Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-18T20:43:56.506Z Has data issue: false hasContentIssue false
  • English
  • Français

MULTI-CLASS RESOURCE SHARING WITH BATCH ARRIVALS

Published online by Cambridge University Press:  21 September 2018

Paul Ezhilchelvan  and
Isi Mitrani
Paul Ezhilchelvan
Affiliation:
School of Computing Science, Newcastle University, Newcastle upon Tyne, NE4 5TG, UK E-mail: [email protected]; [email protected]
Isi Mitrani
Affiliation:
School of Computing Science, Newcastle University, Newcastle upon Tyne, NE4 5TG, UK E-mail: [email protected]; [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

A cloud provider hosts virtual machines (VMs) of different types, with different resource requirements. There are bounds on the total amounts of each kind of resource that are available. Requests arrive in batches of different sizes. Under the ‘complete blocking’ policy, a request is accepted only if all the VMs in its batch can be accommodated. The ‘partial blocking’ policy would accept a request if there is room for at least one of the VMs in the batch. Blocked requests are lost, with an associated loss of revenue. The trade-offs between costs and benefits are evaluated by means of appropriate models, for which novel solutions based on fixed-point iterations are proposed. The applicability of those solutions is extended, by means of simplifications, to very large-scale systems. Numerical examples and comparisons with simulations are presented.

Keywords

applied probabilityqueueing theorysimulation
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 33 , Issue 3 , July 2019 , pp. 348 - 366
Copyright
Copyright © Cambridge University Press 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Bodík, P., Griffith, R., Sutton, C., Fox, A., Jordan, M. & Patterson, D. (2009). Statistical machine learning makes automatic control practical for internet datacenters. Conf. on Hot Topics in Cloud Computing (HotCloud’09), Berkeley, CA, USA.Google Scholar
2.Chao, X. & Miyazawa, M. (1998). On Quasi-reversibility and local balance: an alternative derivation of the product-form results. Operations Research, 46(6): 927–933.Google Scholar
3.Choudhury, G.L., Leung, K.K. & Whitt, W. (1995). Resource-sharing models with state-dependent arrivals of batches. In Stewart, W.J., (ed.), Computations with Markov Chains. Springer, Boston, MA, pp. 225–282.Google Scholar
4.Cromme, L.J. (1997). Fixed point theorems for discontinuous functions and applications. Nonlinear Analysis: Theory, Methods and Applications, 30(3): 1527–1534.Google Scholar
5.Dean, J. & Ghemawat, S. (2008). MapReduce: Simplified data processing on large clusters. Communications of the ACM, 51(1): 107–113.Google Scholar
6.van Doorn, E. A., & Planken, F.J.M. (1993). Blocking probabilities in a loss system with arrivals in geometrically distributed batches and heterogeneous service requirements. ACM/IEEE Transactions on Networking, 1: 664–667.Google Scholar
7.Ezhilchelvan, P. & Mitrani, I. (2015). Static and dynamic hosting of cloud servers. In Beltran, M., Knottenbelt, W. & Bradley, J., (eds.), Computer Performance Engineering LNCS 9272. Springer, Cham, pp. 19–31.Google Scholar
8.Ezhilchelvan, P. & Mitrani, I. (2017). Optimal provisioning of servers for hosting services of multiple types. Simulation Modelling Practice and Theory, 75: 17–28.Google Scholar
9.Ezhilchelvan, P. & Mitrani, I. (2017). Multi-class resource sharing with batch arrivals and complete blocking. 14th Int. Conf. on Quantitative Evaluation of SysTems (QEST 2017), Berlin.Google Scholar
10.Hampshire, R.C., Massey, W.A., Mitra, D. & Wang, Q. (2003). Provisioning for bandwidth sharing and exchange. In Anandalingam, G., Raghavan, S. (eds) Telecommunications Network Design and Management, vol. 23 of series Operations Research/Computer Science Interfaces, Springer, Boston, MA, pp. 207–225.Google Scholar
11.Harrison, P.G. (2004). Reversed processes, product forms and a non-product form. Linear Algebra and its Applications, 386: 359–381.Google Scholar
12.Herings, P.J.-J., van der Laanb, G., Talmanc, D. & Yang, Z. (2008). A fixed point theorem for discontinuous functions. Operations Research Letters, 36(1): 89–93.Google Scholar
13.Kaufman, J.S. (1981). Blocking in a shared resource environment. IEEE Trans. Commun., 29: 1474–1481.Google Scholar
14.Kaufman, J.S. & Rege, K.M. (1996). Blocking in a shared resource environment with batched Poisson arrival processes. Performance Evaluation, 24: 249–263.Google Scholar
15.Kelly, F. (1986). Blocking probabilities in large cirquit switched networks. Advances in Applied Probability, 18: 473–505.Google Scholar
16.Mazzucco, M., Dyachuk, D. & Dikaiakos, M. (2010). Profit-aware server allocation for green internet services. IEEE Int. Symp. on Modeling, Analysis and Simulation of Computer and Telecommunication Systems (MASCOTS), pp. 277–284.Google Scholar
17.Mazzucco, M., Vasar, M. & Dumas, M. (2012). Squeezing out the cloud via profit-maximizing resource allocation policies. IEEE Int. Symp. on Modeling, Analysis and Simulation of Computer and Telecommunication Systems (MASCOTS), pp. 19–28.Google Scholar
18.Mitrani, I. (1998). Probabilistic Modelling. Cambridge University Press, Cambridge, England, UK.Google Scholar
19.Roberts, J.W. (1981). A service system with heterogeneous user requirement. In Pujolle, G., (ed.), Performance of Data Communications Systems and Their Applications. North-Holland, pp. 423–431.Google Scholar
20.Ross, K.W. (1995). Multiservice Loss Models for Broadband Telecommunication Networks. Springer-Verlag, Springer London.Google Scholar
21.Sadre, R., Haverkort, B.R. & Ost, A. (1999). An efficient and accurate decomposition method for open finite- and infinite-buffer queueing networks. Proceedings of the 3rd International Workshop on Numerical Solution of Markov Chains (Eds. Stewart, W. and Plateau, B.), pp. 1–20.Google Scholar
22.Tan, Y., Lu, Y. & Xia, C.H. (2012). Provisioning for large scale loss network systems with applications in cloud computing. ACM SIGMETRICS Performance Evaluation Review, 40(3): 83–85.Google Scholar
23.Whitt, W. (1983). The Queueing Network Analyzer. Bell System Technical Journal, 62(9): 2779–2815.Google Scholar
24.https://aws.amazon.com/ec2/instance-types/, Amazon Web Services, 2016.Google Scholar