Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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A PROCESSOR SHARING MODEL FOR COMMUNICATION SYSTEMS

  • Lim, Jong Seul (Division of Electronics Information Communications Engineering, Sunmoon University) ;
  • Park, Chul Guen (Division of Electronics Information Communications Engineering, Sunmoon University) ;
  • Ahn, Seong Joon (Division of Electronics Information Communications Engineering, Sunmoon University) ;
  • Lee, Seoyoung (Division of Electronics Information Communications Engineering, Sunmoon University)
  • Published : 2004.05.01

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Abstract

we model communication and computer systems that process interactive and several and several types of background jobs. The scheduling policy in use is to share the processor among all interactive jobs and, at most, one background job of each type at a time according to the process sharing discipline. Background jobs of each type are served on a first-come-first-served basis. Such scheduling policy is called Processor Sharing with Background jobs (PSBJ). In fact, the PSBJ policy is commonly used on many communication and computer systems that allow interactive usage of the systems and process certain jobs in a background mode. In this paper, the stability conditions for the PSBJ policy are given and proved. Since an exact analysis of the policy seems to be very difficult, an approximate analytic model is proposed to obtain the average job sojourn times. The model requires the solution of a set of nonlinear equations, for which an iterative algorithm is given and its convergence is proved. Our results reveal that the model provides excellent estimates of average sojourn times for both interactive and background jobs with a few percent of errors in most of the cases considered.

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References

  1. Point process and queues Bremaud, P.
  2. J. Acm. v.17 no.1 Waiting time distributions for processor-sharing systems Coffman, E. G.;Muntz, R. R.;Trotter, H.
  3. Tech. Rap. 69 The multiple phase service network with generalized processor sharing Cohen, J. W.
  4. Introduction to queueing theory Cooper, R. B.
  5. J. Acm. v.27 no.3 Sharing a processor among many job classes Fayolle, G.;Mitrani, I.;Iasnogorodski, R
  6. Adv. Appl. Prob. v.14 The solution of certain two-dimensional Markov models Fayolle, G.;King,P.J.B.;Mitrani, I.
  7. IEEE Trans. On Software Eng. v.Se-9 no.4 Weighted processor sharing-results for hyperexponential servers Ferguson, M. J.
  8. Brownian models of queueing network with heterogeneous customer populations Harrison, J. M.;W. Fleming(ed.)
  9. applications of functional analysis and operator theory Hutson, V.;Pym, J. S.
  10. J. ACM. v.14 no.2 Time-shared systems: A theoretical treatment Kleinrock, L.
  11. Queueing Systems:Theory v.1 Kleinrock, L.
  12. Opns. Res. v.9 A proof of the queueing oformula L = ${\lambda}$W Little, J. D.
  13. Opns. Res. v.30 Poisson arrivals see time averages Wolff, R. W.