Abstract
We consider the scheduling system of a container cloud spot market where the user specifies the requested number of containers and their resource requirements, along with a bid value. Jobs are preemptively ordered based on their bid values as the available capacity, which is excess capacity made available for the spot market, may vary over time. Due to this variation, the number of allocated containers to a job may vary during its lifetime, resulting in users experiencing periods of degraded performance, potentially leading to job slowdown. We want to model and analyze such a scheduling system starting from first principles, inspired by the M/M/1 bribe queue. Thus, we introduce a simple, empirical queueing model which parametrically relates job slowdown to bid values given load and bid distribution. We demonstrate the accuracy of our approximation and parameter estimation through simulation.
This work was done while B. Ghit was an intern at the IBM T.J. Watson Research Center.
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Notes
- 1.
Note that in the case of exponential service time, the preemptive-repeat and preemptive-resume cases result in similar expressions for the average response time.
- 2.
Note that we define the slowdown as the ratio of two average values, and not the average of a ratio of two values. The latter alternative definition would have (1) resulted in a more complex derivation and conditional expression on the service time and, more importantly, (2) necessitated a priori knowledge of job service time, which may not be available in practice.
- 3.
We will use the words bribe and bid interchangeably throughout this paper.
- 4.
In practice, users may favor bidding low.
References
Agmon Ben-Yehuda, O., Ben-Yehuda, M., Schuster, A., Tsafrir, D.: Deconstructing Amazon EC2 spot instance pricing. ACM Trans. Econ. Comput. 1(3), 16:1–16:20 (2013)
Chohan, N., Castillo, C., Spreitzer, M., Steinder, M., Tantawi, A.N., Krintz, C.: See spot run: using spot instances for MapReduce workflows. USENIX HotCloud (2010)
Dowson, D., Wragg, A.: Maximum-entropy distributions having prescribed first and second moments (corresp.). IEEE Trans. Inf. Theor. 19(5), 689–693 (1973)
Forbes, C., Evans, M., Hastings, N., Peacock, B.: Statistical Distributions. Wiley, Hoboken (2011)
Ghit, B., Epema, D.: Better safe than sorry: grappling with failures of in-memory data analytics frameworks. In: ACM HPDC (2017)
Harchol-Balter, M.: Open problems in queueing theory inspired by datacenter computing. Queueing Syst. 97(1), 3–37 (2021). https://doi.org/10.1007/s11134-020-09684-6
Herodotou, H., et al.: Starfish: a self-tuning system for big data analytics. In: CIDR, vol. 11, no. 2011, pp. 261–272 (2011)
Javadi, B., Thulasiramy, R.K., Buyya, R.: Statistical modeling of spot instance prices in public cloud environments. In: 2011 Fourth IEEE International Conference on IEEE Utility and Cloud Computing (UCC), pp. 219–228. IEEE (2011)
Kleinrock, L.: Optimum bribing for queue position. Oper. Res. 15(2), 304–318 (1967)
Liu, H.: Cutting MapReduce cost with spot market. HotCloud (2011)
Shi, J., Zou, J., Lu, J., Cao, Z., Li, S., Wang, C.: MRTuner: a toolkit to enable holistic optimization for mapreduce jobs. In: VLDB Endowment, vol. 7, no. 13, pp. 1319–1330 (2014)
Simon, D.J.: Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches. Wiley, Hoboken (2006)
Unuvar, M., Doganata, Y., Tantawi, A.: Configuring cloud admission policies under dynamic demand. In: 2013 IEEE 21st International Symposium on Modeling, Analysis Simulation of Computer and Telecommunication Systems (MASCOTS), pp. 313–317, August 2013
Venkataraman, S., Yang, Z., Franklin, M.J., Recht, B., Stoica, I.: Ernest: efficient performance prediction for large-scale advanced analytics. In: USENIX NSDI (2016)
Verma, A., Cherkasova, L., Campbell, R.H.: ARIA: automatic resource inference and allocation for MapReduce environments. In: ACM ICAC (2011)
Zafer, M., Song, Y., Lee, K.-W.: Optimal bids for spot VMs in a cloud for deadline constrained jobs. In: IEEE CLOUD (2012)
Zaharia, M., Konwinski, A., Joseph, A.D., Katz, R.H., Stoica, I.: Improving MapReduce performance in heterogeneous environments. In: USENIX OSDI (2008)
Zheng, L., Joe-Wong, C., Tan, C.W., Chiang, M., Wang, X.: How to bid the cloud. ACM SIGCOMM Comput. Commun. Rev. 45(4), 71–84 (2015)
Zheng, T., Woodside, M., Litoiu, M.: Performance model estimation and tracking using optimal filters. IEEE Trans. Softw. Eng. 34(3), 391–406 (2008)
Zheng, T., Yang, J., Woodside, M., Litoiu, M., Iszlai, G.: Tracking time-varying parameters in software systems with extended Kalman filters. In: IBM Press Centre for Advanced Studies on Collaborative Research (2005)
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GhiÈ›, B., Tantawi, A. (2021). An Approximate Bribe Queueing Model for Bid Advising in Cloud Spot Markets. In: Abate, A., Marin, A. (eds) Quantitative Evaluation of Systems. QEST 2021. Lecture Notes in Computer Science(), vol 12846. Springer, Cham. https://doi.org/10.1007/978-3-030-85172-9_10
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