Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
skip to main content
10.4108/eai.14-12-2015.2262730guideproceedingsArticle/Chapter ViewAbstractPublication PagesConference Proceedingsacm-pubtype
Article
Free access

Higher response time moments for M/M/1 discriminatory processor sharing queues

Published: 04 January 2016 Publication History

Abstract

Obtaining response time moments in processor sharing (PS) queues is difficult due to serving of multiple jobs. Egalitarian PS (EPS) queues are limited to one class of arriving jobs. Discriminatory PS (DPS) assigns weights to different job classes and offers more diverse modeling capabilities than EPS. It is known that response time is the representative metric for delay as specified in service level agreements (SLAs), which consider higher moments important. Hence, we build an automated numerical algorithm for calculating higher moments of response time in M/M/1-DPS queues for multiple job classes and test two different case studies.

References

[1]
E. G. Coffman Jr., R. R. Muntz, H. Trotter: Waiting Time Distributions for Processor-Sharing Systems, In Journal ACM, 17, pp. 123-130 (1970).
[2]
T. Chis: Sliding Hidden Markov Model for Evaluating Discrete Data, In Proc. EPEW (2013).
[3]
P. G. Harrison, N. M. Patel: Performance Modelling of Communication Networks and Computer Architectures, Addison-Wesley, 1 (1993).
[4]
M. A. Kjaer, M. Kihl, A. Robertsson: Response-Time Control of a Processor-Sharing System using Virtualised Server Environments, In Proc. IFAC (2008).
[5]
S. W. M. Au-Yeung, N. J. Dingle, W. J. Knottenbelt: Efficient Approximation of Response time Densities and Quantiles in Stochastic Models, In Proc. ACM WOSP (2004).
[6]
T. Chis, P. G. Harrison: Adapting Hidden Markov Models for Online Learning, In Elsevier ENTCS, 318, pp. 109-127 (2015).
[7]
J. Kim, B. Kim: Sojourn time distribution in the M/M/1 queue with discriminatory processor-sharing, In Perform. Eval., 58, pp. 341-365 (2004).
[8]
S. F. Yashkov: Processor-Sharing Queues: Some Progress In Analysis, In Queue. Sys., 2, pp. 1-17 (1987).
[9]
A. Lakhany, H. Mausser: Estimating the parameters of the General Lambda Distribution, In Algo. Research Quarterly, 3, pp. 47-58 (2000).
[10]
T. Chis, P. G. Harrison: Modeling Multi-User Behaviour in Social Networks, In Proc. IEEE MASCOTS (2014).
[11]
J. W. Roberts: A survey on statistical bandwidth sharing, In Computer Networks, 45, pp. 319-332 (2004).
[12]
G. Fayolle, R. Iasnogorodski, I. Mitrani: Sharing a Processor Among Many Job Classes, In Journal ACM, 27(3), pp. 519-532 (1980).
[13]
H. Li, M. Muskulus, L. Wolters: Modeling Job Arrivals in a data-intensive Grid, In Proc. JSSPP Workshop (2006).
[14]
T. Chis, P. G. Harrison: iSWoM: The incremental Storage Workload Model using Hidden Markov Models, In Proc. ASMTA (2013).
[15]
K. Avrachenkov, U. Ayesta, P. Brown, R. Nunez-Queija: Discriminatory Processor Sharing Revisited, In Proc. IEEE Infocom (2005).
[16]
L. Kleinrock: Time-shared systems: A theoretical treatment, In Journal ACM, 14(2), pp. 242-261 (1967).
[17]
T. Chis, P. G. Harrison: Moment-Generating Algorithm for Response Time in Processor Sharing Queueing Systems, In Proc. EPEW (2015).

Recommendations

Comments

Information & Contributors

Information

Published In

cover image Guide Proceedings
VALUETOOLS'15: Proceedings of the 9th EAI International Conference on Performance Evaluation Methodologies and Tools
January 2016
272 pages
ISBN:9781631900969
  • Editors:
  • William Knottenbelt,
  • Katinka Wolter,
  • Ana Busic,
  • Marco Gribaudo,
  • Philipp Reinecke

Publisher

ICST (Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering)

Brussels, Belgium

Publication History

Published: 04 January 2016

Author Tags

  1. discriminatory processor sharing
  2. m/m/1
  3. response time

Qualifiers

  • Article

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • 0
    Total Citations
  • 46
    Total Downloads
  • Downloads (Last 12 months)10
  • Downloads (Last 6 weeks)4
Reflects downloads up to 04 Feb 2025

Other Metrics

Citations

View Options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Login options

Figures

Tables

Media

Share

Share

Share this Publication link

Share on social media