Abstract
The problem of pricing the cloud has attracted much recent attention due to the widespread use of cloud computing and cloud services. From a theoretical perspective, several mechanisms that provide strong efficiency or fairness guarantees and desirable incentive properties have been designed. However, these mechanisms often rely on a rigid model, with several parameters needing to be precisely known in order for the guarantees to hold. In this paper, we consider a stochastic model and show that it is possible to obtain good welfare and revenue guarantees with simple mechanisms that do not make use of the information on some of these parameters. In particular, we prove that a mechanism that sets the same price per time step for jobs of any length achieves at least \(50\%\) of the welfare and revenue obtained by a mechanism that can set different prices for jobs of different lengths, and the ratio can be improved if we have more specific knowledge of some parameters. Similarly, a mechanism that sets the same price for all servers even though the servers may receive different kinds of jobs can provide a reasonable welfare and revenue approximation compared to a mechanism that is allowed to set different prices for different servers.
Keywords
- Simple Pricing Scheme
- Revenue Guarantees
- Truthful Mechanism
- Approximate Welfare
- Individual Price
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
The full version of this paper is available at http://arxiv.org/abs/1705.08563.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
Amazon recently started offering a product called “defined duration spot instances” where users can specify a duration in hourly increments up to six hours [2]. Indeed, the price per hour of this product increases as the number of hours increases.
- 2.
For technical reasons, we will deviate slightly from the usual notion of cumulative distribution function. In particular, if y is a random variable drawn from a distribution, then we define its cumulative distribution function F(x) as \(\text {Pr}[y<x]\) instead of the usual \(\text {Pr}[y\le x]\). This will only be important when we deal with discrete distributions.
- 3.
For the offline optimal welfare, we compute the limit of the expected average offline optimal welfare per time step as the time horizon grows.
References
Abhishek, V., Kash, I.A., Key, P.: Fixed and market pricing for cloud services. In: The 7th Workshop on the Economics of Networks, Systems and Computation (2012)
Amazon EC2 Spot Instances Pricing (2017). http://aws.amazon.com/ec2/spot/pricing. Accessed 1 Aug 2017
Azar, Y., Kalp-Shaltiel, I., Lucier, B., Menache, I., Naor, J.S., Yaniv, J.: Truthful online scheduling with commitments. In: Proceedings of the Sixteenth ACM Conference on Economics and Computation, pp. 715–732 (2015)
Microsoft Azure Pricing Calculator (2016). http://azure.microsoft.com/en-us/pricing/calculator. Accessed 19 Sept 2016
Babaioff, M., Blumrosen, L., Dughmi, S., Singer, Y.: Posting prices with unknown distributions. In: Innovations in Computer Science - ICS 2010, pp. 166–178 (2011)
Blumrosen, L., Holenstein, T.: Posted prices vs. negotiations: an asymptotic analysis. In: Proceedings of the 9th ACM Conference on Electronic Commerce, p. 49 (2008)
Chawla, S., Hartline, J.D., Malec, D.L., Sivan, B.: Multi-parameter mechanism design and sequential posted pricing. In: Proceedings of the 42nd ACM Symposium on Theory of Computing, pp. 311–320 (2010)
Cohen, I.R., Eden, A., Fiat, A., Jez, L.: Pricing online decisions: beyond auctions. In: Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 73–91 (2015)
Cohen-Addad, V., Eden, A., Feldman, M., Fiat, A.: The invisible hand of dynamic market pricing. In: Proceedings of the 2016 ACM Conference on Economics and Computation, pp. 383–400 (2016)
Columbus, L.: Roundup of cloud computing forecasts and market estimates, 2016 (2016). http://www.forbes.com/sites/louiscolumbus/2016/03/13/roundup-of-cloud-computing-forecasts-and-market-estimates-2016. Accessed 19 Sept 2016
Dehghani, S., Kash, I.A., Key, P.: Online stochastic scheduling and pricing the cloud. Working Paper (2016)
Dierks, L., Seuken, S.: Cloud pricing: the spot market strikes back. In: The Workshop on Economics of Cloud Computing (2016)
Disser, Y., Fearnley, J., Gairing, M., Göbel, O., Klimm, M., Schmand, D., Skopalik, A., Tönnis, A.: Hiring secretaries over time: the benefit of concurrent employment. CoRR, abs/1604.08125 (2016)
Dütting, P., Fischer, F.A., Klimm, M.: Revenue gaps for discriminatory and anonymous sequential posted pricing. CoRR, abs/1607.07105 (2016)
Ezra, T., Feldman, M., Roughgarden, T., Suksompong, W.: Pricing identical items. CoRR, abs/1705.06623 (2017)
Feldman, M., Gravin, N., Lucier, B.: Combinatorial auctions via posted prices. In: Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 123–135 (2015)
Friedman, E.J., Ghodsi, A., Psomas, C.: Strategyproof allocation of discrete jobs on multiple machines. In: Proceedings of the Fifteenth ACM Conference on Economics and Computation, pp. 529–546 (2014)
Friedman, E., Rácz, M.Z., Shenker, S.: Dynamic budget-constrained pricing in the cloud. In: Barbosa, D., Milios, E. (eds.) CANADIAN AI 2015. LNCS, vol. 9091, pp. 114–121. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-18356-5_10
Hoy, D., Immorlica, N., Lucier, B.: On-demand or spot? Selling the cloud to risk-averse customers. In: Cai, Y., Vetta, A. (eds.) WINE 2016. LNCS, vol. 10123, pp. 73–86. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-54110-4_6
Jain, N., Menache, I., Naor, J.S., Yaniv, J.: A truthful mechanism for value-based scheduling in cloud computing. In: Persiano, G. (ed.) SAGT 2011. LNCS, vol. 6982, pp. 178–189. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-24829-0_17
Jain, N., Menache, I., Naor, J.S., Yaniv, J.: Near-optimal scheduling mechanisms for deadline-sensitive jobs in large computing clusters. In: Proceedings of the 24th ACM Symposium on Parallelism in Algorithms and Architectures, pp. 255–266 (2012)
Kash, I.A., Key, P.: Pricing the cloud. IEEE Internet Comput. 20(1), 36–43 (2016)
Kash, I.A., Key, P., Suksompong, W.: Simple pricing schemes for the cloud. CoRR, abs/1705.08563 (2017)
Lucier, B., Menache, I., Naor, J.S., Yaniv, J.: Efficient online scheduling for deadline-sensitive jobs. In: Proceedings of the 25th ACM Symposium on Parallelism in Algorithms and Architectures, pp. 305–314 (2013)
Wang, C., Ma, W., Qin, T., Chen, X., Hu, X., Liu, T.-Y.: Selling reserved instances in cloud computing. In: Proceedings of the 24th International Conference on Artificial Intelligence, pp. 224–230 (2015)
Zhang, H., Li, B., Jiang, H., Liu, F., Vasilakos, A.V., Liu, J.: A framework for truthful online auctions in cloud computing with heterogeneous user demands. In: Proceedings of the IEEE INFOCOM 2013, pp. 1510–1518 (2013)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Kash, I.A., Key, P., Suksompong, W. (2017). Simple Pricing Schemes for the Cloud. In: R. Devanur, N., Lu, P. (eds) Web and Internet Economics. WINE 2017. Lecture Notes in Computer Science(), vol 10660. Springer, Cham. https://doi.org/10.1007/978-3-319-71924-5_22
Download citation
DOI: https://doi.org/10.1007/978-3-319-71924-5_22
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-71923-8
Online ISBN: 978-3-319-71924-5
eBook Packages: Computer ScienceComputer Science (R0)