This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
An Approximate Analysis of the Join the Shortest Queue (JSQ) Policy
March 1996 (vol. 7 no. 3)
pp. 301-307

Abstract—This paper presents an accurate analytical model for evaluating the performance of the Join the Shortest Queue (JSQ) policy. The system considered consists of N identical queues each of which may have single or multiple servers. A birth-death Markov process is used to model the evolution of the number of jobs in the system. Our results show that this method provides very accurate estimates of the average job response times.

[1] I.J.B.F. Adan, J. Wessels, and W.H.M. Zijm, "Analysis of the Asymmetric Shortest Queue Problem," Queueing Systems, vol. 8, pp. 1-58, 1991.
[2] J.P.C. Blanc, "The Power-Series Algorithm Applied to the Shortest-Queue Model," Operations Research, vol. 40, no. 1, pp. 157-167, Jan.-Feb. 1992.
[3] J.W. Cohen and O.J. Boxma, Boundary Value Problems in Queueing System Analysis. North-Holland, 1983.
[4] B.W. Conolly, "The Autostrada Queueing Problem," J. Appl. Prob., vol. 21, pp. 394-403, 1984.
[5] A. Ephremides, P. Varaiya, and J. Walrand, "A Simple Dynamic Routing Problem," IEEE Trans. Automatic Control, vol. 25, pp. 690-693, Aug. 1980.
[6] L. Flatto and H.P. McKean, "Two Queues in Parallel," Comm. Pure and Applied Mathematics, vol. 30, pp. 255-263, 1977.
[7] W.K. Grassmann, "Transient and Steady State Results for Two Parallel Queues," Omega, vol. 8, pp. 105-112, 1980.
[8] F.A. Haight, "Two Queues in Parallel," Biometrika, vol. 45, pp. 401-410, 1958.
[9] S. Halfin, "The Shortest Queue Problem," J. Appl. Prob., vol. 22, pp. 865-878, 1985.
[10] G.J. Foschini and J. Salz, "A Basic Dynamic Routing Problem and Diffusion," IEEE Trans. Comm., vol. 26, pp. 320-327, May 1978.
[11] I. Gertsbakh, "The Shorter Queue Problem: A Numerical Study Using the Matrix-Geometric Solution," European J. Operational Research, vol. 15, pp. 374-381, 1984.
[12] P. Heidelberger and P. Welch, "A Spectral Method for Confidence Interval Generation and Run Length Control in Simulations," Comm. ACM, vol. 24, no. 4, pp. 233-245, Apr. 1981.
[13] J.F.C. Kingman, "Two Similar Queues in Parallel," Ann. Math. Stat., vol. 32, pp. 1,314-1,323, 1961.
[14] C. Knessl, B.J. Matkowsky, Z. Schuss, and C. Tier, "Two Parallel M/G/1 Queues Where Arrivals Join the Systems with the Smaller Buffer Content," IEEE Trans. Comm., vol. 35, pp. 1,153-1,158, Nov. 1987.
[15] H.C. Lin and C.S. Raghavendra, “A Dynamic Load-Balancing Policy with a Central Job Dispatcher (LBC),” IEEE Trans. Software Eng., vol. 18, no. 2, pp. 148-158, Feb. 1992.
[16] H.C. Lin and C.S. Raghavendra, "An Analysis of the Join the Shortest Queue (JSQ) Policy," Proc. 12th Int'l Conf. Distributed Computing Systems, pp. 362-366, June, 1992.
[17] H.C. Lin and C.S. Raghavendra, "A State-Aggregation Method for Analyzing Dynamic Load-Balancing Policies," Proc. 13th Int'l Conf. Distributed Computing Systems,Pittsburgh, Penn., May25-28, 1993.
[18] R.D. Nelson and T.K. Philips, "An Approximation to the Response Time for Shortest Queue Routing," ACM Performance Evaluation Review, vol. 17, pp. 181-189, May 1989.
[19] R.D. Nelson and T.K. Philips, "An Approximation for the Mean Response Time for Shortest Queue Routing with General Interarrival and Service Times," Performance Evaluation, vol. 17, pp. 123-139, 1993.
[20] M.F. Neuts, Matrix-Geometric Solutions in Stochastic Models.Baltimore: Johns Hopkins Univ. Press, 1981.
[21] B.M. Rao and M.J.M. Posner, "Algorithmic and Approximation Analyses of the Shorter Queue Model," Naval Research Logistics, vol. 34, pp. 381-398, 1987.
[22] W. Winston, "Optimality of the Shortest Line Discipline," J. Appl. Prob., vol. 14, pp. 181-189, 1977.
[23] Y. Zhao and W.K. Grassmann, "A Numerically Stable Algorithm for Two Server Queue Models," Queueing Systems, vol. 8, pp. 59-79, 1991.

Index Terms:
Analytical approximation, join the shortest queue, load balancing, multiprocessor systems, parallel queues, performance evaluation.
Citation:
Hwa-Chun Lin, C.s. Raghavendra, "An Approximate Analysis of the Join the Shortest Queue (JSQ) Policy," IEEE Transactions on Parallel and Distributed Systems, vol. 7, no. 3, pp. 301-307, March 1996, doi:10.1109/71.491583
Usage of this product signifies your acceptance of the Terms of Use.