniel A. Menasce and Virtilio A. F. Almeida; "Computing Performance Measures of Computer Systems with Variable Degree of Multiprogramming"; Proc. CMG XII, pp. 97--106.
[14]
{Sauer 1981} Charles H. Sauer; "Approximate Solution of Queueing Networks with Simultaneous Resource Possession"; IBM J. Res. Develop. 25, 6, November 1981, pp. 894--903.

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Published In

cover image ACM SIGMETRICS Performance Evaluation Review
ACM SIGMETRICS Performance Evaluation Review  Volume 11, Issue 4
December 1982
258 pages
ISSN:0163-5999
DOI:10.1145/1035332
Issue’s Table of Contents
  • cover image ACM Conferences
    SIGMETRICS '82: Proceedings of the 1982 ACM SIGMETRICS conference on Measurement and modeling of computer systems
    August 1982
    264 pages
    ISBN:0897910796
    DOI:10.1145/1035293
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 30 August 1982
Published in SIGMETRICS Volume 11, Issue 4

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Author Tags

  1. approximate solution technique
  2. computer system performance evaluation
  3. memory constraint
  4. population constraint
  5. queueing network model

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  • (2009)Solving Semi-Open Queuing NetworksOperations Research10.1287/opre.1080.062757:2(391-401)Online publication date: 1-Mar-2009
  • (2009)RETRACTED ARTICLE: The performance of a memory restricted computer with a state-dependent job admission policyKorean journal of computational & applied mathematics10.1007/BF030089612:2(21-46)Online publication date: 1-Jan-2009
  • (1990)Modelling contention sensing memory management systemsMathematical and Computer Modelling: An International Journal10.1016/0895-7177(90)90172-J14(184-189)Online publication date: 1-Jan-1990
  • (1990)Approximate analysis of general open queuing networks with restricted capacityPerformance Evaluation10.1016/0166-5316(90)90013-911:3(209-222)Online publication date: 1-Sep-1990
  • (1985)Theory of queuing networks and its applications to the analysis of information-computing systemsJournal of Soviet Mathematics10.1007/BF0210483029:1(951-1050)Online publication date: Apr-1985
  • (1995)Remarks on DQDB-analysis: multi-queue stations with 1-limited serviceProceedings IEEE International Conference on Communications ICC '9510.1109/ICC.1995.524211(788-792)Online publication date: 1995
  • (1992)Analysis of a queueing network model with class dependent window flow control[Proceedings] IEEE INFOCOM '92: The Conference on Computer Communications10.1109/INFCOM.1992.263445(968-977 vol.2)Online publication date: 1992
  • (1990)Modelling contention sensing memory management systemsMathematical and Computer Modelling: An International Journal10.1016/0895-7177(90)90172-J14(184-189)Online publication date: 1-Jan-1990
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