Dynamic Budget-Constrained Pricing in the Cloud
We introduce a new model of user-based dynamic pricing in which decisions occur in real time and are strongly influenced by the budget constraints of users. This model captures the fundamental operation of many electronic markets that are used for allocating resources. In particular, we focus on those used in data centers and cloud computing where pricing is often an internal mechanism used to efficiently allocate virtual machines. We study the allocative properties and dynamic stability of this pricing model under a standard framework of cloud computing systems which leads to highly degenerate systems of prices. We show that as the size of the system grows the user-based budget-constrained dynamic pricing mechanism converges to the standard Walrasian prices. However, for finite systems, the prices can be non-degenerate and the allocations unfair, with large groups of users receiving allocations significantly below their fair share. In addition, we show that improper choice of price update parameters can lead to significant instabilities in prices, which could be problematic in real cloud computing systems, by inducing system instabilities and allowing manipulations by users. We construct scaling rules for parameters that reduce these instabilities.
KeywordsCloud Computing Virtual Machine Equilibrium Price Dynamic Price Price Mechanism
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- 1.Ananthanarayanan, G., Ghodsi, A., Shenker, S., Stoica, I.: Disk-locality in datacenter computing considered irrelevant. In: Proceedings of the 13th USENIX Workshop on Hot Topics in Operating Systems, pp. 1–5 (2011)Google Scholar
- 2.Bhattacharya, A.A., Culler, D., Friedman, E., Ghodsi, A., Shenker, S., Stoica, I.: Hierarchical scheduling for diverse datacenter workloads. In: Proceedings of ACM Symposium on Cloud Computing, SoCC 2013 (2013)Google Scholar
- 4.Cole, R., Fleischer, L.: Fast-Converging tatonnement algorithms for one-time and ongoing market problems. In: Proceedings of the 40th Annual ACM Symposium on Theory of Computing, pp. 315–324. ACM (2008)Google Scholar
- 6.Friedman, E.J., Halpern, J.Y., Kash, I.: Efficiency and nash equilibria in a scrip system for P2P networks. In: Feigenbaum, J., Chuang, J., Pennock, D. (eds.) ACM Conference on Electronic Commerce (EC), pp. 140–149 (2006)Google Scholar
- 7.Ghodsi, A., Zaharia, M., Shenker, S., Stoica, I.: Choosy: max-min fair sharing for datacenter jobs with constraints. In: Proceedings of the 8th ACM European Conference on Computer Systems, pp. 365–378. ACM (2013)Google Scholar
- 8.Hahne, E.L., Gallager, R.G.: Round robin scheduling for fair flow control in data communication networks. NASA STI/Recon Tech. Rep. N 86, 30047 (1986)Google Scholar
- 9.Hindman, B., Konwinski, A., Zaharia, M., Ghodsi, A., Joseph, A.D., Katz, R.H., Shenker, S., Stoica, I.: Mesos: a platform for fine-grained resource sharing in the data center. In: Proceedings of NSDI (2011)Google Scholar
- 14.Walras, L.: Elements of Pure Economics Or The Theory of Social Wealth (1954)Google Scholar
- 15.Yin, G., Zhang, Q.: Continuous-Time Markov Chains and Applications: A Two-Time-Scale Approach, vol. 37. Springer (2012)Google Scholar