Abstract
A broad class of parallel server systems is considered, for which we prove the steady-state asymptotic independence of server workloads, as the number of servers goes to infinity, while the system load remains sub-critical. Arriving jobs consist of multiple components. There are multiple job classes, and each class may be of one of two types, which determines the rule according to which the job components add workloads to the servers. The model is broad enough to include as special cases some popular queueing models with redundancy, such as cancel-on-start and cancel-on-completion redundancy. Our analysis uses mean-field process representation and the corresponding mean-field limits. In essence, our approach relies almost exclusively on three fundamental properties of the model: (a) monotonicity, (b) work conservation and (c) the property that, on average, “new arriving workload prefers to go to servers with lower workloads.”
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Adan, I., Kleiner, I., Righter, R., Weiss, G.: FCFS parallel service systems and matching models. Perform. Eval. 127, 253–272 (2018)
Ayesta, U., Bodas, T., Verloop, I.M.: On a unifying product form framework for redundancy models. Perform. Eval. 127, 93–119 (2018)
Ayesta, U., Bodas, T., Verloop, I.M.: On redundancy-d with cancel-on-start aka join-shortest-work (d). ACM SIGMETRICS Perform. Eval. Rev. 46(2), 24–26 (2018)
Bramson, M.: Stability of join the shortest queue networks. Ann. Appl. Probab. 21, 1568–1625 (2011)
Bramson, M., Lu, Y., Prabhakar, B.: Asymptotic independence of queues under randomized load balancing. Queueing Syst. 71, 247–292 (2012)
Foss, S., Chernova, N.: On the stability of a partially accessible multi-station queue with state-dependent routing. Queueing Syst. 29, 55–73 (1998)
Gardner, K., Harchol-Balter, M., Scheller-Wolf, A., Velednitsky, M., Zbarsky, S.: Redundancy-d: the power of d choices for redundancy. Oper. Res. 65(4), 1078–1094 (2017)
Gardner, K., Zbarsky, S., Doroudi, S., Harchol-Balter, M., Hyytia, E.: Reducing latency via redundant requests: exact analysis. ACM SIGMETRICS Perform. Eval. Rev. 43(1), 347–360 (2015)
Greenberg, A., Malyshev, V., Popov, S.: Stochastic model of massively parallel computation. Markov Process. Relat. Fields 2, 473–490 (1997)
Hellemans, T., Bodas, T., Van Houdt, B.: Performance analysis of workload dependent load balancing policies. Proc. ACM Meas. Anal. Comput. Syst. 3(2), 35 (2019)
Pang, G., Talreja, R., Whitt, W.: Martingale proofs of many-server heavy-traffic limits for Markovian queues. Probab. Surv. 4, 193–267 (2007)
Shah, N.B., Lee, K., Ramchandran, K.: When do redundant requests reduce latency? IEEE Trans. Commun. 64(2), 715–722 (2015)
Stolyar, A.L.: Pull-based load distribution in large-scale heterogeneous service systems. Queueing Syst. 80(4), 341–361 (2015)
Stolyar, A.L.: Pull-based load distribution among heterogeneous parallel servers: the case of multiple routers. Queueing Syst. 85(1–2), 31–65 (2017)
Vulimiri, A., Godfrey, P., Mittal, R., Sherry, J., Ratnasamy, S., Shenker, S.: Low latency via redundancy. CoNEXT 2013—Proceedings of the 2013 ACM International Conference on Emerging Networking Experiments and Technologies. Association for Computing Machinery, pp. 283–294 (2013)
Vvedenskaya, N., Dobrushin, R., Karpelevich, F.: Queueing system with selection of the shortest of two queues: an asymptotic approach. Probl. Inf. Transm. 32(1), 20–34 (1996)
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Shneer, S., Stolyar, A.L. Large-scale parallel server system with multi-component jobs. Queueing Syst 98, 21–48 (2021). https://doi.org/10.1007/s11134-021-09686-y
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DOI: https://doi.org/10.1007/s11134-021-09686-y
Keywords
- Large-scale service systems
- Steady-state
- Asymptotic independence
- Multi-component jobs
- Redundancy
- Replication
- Cancel on start
- Cancel on completion
- Load distribution and balancing