Forecast Uncertainty in Procurement Decisions for Cloud Storage

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1 214 UKSim-AMSS 16th International Conference on Computer Modelling and Simulation Forecast Uncertainty in Procurement Decisions for Cloud Storage Maurizio Naldi Dpt. of Computer Science and Civil Engineering Università di Roma Tor Vergata Roma, Italy Abstract In public vs private solutions (i.e. cloud vs. inhouse, or leased vs. owned) for storage, both alternatives have their pros and cons. Cloud storage can easily adapt to the company needs, but exhibits a higher unit cost than in-house solutions. On the other hand, if the company relies on its own storage equipment, it must periodically purchase it on the basis of forecasts, which may prove imprecise and lead to idle equipment. In this paper, we propose a comparative evaluation tool for the two procurement approaches, where the cloud can play the role of either exclusive storage medium or supplement to in-house equipment (in the case of underestimation of storage needs). The tool considers the impact of equipment acquisition intervals and forecast accuracy over a long time horizon, adopting a Geometric Brownian Motion model for the evolution of storage capacity needs; it can be employed as a decision support tool for procurement decisions. Keywords-cloud storage; procurement; forecasting; I. INTRODUCTION In cloud storage a company decides to store its data on repositories (the cloud) owned by an external party (the cloud provider) rather than on its own storage facilities. The external repository may be employed as a back-up or as a complete replacement. In the former case, the company has to maintain an in-house storage facility, while the alternative allows the company to get rid of it. With the migration of all its data to the cloud, the company zeroes its investments in storage devices and switches from an infrastructure-based to a service-based mode of operation. Actually, cloud storage is a major example of the IaaS (Infrastructure as a Service) paradigm and an important component of the current virtualization trend [1]. Since migration involves a significant one-off effort to move all the data on the new platform, and that can be exploited by cloud providers to cage the company in a lockin condition, the decision to migrate has to be examined thoroughly. A major promise of cloud storage is to reduce costs for the company. Actually shifting to IaaS means trading capital expenditures (), due to disk purchase, for operational expenditures (), due to paying for the service offered by cloud providers. Aside from the organizational, security, and reliability issues that are involved in the migration to the cloud, the main focus in an economical analysis is on the comparison between the costs involved in the two alternatives. Some cost analyses have been conducted on clouds. In [2], a cost breakdown has been provided for data centers, which includes the costs of servers and networking facilities in addition to storage facilities and power. A comprehensive cost model for hybrid clouds, including both private and public clouds has been described in [3]. A toolkit has been described in [4] that allows to compute the cost of cloud adoption on the basis of a detailed schedule of resource needs. While all these papers consider the more general cloud computing service rather than simply cloud storage, their focus is on the cost analysis of the cloud solution rather than the comparison with the in-house storage alternative. An economical comparison of the owned and leased storage solutions is instead provided in [5], where forecasts for the price of disks are employed to obtain a single figure of comparison between the two alternatives, based on the tool of the Net Present Value. The framework employed in [5] is however completely deterministic. In [6], that framework has been replaced by a probabilistic one which allows to model the uncertainty unavoidably associated to future trends in both prices and storage demand and breakdown of equipment that calls for tis replacement. Another shortcoming of the deterministic approach proposed in [5] is that it does not allow to evaluate the risk associated to migration. In fact, the decision taken on the basis of that single comparison figure may turn out to be wrong. An early attempt to provide a risk measure in the cloud adoption decision has been provided in [7], while in [8] a possible countermeasure has been envisaged through insurance policies against cloud storage price increases. In [9], the impact of the length of the acquisition interval in the procurement process has been considered. While previous analyses considered a long term process in which the procurement activities took place once a year, that paper has analysed how a shortening of the procurement cycle may affect the convenience of either storage approaches. However, the framework adopted in [9] is completely deterministic, while in both [6] and [7] the stochastic nature of most variables had been highlighted. In this paper, we follow in the steps of the procurement /14 $ IEEE DOI 1.119/UKSim

2 process analysis conducted in [9], but we introduce a stochastic framework by considering both a stochastic evolution of the storage demand and the error that is embedded in the forecasting process of the future demand for storage. We provide simple expressions for the costs under either storage solution and analyse their economic convenience over a medium term horizon. The paper is organized as follows. In Section II, we provide a stochastic model for the growth of data and storage needs. In Section III, we describe the two storage approaches and determine their costs. Finally, in Section IV, we compare those costs in a number of scenarios. Storage demand Time (no. of acquisition intervals) II. STORAGE DEMAND The development of digital consumer electronics has moved to the digital domain much of the content that was stored in an analog fashion, e.g., documents, photos, videos. In addition, native digital applications (e.g., the apps running on tablets or smartphones) continually generate new data. The total amount of data generated in the world has grown from 2.6 exabytes in 1986 to 295 exabytes in 27, with a 23% compound annual growth rate (CAGR) over the latest 2 decades [1]. More recent data, extending into 211, show that the total amount of generated digital data was 1699 exabyte in 211, with a 55.7% CAGR over the years [11]. Actually, that relatively low value reported in [1] was due to the high base level provided by analog storage devices prevalent at the beginning of the analysis period. As reported by Hilbert and López, roughly half of this volume of data is stored on hard disks, servers, and mainframe systems [1]. Nearly a decade ago, Coughlin provided historical data and a forecast concerning the amount of digital memory installed. His study spanned the period from 2 to 25, including an exponential growth trend with a yearly growth rate of 7% (the amount of memory installed would double every 15.7 months) [12]. In two previous analyses of the profitability of data migration [5] [6], the overall size of data stored by the company was assumed to grow linearly over time. Actually, the data reported above show that the amount of digital data to be stored is growing much faster. Here we assume that the demand for storage grows at an exponential rate. However, growth does not follow a deterministic behaviour. It is therefore safe to assume that the growth is represented by a random process M(t), whose expected value follows an exponential trend E[M t ]=M (1 + g) t, (1) where t is the number of time periods from now, and g is the growth rate on the single time period. Figure 1. Example of growth of storage demand A stochastic model suitable to describe that exponential trend is the Geometric Brownian Motion [13]: M t = M e νt+σw(t) = M e (μ σ2 /2)t+σW(t), (2) where W (t) is a Wiener process, and the terms ν and σ 2 are respectively the drift and variance of the process. Since the expected value of such process is E[M t ]=M e μt, (3) we can easily match the characteristics of this process with our assumption (1) on the expected value of the storage demand. Namely, the match is perfect by setting μ =ln(1+g). At any time t the demand for storage follows a lognormal distribution around its exponential trend. A sample curve showing the evolution of demand for storage when the growth rate is 5% a year is shown in Figure 1. III. ALTERNATIVE STORAGE SOLUTIONS In order to accommodate the growing storage needs described in Section II, we consider that the company may follow two alternative paths: either developing and maintaining its own storage infrastructure or leasing storage space from a public provider. We consider that the latter is nowadays a synonym for public cloud storage, since most storage providers have a distributed infrastructure. Instead the former may rely either on a single-location data center or on a number of centers scattered on several locations, but anyway wholly owned by that company. For simplicity, we refer to the two solutions respectively as the public cloud and the private cloud. The two alternatives pose different problems and exhibit different costs. In this section, we describe them in more detail and provide the pertaining cost expressions. 238

3 Item Disks Controller Cooling Power Networking Personnel Space Security Safety Category / Table I COST COMPONENTS IN THE PRIVATE CLOUD SOLUTION Cost fraction [%] Table II COSTS IN THE DATA CENTER Components 45 Servers (CPU, memory, storage systems) 25 Infrastructure (Power distribution and cooling) 15 Power consumption (Electrical utility costs) 15 Network (Links, transit, equipment) A. The private cloud In the private cloud solution, the company has to build its own data center, maintain and manage it. That basically involves paying for the infrastructure space, buying discs, carry out their maintenance, replacing them when they fail, and running the daily operations of the data center. In [5] and [7] those components have been accounted for, while a wide selection of the cost factors involved in a data center is provided in [14]. Some of the costs involved are, i.e. they are spent just once, and some are (i.e., they are recurring). Some items, like disks, are considered as, though they have to be replaced because of failures. Table I reports a summary of the main costs involved, as obtained by merging the cost items considered in [7] and [14]. Some items are doubly labelled as and, since they may fall in either category, depending on the choice made by the company. For example, the cost of the space needed to host the equipment is a item if the place is bought by the company, but is an item if the company hires it and pays a monthly rental. In Table II, extracted from [2], we see that (e.g., the first two items in the table) represent more than 6% of the overall cost. According to the white paper [15], the sum of site infrastructure capital costs and IT capital costs in a data center accounts for roughly 7% of the total cost. Though the costs are of a different nature, we assume that they may be summarized by a unit cost (e.g., per Gigabyte), which companies bear periodically over any period of time. This is quite straightforward for, while costs are spent at a given time but their effects reverberate over several periods. We may adopt the same approach taken in financial statements, where the expenses related to long-term assets are actually distributed in time through a depreciation plan, e.g. evenly over the lifetime of the asset [16]. Under this hypothesis, following the same approach as in [9], we can summarize all the cost items into a single unit cost p per Gigabyte, which is considered constant throughout the observation period. We assume that the acquisitions consisting in the purchase of equipment and in the purchase or renewal of services (which make up the procurement process) are carried out periodically, every τ time units. The decisions about the quantities to purchase are based on the forecasts of the future storage needs: the procurement must be futureproof in the sense that it must cover the needs occurring during the time interval till the next acquisition time. Since all the studies recalled in Section II point to a growing trend, we can consider that the acquisition at time iτ is done for the quantity s((i +1)τ), which will take place at the next acquisition time (i +1)τ. Actually, the company does not know exactly that future quantity, so that it must rely on a forecasting process. We assume that the estimate ŝ(t) of the future demand at time t is unbiased, but subject to an error, so that ŝ(iτ) =s(iτ)+e i, (4) where e i is a random variable representing the forecast error. Due to the unbiasedness hypothesis, we have E[e i ]=. We also assume that the error does not depend on the specific acquisition interval, so that the e i s are i.i.d. The presence of forecast errors leads to the possibility that the storage infrastructure may sometimes be inadequate for the storage needs. In [9], this problem is solved by resorting to an overdimensioning of the storage infrastructure, which is done by introducing a safety margin. Though this approach may provide additional robustness, it exhibits three major shortcomings. First, it does not provide an absolute guarantee that the margin introduced will anyway be enough to cover all sudden storage needs. Second, it increases considerably the expense associated to owning a storage infrastructure. Third, the safety margin is introduced by a subjective evaluation, which may alter the evaluation framework. For that reason, we prefer to consider that the company may rely on a public cloud to cover its needs when its storage infrastructure is not large enough. This solution represents a minimal implementation of what is often called a hybrid cloud (see Sections 1.3 and 9.5 of [17]). We assume that the use of the public cloud is perfectly elastic, so that the company may lease exactly the amount of storage that exceeds its storage capability. The price per unit storage is larger than the cost of the private solution by a factor u>1. This factor is called the utility premium in [9], where a value of 1 is considered typical. In the 239

4 following, we will refer to it either as the utility premium or the surcharge ratio. The overall cost of the private solution is therefore made of two components: one determined by the periodic acquisition expenses, and the other occasionally due to leases from the public cloud to cover for sudden increases in storage needs. The complete expression of the cost of the private (owned) solution over n acquisition intervals is then n n iτ C o = p ŝ(iτ)+up max[s(t) ŝ(iτ), ]dt. B. The public cloud (i 1)τ (5) Probability Density Function Figure Cost Ratio Empirical probability density function of the cost ratio The alternative to the private (or rather hybrid) solution described in Section III-A is to rely completely on a public cloud. In a first approximation this reduces the expenses to those incurred for leasing the amount of storage needed (actually the company has anyway to spend for the technical and management infrastructure to connect with the cloud, as described in [6]). As already anticipated in Section III-A, the cost for the company to lease storage space is simply the product of the unit price (in turn represented as u times the unit cost of private storage) and the amount of storage needed. This model can be considered as representative enough of the reality of current cloud storage providers (see [18] for a survey of the current pricing policies). Assuming again that the storage on the cloud can follow exactly the needs of the company, the overall cost of the public (leased) solution over the same period of n acquisition intervals is nτ C l = up s(t)dt. (6) IV. DECISION CRITERION In Section III we have obtained the expressions for the cost of the two alternative solution for storage. The decision faced by the company is to opt for either on a cost basis, assuming that all other factors are kept equal. If other factors (e.g., improved reliability or security measures) are kept equal by introducing additional costs, these can be factored in the surcharge ratio u. We have already envisaged that the comparison has to be conducted over a long enough period of time, encompassing several acquisition intervals. In this section, we consider a simple metric that can aid in this decision and examine its characteristics. Since we prefer the least cost solution, we can form the cost ratio R, defined as the ratio of the cost of the private solution to the cost of the public solution. Recalling Equations (5) and (6), we have R = C o C l n = ŝ(iτ) n iτ u nτ s(t)dt + (i 1)τ max[s(t) ŝ(iτ), ]dt nτ, s(t)dt (7) where we can recognize that the second term represent the extra-expense due to inaccurate forecasts in the private solution, which have to be remedied by resorting to the public cloud. If R < 1 the in-house solution is to be preferred. This ratio is however a random variable, depending essentially on four quantities: the surcharge ratio u by which the storage on a public cloud is priced with respect to its cost; the overall period of time along which the evaluation is performed; the growth rate g; the accuracy of the forecast, embodied by the variance of the errors e i. In Figure 2, we can see a sample probability density function of the cost ratio R, as computed over 5 years with a yearly growth rate of 5%, when the utility premium u is 1 and the standard error of the forecast is 5% of the actual value. In this case, the expected value of R is 1.95, while its standard deviation is.483, as evaluated by a MonteCarlo simulation with 1 runs. We consider now the dependence on these factors in some sample scenarios. We see first the dependence on the surcharge ratio u. We know from Equation (7) and common sense, that the public cloud solution becomes less preferable as its price increases. In Figure 3, we see that the cost ratio (actually, its expected value, that we have estimated by simulation) decreases as the surcharge ratio u increases. That picture has been 24

5 2 1 u=1 Cost ratio (R) Cost ratio (R) u= Surcharge ratio (u) Yearly growth rate [%] Figure 3. Impact of the public cloud price on the cost ratio Figure 4. Impact of the growth rate on the cost ratio obtained for a time horizon of 5 years, with a yearly growth rate of 5% and a standard error of the forecast of 5%. Here we can see that the private solution becomes preferable when the surcharge ratio becomes larger than Actually, from Equation (7) we can easily recover the maximum surcharge ratio that is tolerable for the public cloud solution to be the least costly of the two, by imposing that R>1 n u max = ŝ(iτ) nτ s(t)dt n iτ max[s(t) ŝ(iτ), ]dt. (i 1)τ (8) Another factor to consider in the decision is the growth rate of the demand for storage. We have seen in Section II that a general consensus exists for an exponential growth of the production of data and the amount to store. This trend has been observed for a number of years now and is expected to continue in the coming years. The rate at which the amount of data grows may pose significant problems with the infrastructure, since it calls for more frequent additions to the installed infrastructure or larger investments to cover the larger needs associated to the time interval between two procurement events. Hence, we expect that a faster growth rate makes the private approach more difficult. Though the impact of the growth rate is not immediately visible in Equation (7), since it is embedded in both s(t) and ŝ(t), we can validate our hypothesis by simulating what happens in a sample scenario. We consider here again a horizon of 5 years with procurement events twice a year and a standard error of 5%. In Figure 4, we can see how the cost ratio behaves in two cases, characterized by higher or lower prices of the public cloud solution. In both cases, the private solution becomes less convenient as the growth becomes faster, but the effect of the growth rate is rather limited: the cost ratio increases, over the range of growth rates examined, by 8.65% when u =1and quite similarly by 8.87% when u =15. V. CONCLUSION We have compared the costs incurred when a company adopts either a public cloud solution for its storage needs or an in-house approach. The procurement process is explicitly taken into account through a periodic reassessment of the storage needs, forecasting the growth over the next interval and purchasing additional disks. The convenience of one solution over the other can be assessed through the ratio of their costs. The presence of a stochastic evolution of the storage demand and of the forecast error makes such ratio a random variable. By simulating a number of scenarios, we observe that the public cloud price represents a major factor in the decision. Instead the impact of the growth rate is rather limited. REFERENCES [1] A. Lenk, M. Klems, J. Nimis, S. Tai, and T. Sandholm, What s inside the cloud? an architectural map of the cloud landscape, in Proceedings of the 29 ICSE Workshop on Software Engineering Challenges of Cloud Computing, ser. CLOUD 9, 29, pp [2] A. G. Greenberg, J. R. Hamilton, D. A. Maltz, and P. Patel, The cost of a cloud: research problems in data center networks, Computer Communication Review, vol. 39, no. 1, pp , 29. [3] M. M. Kashef and J. Altmann, A Cost Model for Hybrid Clouds, SeouL National University, College of Engineering Technology Management, Economics, and Policy Program, TEMEP Discussion Paper 211:82, 211. [4] A. Khajeh-Hosseini, D. Greenwood, J. W. Smith, and I. Sommerville, The cloud adoption toolkit: supporting cloud adoption decisions in the enterprise, Softw., Pract. Exper., vol. 42, no. 4, pp , 212. [5] E. Walker, W. Brisken, and J. Romney, To lease or not to lease from storage clouds, IEEE Computer, vol. 43, no. 4, pp. 44 5,

6 [6] L. Mastroeni and M. Naldi, Storage Buy-or-Lease Decisions in Cloud Computing under Price Uncertainty, in 7th EuroNF Conference on Next Generation Internet, Kaiserslautern, 211. [7], Long-range evaluation of risk in the migration to cloud storage, in 13th IEEE Conference on Commerce and Enterprise Computing, CEC 211, Luxembourg, September 5-7, 211, pp [8], Pricing of insurance policies against cloud storage price rises, SIGMETRICS Performance Evaluation Review, vol. 4, no. 2, pp , 212. [9] G. Laatikainen, O. Mazhelis, and P. Tyrväinen, Role of acquisition intervals in private and public cloud storage costs, Decision Support Systems, vol. 57, pp , 214. [1] M. Hilbert and P. López, The Worlds Technological Capacity to Store, Communicate, and Compute Information, Science, vol. 332, no. 625, pp. 6 65, April 211. [11] A. V. Makarenko, Phenomenological model for growth of volumes digital data, CoRR, vol. abs/112.55, 211, arxiv preprint series. [12] T. Coughlin, Current trends in data storage backup and restoration, Presentation, 13 February 23. [13] N. H. Chan and H. Y. Wong, Simulation techniques in financial risk management. John Wiley, 26. [14] C. D. Patel and A. J. Shah, Cost Model for Planning, Development and Operation of a Data Center, HP, Tech. Rep. HPL-25-17R1, 25. [15] J. Koomey, K. Brill, P. Turner, J. Stanley, and B. Taylor, A Simple Model for Determining True Total Cost of Ownership for Data Centers, Uptime Insitute, Tech. Rep., 27. [16] K. Subramanyam and J. Wild, Financial Statement Analysis. McGraw-Hill Education, 213. [17] R. Buyya, J. Broberg, and A. M. Goscinski, Cloud computing: Principles and paradigms. John Wiley & Sons, 21, vol. 87. [18] M. Naldi and L. Mastroeni, Cloud storage pricing: a comparison of current practices, in HotTopiCS Workshop, 4th ACM/SPEC International Conference on Performance Engineering, Prague, April

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