Abstract
In this paper the class of acyclic fork-join queuing networks that arise in various applications, including parallel processing and flexible manufacturing are studied. In such queuing networks, a fork describes the simultaneous creation of several new customers, which are sent to different queues. The corresponding join occurs when the services of all these new customers are completed. The evolution equations that govern the behavior of such networks are derived. From this, the stability conditions are obtained and upper and lower bounds on the network response times are developed. These bounds are based on various stochastic ordering principles and on the notion of association of random variables.
- 1 BACCELLI, F. Two parallel queues created by arrivals with two demands: The M/G/2 symmetrical case. Report INRIA, No. 426, July 1985.Google Scholar
- 2 BACCELLI, F., AND BREMAUD, P. Palm probabilities and stationary queues. In Lecture Notes in Statistics, vol. 41, Springer-Verlag, New York, 1987.Google Scholar
- 3 BACCELLI, F., AND MAKOWSKI, A. Simple computable bounds for the fork-join queue. In Proceedings of the Conference oJ lnJormation Science Systems. Johns Hopkins Univ., Baltimore, Md., Mar. I985, pp. 436-44I.Google Scholar
- 4 BACCELLI, F., AND MAKOWSKI, A. Stability and bounds for single server queues in random environment, in Stochasiic/vlodels, vol. 2, no. 2. Marcel Dekker, 1986.Google Scholar
- 5 BACCELLI, F., AND MASSEY, W.A. Series-parallel, fork-join queueing networks and their stochastic ordering. INRIA Report No 534. INRIA, Paris, France, June 1986.Google Scholar
- 6 BACCELLI, F., Gelenbe, E., AND PLATEAU, B. An end to end approach to the resequencing problem. J. ACM 31, 3 (July 1984), 474-485. Google Scholar
- 7 BACCELLI, F., MAKOWSKI, A., AND SHWARTZ, A. Fork-join queue and related systems with synchro_niTation cnn~traint.~: ~qtaehn~tie ordering, approximations and comp,~tnhle bo,,nd~ J. App/. Prob., to appear.Google Scholar
- 8 BACCELLI, F., MASSEV, W. A., AND TOWSLEY, D. Acyclic fork-join queueing networks. Int. Rep., Comput. Sci. Dept., Univ. of Massachusetts, Boston, Mass., Apr. 1987. Google Scholar
- 9 BARLOW, R., AND PROSCHAN, F. Statistical theory of reliability and life testing. Holt, Rinehart, and Winston, New York, 1975.Google Scholar
- 10 BRINCH HANSEN, P. The programming language concurrent Pascal. IEEE Trans. Softw. Eng. SE-I (June 1975), 199-207.Google Scholar
- 11 COHEN, J.W. The Single Server Queue. North Holland, Amsterdam, 1982.Google Scholar
- 12 FLATTO, L., AND HAHN, S. Two parallel queues created by arrivals with two demands, }. SIAM J. Appl. Math. 44 (1984), 1041-1053.Google Scholar
- 13 HAJEK, B. The proof of a folk theorem on queuing delay with applications to routing in networks. J. ACM 30, 4 (Oct. 1983), 834-851. Google Scholar
- 14 IqOARE, C. A.R. Communicating Sequential Processes. Prentice-Hail, London, England, i 985.Google Scholar
- 15 KRUSKAL, C. P., AND WEISS, A. Allocating independent subtasks on parallel processors. IEEE Trans. Sofiw. Eng. SE-11 (Oct. 1985), 1001-1016. Google Scholar
- 16 LO~Ne~, K. ~v,. The stability of queues with nonindependent interarrival and service times. Proc. Cambridge Phys. Soc. 58 (1962), 497-510.Google Scholar
- 17 MASSEV, W.A. Asymptotic analysis of the time dependent M/M/1 Queue. Math. Oper. Res. I0, i- \ZVAUV t --'~--J~. t.Google Scholar
- 18 NELSON, R., AND TANTAWI, A.N. Approximate analysis of fork/join synchronization in parallel queues. IEEE Trans. Comput. 37, 6 (June 1988), 739-743. Google Scholar
- 19 NELSON, R., TOWSLEY, O., AND TANTAWl, A. N. Performance analysis of parallel processing systems. IEEE Trans. Sofiw. Eng. 14, 4 (Apr. 1988), 532-540. Google Scholar
- 20 PYLE, I.C. The Ada Programming Language. Prentice-Hall, London, England, 198 i. Google Scholar
- 21 ROLSKI, T. Comparison theorems for queues with dependent inter-arrival times. In Modelling and Performance Evaluation Methodology. Lecture Notes in Control and Information Sciences, vol. 60, Springer-Verlag, New York, 1984.Google Scholar
- 22 SIGMAN, K. Queues as Harris recurrent Markov chains. Queueing Syst. 3 (1988), 179-198. Google Scholar
- 23 STOYAN, D. Comparison Methods for Queues and Other Stochastic Models, English translation, D. J. Daley, ed. Wiley, New York, 1984.Google Scholar
- 24 TOWSLEY, O., AND YU, S.P. Bounds for two server fork-join queueing systems. Tech. Rep. TR 87-i23. Dept. Computer & lnlormation Science, Univ. of Massachusetts, Boston, Mass., Nov. 1987. Google Scholar
- 25 TOWSLEY, O., ROMMEL, J. A., AND STANKOVIC, J. A. The performance of processor sharing schedulding fork-join in multiprocessing.In High-Performance Computer Systems, E.Gelenbe, ed. North-Holland, Amsterdam, 1988, pp. 146-156.Google Scholar
- 26 WmTT, W. Comparing and counting processes and queues. Adv. Appl. Prob. 13 (1981), 207-220.Google Scholar
- 27 WHITT, W. Minimizinga delays in the GI/G/I queue. Oper. Res. 32(1984), 41-51.Google Scholar
Index Terms
- Acyclic fork-join queuing networks
Recommendations
Computable Bounds in Fork-Join Queueing Systems
SIGMETRICS '15: Proceedings of the 2015 ACM SIGMETRICS International Conference on Measurement and Modeling of Computer SystemsIn a Fork-Join (FJ) queueing system an upstream fork station splits incoming jobs into N tasks to be further processed by N parallel servers, each with its own queue; the response time of one job is determined, at a downstream join station, by the ...
Comments