Abstract
We consider a system of parallel queues where tasks are assigned (dispatched) to one of the available servers upon arrival. The dispatching decision is based on the full state information, i.e., on the sizes of the new and existing jobs. We are interested in minimizing the so-called mean slowdown criterion corresponding to the mean of the sojourn time divided by the processing time. Assuming no new jobs arrive, the shortest-processing-time-product (SPTP) schedule is known to minimize the slowdown of the existing jobs. The main contribution of this paper is three-fold: 1) To show the optimality of SPTP with respect to slowdown in a single server queue under Poisson arrivals; 2) to derive the so-called size-aware value functions for M/G/1-FIFO/LIFO/SPTP with general holding costs of which the slowdown criterion is a special case; and 3) to utilize the value functions to derive efficient dispatching policies so as to minimize the mean slowdown in a heterogeneous server system. The derived policies offer a significantly better performance than e.g., the size-aware-task-assignment with equal load (SITA-E) and least-work-left (LWL) policies.
- S. Aalto, U. Ayesta, S. Borst, V. Misra, and R. Núnez-Queija. Beyond processor sharing. SIGMETRICS Perform. Eval. Rev., 34:36--43, 2007. Google ScholarDigital Library
- S. Aalto, U. Ayesta, and R. Righter. On the Gittins index in the M/G/1 queue. Queueing Systems, 63(1--4):437--458, 2009. Google ScholarDigital Library
- S. Aalto and J. Virtamo. Basic packet routing problem. In NTS-13, Trondheim, Norway, Aug. 1996.Google Scholar
- E. Bachmat and H. Sarfati. Analysis of SITA policies. Performance Evaluation, 67(2):102--120, 2010. Google ScholarDigital Library
- C. E. Bell and J. Shaler Stidham. Individual versus social optimization in the allocation of customers to alternative servers. Management Science, 29(7):831--839, July 1983.Google ScholarDigital Library
- M. E. Crovella, M. Harchol-Balter, and C. D. Murta. Task assignment in a distributed system: Improving performance by unbalancing load. In ACM SIGMETRICS, pages 268--269, June 1998. Google ScholarDigital Library
- A. Downey. A parallel workload model and its implications for processor allocation. In IEEE HPDC'97, pages 112--123, Aug. 1997. Google ScholarDigital Library
- A. Ephremides, P. Varaiya, and J. Walrand. A simple dynamic routing problem. IEEE Transactions on Automatic Control, 25(4):690--693, Aug. 1980.Google ScholarCross Ref
- H. Feng and V. Misra. Mixed scheduling disciplines for network flows. SIGMETRICS Perform. Eval. Rev., 31:36--39, Sept. 2003. Google ScholarDigital Library
- H. Feng, V. Misra, and D. Rubenstein. Optimal state-free, size-aware dispatching for heterogeneous M/G/-type systems. Perform. Eval., 62(1--4), 2005. Google ScholarDigital Library
- J. Gittins. Multi-armed Bandit Allocation Indices. Wiley, 1989.Google Scholar
- V. Gupta, M. Harchol-Balter, K. Sigman, and W. Whitt. Analysis of join-the-shortest-queue routing for web server farms. Performance Evaluation, 64(9--12):1062--1081, Oct. 2007. Google ScholarDigital Library
- M. Harchol-Balter. Task assignment with unknown duration. J. ACM, 49(2):260--288, Mar. 2002. Google ScholarDigital Library
- M. Harchol-Balter, M. E. Crovella, and C. D. Murta. On choosing a task assignment policy for a distributed server system. Journal of Parallel and Distributed Computing, 59:204--228, 1999. Google ScholarDigital Library
- M. Harchol-Balter and A. B. Downey. Exploiting process lifetime distributions for dynamic load balancing. ACM Transactions on Computer Systems, 15(3):253--285, Aug. 1997. Google ScholarDigital Library
- M. Harchol-Balter, A. Scheller-Wolf, and A. R. Young. Surprising results on task assignment in server farms with high-variability workloads. In ACM SIGMETRICS, pages 287--298, 2009. Google ScholarDigital Library
- M. Harchol-Balter, K. Sigman, and A. Wierman. Asymptotic convergence of scheduling policies with respect to slowdown. Perform. Eval., 49(1--4):241--256, Sept. 2002. Google ScholarDigital Library
- M. Haviv and T. Roughgarden. The price of anarchy in an exponential multi-server. Oper. Res. Lett., 35(4):421--426, 2007. Google ScholarDigital Library
- E. Hyytia, S. Aalto, and A. Penttinen. Minimizing slowdown in heterogeneous size-aware dispatching systems (full version). Technical report, Mar. 2012. arXiv:1203.5040.Google Scholar
- E. Hyytia, A. Penttinen, and S. Aalto. Size- and state-aware dispatching problem with queue-specific job sizes. European Journal of Operational Research, 217(2):357--370, Mar. 2012.Google ScholarCross Ref
- E. Hyytia, A. Penttinen, S. Aalto, and J. Virtamo. Dispatching problem with fixed size jobs and processor sharing discipline. In ITC'23, SFO, USA, Sept. 2011. Google ScholarDigital Library
- E. Hyytia, J. Virtamo, S. Aalto, and A. Penttinen. M/M/1-PS queue and size-aware task assignment. Performance Evaluation, 68(11):1136--1148, Nov. 2011. Google ScholarDigital Library
- K. R. Krishnan. Joining the right queue: a state-dependent decision rule. IEEE Transactions on Automatic Control, 35(1):104--108, Jan. 1990.Google ScholarCross Ref
- Z. Liu and R. Righter. Optimal load balancing on distributed homogeneous unreliable processors. Operations Research, 46(4):563--573, 1998. Google ScholarDigital Library
- Z. Liu and D. Towsley. Optimality of the round-robin routing policy. Journal of Applied Probability, 31(2):466--475, June 1994.Google ScholarCross Ref
- L. Schrage. A proof of the optimality of the shortest remaining processing time discipline. Operations Research, 16(3), 1968.Google Scholar
- W. Whitt. Deciding which queue to join: Some counterexamples. Oper. Res., 34(1):55--62, 1986. Google ScholarDigital Library
- A. Wierman. Fairness and scheduling in single server queues. Surveys in Operations Research and Management Science, 16(1):39--48, 2011.Google ScholarCross Ref
- A. Wierman, M. Harchol-Balter, and T. Osogami. Nearly insensitive bounds on SMART scheduling. In ACM SIGMETRICS, pages 205--216, 2005. Google ScholarDigital Library
- W. Winston. Optimality of the shortest line discipline. Journal of Applied Probability, 14:181--189, 1977.Google ScholarCross Ref
- S. Yang and G. de Veciana. Size-based adaptive bandwidth allocation: optimizing the average QoS for elastic flows. In IEEE INFOCOM, 2002.Google Scholar
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- Minimizing slowdown in heterogeneous size-aware dispatching systems
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