This Article 
 Bibliographic References 
 Add to: 
Performance Evaluation of Dynamic Sharing of Processors in Two-Stage Parallel Processing Systems
March 1993 (vol. 4 no. 3)
pp. 306-317

The performance of job scheduling is studied in a large parallel processing system where a job is modeled as a concatenation of two stages which must be processed in sequence.P/sub i/ is the number of processors required by stage P as the total number ofprocessors in the system. A large parallel computing system is considered whereMax(/math/). For such systems, exact expressions for the mean system delay are obtained for variousjob models and disciplines. The results show that the priority should be given to jobsworking on the stage which requires fewer processors. The large parallel system condition is then relaxed to obtain the mean system time for two job models whenthe priority is given to the second stage. Moreover, a scale-up rule is introduced toobtain the approximated delay performance when the system provides more processorsthan the maximum number of processors required by both stages. An approximation model is given for jobs with more than two stages.

[1] O. J. Boxma, J. W. Cohen, and N. Huffels, "Approximations of the mean waiting time in an M/G/cqueueing system,"Oper. Res., vol. 27, pp. 1115-1127, 1979.
[2] S.L. Brumelle, "Some inequalities for parallel server queues,"Oper. Res., vol. 19, pp. 402-413, 1971.
[3] G. P. Cosmetatos, "Some approximation equilibrium results for the multi-server queue (M/G/r),"Opnl. Res. Quart., vol. 27, pp. 615-620, 1976.
[4] C. D. Crommelin, "Delay probability formulae,"P.O. Elec. Eng. J., vol. 26, pp. 266-274, 1934.
[5] F. S. Hillier and F. D. Lo, "Tables for multiple-server queueing systems involving Erlang distribution," Tech. Rep. 31, Dep. of Oper. Res., Stanford Univ., 1971.
[6] M. H. van Hoorn and H. C. Tijms, "Approximations for the waiting time distribution of the M/G/cqueue,"Perform. Eval, vol. 2, pp. 22-28, 1982.
[7] J. Huang, "On the behavior of algorithms in a multiprocessing environment," Ph.D. diss., Computer Sci. Dept., UCLA, 1988.
[8] J. F. C. Kingman, "Inequalities in the theory of queues,"J. Royal Statistical Society, Series B, vol. 32, pp. 102-110, 1970.
[9] L. Kleinrock,Queueing Systems, Vol. 1: Theory. New York: Wiley-Interscience, 1975.
[10] L. Kleinrock,Queueing Systems, Vol. 2: Computer Applications. New York: Wiley-Interscience, 1976.
[11] L. Kleinrock, "Performance models for distributed systems," inTeletraffic Analysis and Computer Performance Evaluation, Proc. International Seminar held at the centre for Mathematics and Computer Science (CWI), Amsterdam, The Netherlands, June 2-6, 1986, pp. 1-15.
[12] J. D. C. Little, "A proof of the queueing formulaL =λW," Oper. Res., vol. 9, pp. 383-387, 1961.
[13] E. Maaloe, "Approximation formulae for estimation of waiting-time in multiple-channel queueing system,"Mgmt. Sci., vol. 19, pp. 703-710, 1973.
[14] S. A. Nozaki and S. M. Ross, "Approximations in finite-capacity multiserver queues with Poisson arrivals,"J. Appl. Probability, vol. 15, no. 4, pp. 826-834, Dec. 1978.
[15] R. Syski,Introduction Congestion Theory in Telephone Systems, second ed. Amsterdam, The Netherlands: North Holland, 1984.
[16] Y. Yakahashi, "An approximation formula for the mean waiting time of an M/G/mqueue,"J. Oper. Res. Soc. Japan, vol. 20, pp. 150-163, 1977.
[17] P. Ein-Dor, "Grosch's law re-revisited: CPU power and the cost of computation,"Commun. ACM, vol. 28, pp. 142-151, Feb. 1985.
[18] B. Kraimeche and M. Schwartz, "Bandwidth allocation strategies in wide-band integrated networks,"IEEE J. Select. Areas Commun., vol. SAC-4, pp. 869-878, Sept. 1986.
[19] L. Green, "A queueing system in which customers require a random number of servers,"Oper. Res., vol. 28, no. 6, pp. 1335-1346, Nov.-Dec. 1980.
[20] A. M. Law and W. David Kelton,"Simulation Modeling and Analysis. New York: McGraw-Hill, 1982.

Index Terms:
Index Termsperformance evaluation; dynamic sharing of processors; two-stage parallel processingsystems; job scheduling; mean system delay; mean system time; scale-up rule;approximated delay performance; approximation model; delays; parallel processing;performance evaluation; scheduling
J.H. Huang, L. Kleinrock, "Performance Evaluation of Dynamic Sharing of Processors in Two-Stage Parallel Processing Systems," IEEE Transactions on Parallel and Distributed Systems, vol. 4, no. 3, pp. 306-317, March 1993, doi:10.1109/71.210813
Usage of this product signifies your acceptance of the Terms of Use.