RESEARCH Open Access

An optimization approach to capacityevaluation and investment decision ofhybrid cloud: a corporate customer’sperspectiveIn Lee

Abstract

While the rapid growth of cloud computing is driven by the surge of big data, the Internet of Things, and socialmedia applications, an evaluation and investment decision for cloud computing has been challenging for corporatemanagers due to a lack of proper decision models. This paper attempts to identify critical variables for making acloud capacity decision from a corporate customer’s perspective and develops a base mathematical model to aid ina hybrid cloud investment decision under probabilistic computing demands. The identification of the critical variablesprovides a means by which a corporate customer can effectively evaluate various cloud capacity investmentopportunities. Critical variables included in this model are an actual computing demand, the amount of private cloudcapacity purchased, the purchase cost of the private cloud capacity, the price of the public cloud, and the defaultdowntime loss/penalty cost. Extending the base model developed, this paper also takes into consideration theinteroperability cost incurred in cloud bursting to the public cloud and derives the optimal investment. The interoperablecloud systems require time and investment by the users and/or cloud providers and there exists a diminishing return onthe investment. Hence, the relationship between the interoperable cloud investment and return on investment is alsoinvestigated.

Keywords: Hybrid cloud, Interoperability, Public cloud, Private cloud, Decision model, Optimization, ROI

IntroductionThe evolution of the Internet, storage technologies, service-oriented architecture, and grid computing has led to thedevelopment of cloud computing. Cloud computing hasemerged as a disruptive innovation offering a variety ofcomputing services and resources to individual users andcorporate customers. Cloud infrastructure that was trad-itionally limited to single provider data centers is now evolv-ing to the use of infrastructure from multiple providers [1].A wide variety of deployment models, service models, andpricing schemes are flexibly integrated with each other tohelp enterprises transform the way they conduct businessand meet their idiosyncratic computing needs.Cloud computing complements traditional client-server

computing to support the computing needs of businesses

with a range of benefits such as lower IT expenditures, re-source pooling, single source application updates, and scal-ability. Many cloud computing providers such as Google,Microsoft, IBM, and Amazon have been heavily investingin cloud technology and are leading various cloud servicesmarkets [2]. However, the increasing dissemination of cloudservices and the growing number of cloud service providers(CSPs) have resulted in uncertainty for corporate customersin adopting cloud services [3]. Opara-Martins, Sahandi, andTian [4] find that the most cited reasons for adopting cloudcomputing include better scalability of IT resources(45.9%), collaboration (40.5%), cost savings (39.6%), andincreased flexibility (36.9%).The most cited challenge among corporate customers is

managing costs, but they underestimate the amount ofwasted cloud expense [5]. Respondents estimate 27% waste,while RightScale [5] has measured actual waste at 35%. 84%of the respondents with more than 1000 employees are

© The Author(s). 2019 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, andreproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link tothe Creative Commons license, and indicate if changes were made.

Correspondence: I-Lee@wiu.eduCecil P. McDonough Endowed Professor in Business, School of ComputerSciences, Western Illinois University, Macomb, IL 61455, USA

Journal of Cloud Computing:Advances, Systems and Applications

Lee Journal of Cloud Computing: Advances, Systems and Applications (2019) 8:15 https://doi.org/10.1186/s13677-019-0140-0

using a multi-cloud strategy and 58% are using the hybridcloud. Cloud cost saving is the top priority across allcorporate customers (64%). Therefore, this studycannot emphasize enough the importance of the solidjustification of the economic capacity evaluation andmanagement of cloud computing as a capacity evalu-ation and investment decision.Capacity planning is a challenging task when there is an

unpredictable, fluctuating computing demand with manypeaks and troughs [6]. Without a solid evaluation model,estimating the tradeoff between the benefits and costsincurred in order to cover peak computing demand ischallenging. Therefore, overcapacity or under-capacity is acommon phenomenon in the investment of cloud cap-acity. Overcapacity puts companies at a cost disadvantagedue to a low utilization of cloud resources. On the otherhand, under-capacity puts them at a strategic disadvantagedue to customer/user dissatisfaction, high penalty costs,and potential sales loss.The hybrid cloud enjoys the benefits of both private and

public clouds, but the combination of the two has intro-duced challenging issues such as data security, perform-ance, and cost optimization [7]. According to RightScale’s2019 State of the Cloud Report [5], the hybrid cloud is themost preferred cloud for corporate cloud capacity invest-ment. The hybrid cloud is flexible enough to handle thespike of computing demand while at the same time redu-cing computing costs. The hybrid cloud is a cloud environ-ment in which an organization owns and manages theirinternal private cloud and uses a public cloud or a commu-nity cloud externally when necessary. In the hybrid cloud,typically, non-critical computing resources are outsourcedto the public cloud, while mission-critical applications anddata are kept in the private cloud under the strict controlof the organization. Researchers used the MapReduce para-digm to split a data-intensive workload into mapping taskssorted by the sensitivity of the data, with the most sensitivedata being processed at on-premise servers and the leastsensitive processed in a public cloud [8]. Many leading en-terprises such as Uber, GM, and JP Morgan are adopters ofthe hybrid cloud. For example, Uber relies on a hybridcloud infrastructure that combines the use of public cloudservices with standardized on-premise server racks in itsdatacenters [9].Whether to utilize cloud computing or internal IT re-

sources for business purposes is a critical decision fororganizations and decision makers [10]. For companies,the cloud evaluation and investment decision tominimize the total computing costs requires a basic un-derstanding of the relationships between the cost ofcomputing resources, a penalty for computer downtime,and a probability distribution of the computing demand.In light of the lack of studies in the cloud investmentarea and the corporate trend of migrating to the hybrid

cloud, this paper proposes an optimization approach tocloud evaluation and an investment decision of the hy-brid cloud for corporate decision makers. The remainderof this paper includes a literature review on cloud cap-acity investment decisions, the base decision model, anillustration of the model operation, a model extensionwith an interoperability cost for cloud bursting, and re-turn on investment (ROI) management.

Literature reviewWhile exact modeling of cloud centers is not feasible dueto the nature of cloud centers and the diversity of user re-quests [11], workload modeling has been used to increasethe understanding of typical cloud workload patterns andhas led to more informed resource management decisions[12]. Workload modeling and characterization is especiallychallenging when applied in a highly dynamic environ-ment for reasons such as heterogeneous hardware in asingle data center and complex workloads composed of awide variety of applications with different characteristicsand user profiles [13]. In a large-scale system faced bytime varying and regionally distributed demands for vari-ous resources, there is a tradeoff between optimizing theresource placement to meet its demand and minimizingthe number of added and removed resources to the place-ment. Novel analytic techniques utilizing graph theorymethodologies are proposed that overcome this difficultyand yield very efficient dynamic placements with boundedrepositioning costs [14].A number of studies on models of computing resources

assume the exponential distribution or the Weibull distri-bution of computing requests and conduct mathematicalanalyses of system performance [11, 15, 16]. For example, acloud center is modeled as a classic open network with asingle arrival from which the distribution of response timeis obtained, assuming that both interarrival and servicetimes are exponential [17]. A recent study of Patch andTaimre [18] also assumes that tasks require an exponen-tially distributed service time for transient provisioning andperformance evaluation of cloud computing platforms.Wolski and Brevik [19] conduct a simulation of work-

load patterns with real data and compare the efficacy ofthe lognormal distribution, the 3-phase hyper exponen-tial distribution, and the pareto distribution and findthat the use of the 3-phase hyper exponential distribu-tion is the most appropriate based on the Kolmolgrov-Smirnov statistic which has been widely used to com-pute the goodness-of-fit between the observed data anda distribution fit to it. With the goal of providing a re-pository where practitioners and researchers can ex-change grid workload traces, a research team from theDelft University of Technology maintains an archive thatcontains an extensive set of grid workload data as wellas the results of the Kolmolgrov-Smirnov (KS) tests [20].

Lee Journal of Cloud Computing: Advances, Systems and Applications (2019) 8:15 Page 2 of 13

The Kolmolgrov-Smirnov static of the various workloadsshow that overall, the Weibull, the lognormal, and thegamma distributions have a better fit than others. Whilea workload analysis can be used for scheduler design, itis also useful for capacity planning.The efficient and accurate assessment of cloud-based in-

frastructure is essential for guaranteeing both business con-tinuity and uninterrupted services for computing jobs [21].However, efficient resource management of the cloud infra-structures is challenging [22]. In the capacity planning andmanagement area, most studies focus on micro-level sched-uling such as dynamic resource allocation and prioritizationof computing jobs. Widely used resource managementmethods such as Amazon Web Services (AWS) Auto Scal-ing and Windows Azure Autoscaling Application Block,are reactive. While these reactive approaches are an effect-ive way to improve system availability, optimize costs, andreduce latency, it exhibits a mismatch between resource de-mands and service provisions, which could lead to under orover provisioning [23]. Hence, predictive resource scalingapproaches have been proposed to overcome the limita-tions of the reactive approaches most often used [24–26].Misra and Monda [27] point out that a challenge arises

when companies with an existing data center make a deci-sion on whether cloud computing would be helpful forthem or if they should stick to their own in-house infra-structure for the expansion and consolidation of the exist-ing data centers. They analyze the cost side aspect with asimulation model that not only helps assess the suitabilityof the cloud computing but also measures its profitability.Recently, Patch and Taimre [18] demonstrate that takinginto account each of the characteristics of fluctuating userdemand of cloud services can result in a substantial reduc-tion of losses. Their transient provisioning framework al-lows for a wide variety of system behaviors to be modeledin the presence of various model characteristics throughthe use of matrix analytic methods to minimize the revenueloss over a finite time horizon.de Assunção, di Costanzo, and Buyya [28] investigate the

benefits that organizations can reap by using a public cloudto augment their local computing capacity. They evaluatesix scheduling strategies to understand how these strategiesachieve a balance between performance and usage cost, andhow much they improve response time. Gmach, Rolia,Cherkasova, and Kemper [29] describe a capacity manage-ment process for resource pools. They use a trace-based ap-proach which predicts future per-server required capacityand achieve a 35% reduction in processor usage as com-pared to the benchmark best practice.The hybrid cloud can potentially reduce the financial

burden of overcapacity investment and technologicalrisks related to a full ownership of computing resourcesand can allow companies to operate at a cost-optimalscale and scope under demand uncertainty [30]. The

hybrid cloud allows users to scale computing require-ments beyond the private cloud and into the publiccloud - a capability called cloud bursting in which an ap-plication runs in its own private resources for the majorityof its computing and bursts into the public cloud when itsprivate resources are insufficient for the peaks in comput-ing demand [31]. For example, a popular and cost-effective way to deal with the temporary computationaldemand of big data analytics is hybrid cloud bursting thatleases temporary off-premise cloud resources to boost theoverall capacity during peak utilization [32]. Academic re-search into the hybrid cloud has focused on the middle-ware and abstraction layers for creating, managing, andusing the hybrid cloud [8]. Commercial support for thehybrid cloud is growing in response to the increasing de-mand for the hybrid cloud. Container technologies willimprove portability between different cloud providers.While potential benefits of the hybrid cloud arise in the

presence of variable demand for many real-world comput-ing workloads, additional costs related to hybrid cloudmanagement, data transfer, and development complexitymust be taken into account [33]. Bandwidth, latency, loca-tion of data, and communication performance need to beconsidered for integrating a public cloud with a privatecloud [34]. The interoperability and portability issuesbetween the public cloud and the on-premise privatecloud also continue to be barriers to its adoption. Theseissues arise when cloud providers develop services withnon-compatible proprietary technologies [4]. While vari-ous standardized solutions have been developed for di-verse cloud computing services [35], cloud providers oftendevelop their own proprietary services as a way to lock inclients, differentiate their services, and achieve a marketmonopoly in the early stages of innovation. A lack ofstandardization poses challenges to cloud users who needto integrate diverse cloud services obtained from multiplecloud providers [36] and perform cloud bursting in the hy-brid cloud environment.While the above-mentioned studies investigate micro-

level scheduling schemes for cloud resources, few studieshave analyzed how cloud capacity for the public, private,and hybrid cloud interacts with the service level andprices in a given decision horizon. Furthermore, mostprevious studies did not attempt to develop any closedform solution for an optimal cloud capacity decision.Cloud computing is in an expansion stage of techno-

logical diffusion and is projected to grow more rapidlywith the advances in big data, artificial intelligence, andthe Internet of Things. Given the growing interest in thecloud capacity decision by managers, researchers need todevelop cost-benefit evaluation models and tools that willhelp managers make a judicious cloud capacity decision.The development of a quantifiable cost-benefit decisionmodel is of vital importance to avoid intuition-based gut-

Lee Journal of Cloud Computing: Advances, Systems and Applications (2019) 8:15 Page 3 of 13

feeling investment decisions. In an attempt to fill a gap inthe current studies, the next section provides a normativemodel for the cloud capacity decision.

A capacity evaluation and investment decisionmodel of hybrid cloudThis section proposes a capacity evaluation and investmentdecision model of the hybrid cloud and examines the rela-tionships between model parameters and cloud invest-ments. This model derives the optimal capacity decision ofthe private cloud and the public cloud to minimize the totalcomputing costs. The optimal decision is based on the coststructure and a probability density function for computingdemand in a given period. This model reflects customers’perspectives and utilizes a model presented by Henneberger[37] which extends the classic newsvendor problem and de-rives a critical fractile formula using an inverse cumulativedistribution function of computing demand. This news-vendor problem has been widely used in inventory manage-ment. For example, Fan et al. [38] apply the newsvendormodel to analyze the reduction of inventory shrinkage withthe use of RFID. While Henneberger’s model did notpresent a closed-form solution, the proposed model derivesa closed-form solution for a capacity evaluation and deci-sion problem with an exponential probability distributionof computing demand. Later, the base model is extended tofind the optimal solution for two investment decision vari-ables simultaneously: (1) the optimal cloud capacity for theprivate cloud and (2) the optimal investment in the inter-operability enhancement for cloud bursting in the hybridcloud environment.

A hypothetical cloud capacity evaluation and investmentdecision problemA company needs to decide how much private cloud theyneed to invest in and how much public cloud they need touse to minimize the total computing costs in a given deci-sion horizon. While the company can choose to use a pri-vate cloud only, a public cloud only, or a hybrid cloud, theyrealize that the hybrid cloud has a cost advantage when acompany has a wide range of peaks and troughs in comput-ing demand. The company can purchase a private cloudcapacity in its own virtual machine (VM) environment, andcan use the pay-as-you-go public cloud for peak-time com-puting demands. The proposed model helps find an optimalmix of the private and public cloud to minimize the totalcomputing costs. The following is the nomenclature usedthroughout this paper.

Nomenclature

x: an actual computing demand occurring in each timeunit with an exponential probability distributionfunction

λe−λx: an exponential probability distribution functionfor computing demand1-e−λx: a cumulative exponential distribution functionfor computing demandc: units of private cloud capacity purchased at thebeginning of a decision periodk: one-time purchase cost per unit of the private cloudcapacity for a decision horizonp: the price of the public cloud per time unitq: the guaranteed service levelka: the default downtime loss/penalty costt: the number of time units in a decision horizon

This section presents a base model for the cloud evalu-ation and investment decision problem. The followingseveral assumptions used in this paper are from Henne-berger [37]. It is assumed that private cloud resources arepurchased or contracted at the beginning of the decisionhorizon, that the public cloud provider has a sufficientcapacity to satisfy the peak demand of the company, andthat the probability distribution for computing demandcan be estimated based on real demand data and eachdemand can be split into the private and public clouds ifcloud bursting is necessary. The unit price of the publiccloud remains the same over the planning horizon.Figure 1 shows a simulated demand distribution

based on an exponential probability distribution. It isnoted that a number of previous studies on models ofcomputing resources assume the exponential distribu-tion or the Weibull distribution of computing requests[11, 15, 16]. It is possible to use any probability distri-bution with real data, but no closed form solution maybe obtainable and a simulation approach may be moreappropriate over an analytical approach. x representsan actual computing demand and c represents the pri-vate cloud capacity purchased. When the actual com-puting demand x is below the purchased capacity c, theprivate cloud will be used. In this situation, c-x is anexcess private cloud capacity. When x is the same as c,the private cloud is fully utilized without the need forthe public cloud. When the computing demand x ex-ceeds c, then x-c units of the public cloud are pur-chased from a public cloud provider via cloud bursting.In this model, the decision variable is the units ofprivate cloud capacity to be purchased, c. Among themodel variables, critical model variables include a prob-ability distribution function for the computing demand,the price of the public cloud, and the purchase cost perunit of the private cloud.

The base modelThe objective of the base model is to decide the optimalprivate cloud capacity to minimize the total cloud costs.

Lee Journal of Cloud Computing: Advances, Systems and Applications (2019) 8:15 Page 4 of 13

The base model of the hybrid cloud is given as the totalcost minimization function (1).

Min TC ¼ k � c

þ q �Z ∞

cλe−λx x−cð Þdx � pþ 1−qð Þ �

Z ∞

cλe−λx x−cð Þdx � ka

� �� t

ð1Þwhere k ⋅ c is the total private cloud costs at the beginningof the investment horizon, q � R∞

c λe−λxðx−cÞdx � p is thecosts of the public cloud per time unit, and ð1−qÞ � R∞

c λe−λx

ðx−cÞdx � ka is the default downtime penalty cost related tothe out-of-service situation from the public cloud provider.The cost structure follows Henneberger [37]. Applying inte-gration techniques, Eq. (1) is transformed into Eq. (2).

TC ¼ k � cþ qpt þ 1−qð Þkatð Þ 1λe−λc

� �ð2Þ

Differentiating Eq. (2) in terms of c leads to:

dTCdc

¼ k−e−λc qpt þ 1−qð Þkatð Þ ð3Þ

To get the closed form optimal value of c, Eq. (3) is setto zero. Then, the optimal private cloud capacity re-quired is:

c� ¼ln

kqpt þ 1−qð Þkatð Þ

� �

−λð4Þ

Equation (5) is the second derivative of Eq. (2). As thesecond derivative is always greater than zero for thevalue of c, the objective function (2) is convex with aminimum at c*.

d2TC

dc2¼ λe−λc qpt þ 1−qð Þkatð Þ ð5Þ

The utilization rate of the private cloud c is given by:

u ¼−1λe−λc þ 1

λc

ð6Þ

An illustration of the base model operationAs an illustration of the model operation, assume the fol-lowing: λ = 0.001; k = $10,000; p = $1.9; q = 0.9945; ka =$100; t = 10,000. In this scenario, the unit price of the pri-vate cloud capacity is set to about 53% of the equivalentusage of the public cloud (i.e., $10,000/($1.9*10,000)). Thispricing assumption reflects the current cloud market. As ofJanuary 2018, Microsoft Azure provides cost savings of 40%to 68% for an advanced purchase of a virtual machine forone or 3 years compared to the hourly-based pay-as-you-goservices (see https://azure.microsoft.com/en-us/pricing/de-tails/virtual-machines/linux/). 451 Research [39] also re-ported significant cost savings with the private cloud. Theexpected demand is 1000 capacity units (e.g., virtual ma-chines or physical machines) with the exponential probabil-ity (λ = 0.001). Then, the optimal private cloud capacity, c*,is 891.8 units, and the total computing cost, TC, is $18,918,135. The optimal utilization rate of the private cloudis 66.17%.

Analysis of model behaviorsThis section analyzes the relationship between the cap-acity decision and model variables. The experiment con-siders a set of possible pricing scenarios and determinesthe optimal cloud capacity to minimize the total costs.

Fig. 1 An Example of a Demand Distribution based on an Exponential Probability Distribution

Lee Journal of Cloud Computing: Advances, Systems and Applications (2019) 8:15 Page 5 of 13

Figures 2 and 3 show that as the price of the private cloudincreases, the optimal private cloud capacity decreasesrapidly from over 1400 to less than 600, but the optimalutilization rate of the private cloud increases slowly from0.54 to 0.77. It is conventional wisdom that a higherutilization rate is desirable. A high utilization rate is notnecessarily desirable since it is possible to achieve the highutilization rate with an under-capacity investment in theprivate cloud. It is interesting to note that the slight im-provement of the utilization rate comes with a muchgreater reduction rate of the private cloud capacity.Figure 4 shows that as the price of the public cloud in-

creases, the use of the public cloud decreases, but, theuse of the private cloud increases to meet the computingdemand. Note that the total usage of both private andpublic cloud is 1000 units. When the price of the publiccloud is $1.46, the usage of the public cloud is approxi-mately equal to the usage of the private cloud. It is inter-esting to note that the usage lines of the public and theprivate cloud have the same distance from the straightline of the 500 units.

An evaluation and investment in interoperabilityfor cloud burstingThe hybrid cloud requires interoperability of the privateand the public cloud to support cloud bursting. Sincecloud providers often offer their own proprietary applica-tions, interfaces, and infrastructures, users have difficultyin migrating to cloud providers [40]. Two major ap-proaches were proposed to improve cloud interoperability:provider-centric and user-centric approaches [41]. Theprovider-centric approaches are driven by a service pro-vider who offers specific services and is willing to developstandards and technologies for customers to achieve aspecified level of interoperability between the private andpublic cloud. On the other hand, the user-centric

approaches are driven by the cloud users who either relyon their own in-house IT personnel or a third party (e.g.,a cloud broker) to achieve the desired level of interoper-ability. For example, cloud users may develop a separatelayer to handle heterogeneity in cloud environments [42].In the hybrid computing environment, it is also challen-ging to decide which applications should be transitionedinto the public cloud in time of cloud bursting. Loweringthe bursting time and automating the movement processat the proper time require interoperable cloud systems.However, existing commercial tools rely heavily on thesystem administrator’s knowledge to answer key questionssuch as when a cloud burst is needed and which applica-tions must be moved to the cloud [31].One benefit of interoperable cloud systems is that it re-

duces the cost of cloud bursting for users. The interoper-able cloud systems may be achieved by using standardizeddata formats, open source cloud systems, application pro-gram interface (API), and specialized middleware. All theserequire time and investment by the users and/or cloud pro-viders and there may exist a diminishing return on the in-vestments. For example, cloud bursting requires that thecompany’s software is configured to run multiple instancessimultaneously and they may need to retrofit existing appli-cations to accommodate multiple instances [43]. Therefore,it is important to evaluate the value of the interoperability-enhancing technologies to support cloud bursting.This section focuses on the user-centric approaches

where a corporate cloud customer decides to investin interoperability enhancement such as the develop-ment of a layer to handle cloud bursting. Mathemat-ical procedures are developed to evaluate investmentdecisions for the hybrid cloud capacity and the inter-operability enhancement simultaneously. The basemodel is extended to include the investment decisionvariable for the interoperability enhancement. The

Fig. 2 Optimal Capacity of Private Cloud

Lee Journal of Cloud Computing: Advances, Systems and Applications (2019) 8:15 Page 6 of 13

simultaneous cloud-interoperability decisions refer tothe investment decisions for which both the variablefor the cloud capacity and the variable for the inter-operability enhancement are solved at the same timein the hope of reducing the total cloud costs synergis-tically. The cloud-interoperability evaluation and in-vestment model is given as the total costminimization function (7).

Min TC ¼ k � cþ �q �

Z ∞

cλe−λx x−cð Þdx � pþ q �

Z ∞

cλe−λx x−cð Þdx � z þ 1−qð Þ �

Z ∞

cλe−λx x−cð Þdx � kaÞ � t þ G

ð7Þ

Where z is a per-unit interoperability cost, q � R∞c λ

e−λxðx−cÞdx � z is the total interoperability cost of thepublic cloud per time unit when cloud bursting oc-curs, and G is the investment to enhance the inter-operability. Note that all other terms are the same asthose in the base model. The total cost minimizationfunction (7) is transformed to Eq. (8).

TC ¼ k � cþ qpt þ qzt þ 1−qð Þkatð Þ 1λe−λc

� �þ G ð8Þ

Now, the per-unit interoperability cost, z, is defined asan exponential function of the investment, G, as follows.

z ¼ U þ W−Uð Þe−βG; G≥0; and 0≤U ≤z≤W ð9Þ

where W is the highest interoperability cost per timeunit of the public cloud incurred when there is no in-vestment in the interoperability enhancement and U isthe lowest interoperability cost achievable with the in-vestment of G.Differentiating Eq. (8) in terms of c and G, respectively

leads to:

dTCdc

¼ k−e−λc qpt þ qzt þ 1−qð Þkatð Þ ð10Þ

dTCdG

¼ qz0t

� � 1λe−λc

� �þ 1 ð11Þ

To simplify the mathematical procedures,set e−λc = gEquation (11) leads to:

Fig. 3 Optimal Utilization Rate of Private Cloud

Fig. 4 Comparison of Cloud Usage

Lee Journal of Cloud Computing: Advances, Systems and Applications (2019) 8:15 Page 7 of 13

dzdG

¼ −λqtg

ð12Þ

The first derivative of Eq. (9) is taken with regard toG. The result is given by:

dzdG

¼ −β z−Uð Þ < 0 ð13Þ

Setting two Eqs. (12) and (13) equal leads to:

z ¼ λþ Uβqtgβqtg

ð14Þ

If the optimal private cloud capacity c*is given, the op-timal z* is:

z� ¼ λþ Uβqte−λc�

βqte−λc�ð15Þ

To find the simultaneous solution for both the privatecloud capacity and the interoperability enhancement, setEq. (10) to zero, and plug Eq. (14) in the equation to get:

g ¼ βk−λð Þβqpt þ Uβqt þ βkat−βqkatð Þ ð16Þ

Given the optimal g* (i.e., e-λc), z*, c*, and G* are ob-tained as follows:

z� ¼ λþ Uβqtg�

βqtg�ð17Þ

c� ¼ − lng�

λð18Þ

G� ¼− ln

z�−Uð ÞW−Uð Þ

� �

βð19Þ

Table 1 shows the improvement made by the simultan-eous cloud-interoperability investment decision over the se-quential cloud-interoperability investment decision and noinvestment decision. The sequential cloud-interoperabilityinvestment decision refers to the evaluation process inwhich only one decision variable is solved at a time. First,using Eq. (4), the optimal private cloud capacity, c*, is deter-mined without considering the optimal interoperability in-vestment, G*. Second, based on the optimal private cloud

capacity, using Eq. (15), the investment in the optimal inter-operability enhancement is determined. For example,assume the same base model’s parameters. Then, the opti-mal private cloud capacity c* ≈ 435. Then, g = e−λc = e(−0.001∗ 435) = 0.64746. The optimal interoperability cost, z*, is$0.4883. The optimal investment in the interoperability en-hancement, G*, is $1,807,338. Table 1 shows that the se-quential cloud-interoperability investment decision resultsin a lower interoperability cost per computing unit than thesimultaneous cloud-interoperability investment decision,but it brings about overinvestment in the interoperabilityenhancement and consequently larger total cloud costs, asit does not take into consideration the synergy effect. Onthe other hand, the simultaneous cloud-interoperability in-vestment decision leads to an optimal investment, consider-ing the synergy effect between the interoperability cost andthe cloud capacity cost. Surprisingly, the sequential inter-operability investment generates a higher total cost than nointeroperability investment.

Sensitivity analysis of cloud-interoperabilityinvestment decisionThis section further evaluates the performance of thesequential and simultaneous investment approachesdiscussed above and conducts sensitivity analyses to under-stand model behaviors of the investment decisions by chan-ging parameter values. The base parameter values assumedare presented below.

Base parameters

k: a cost of $10,000 per unit private cloud capacityp: the unit price of $1.0 for public cloud service pertime unitz: the interoperability cost of $0.9 without investmentq: the guaranteed service level of 99.45%ka: a default downtime loss/penalty cost of $100 pertime unitt: 10,000 time units in a decision horizonU = $0.1W = $0.9λ = 0.001β = 0.0000004

Table 1 Comparison of investment approaches

No InteroperabilityInvestment (A)

Sequential InteroperabilityInvestment (B)

Simultaneous InteroperabilityInvestment (C)

Improvement(A-C)

Improvement(B-C)

TC* $18,918,136 $19,298,239 $18,779,969 $138,167 $518,270

z* $0.9000 $0.4883 $0.6510 $0.2490 -$0.1628

c* 892 435 785 107 −350

G* $0 $1,807,338 $932,129 -$932,129 $875,209

Lee Journal of Cloud Computing: Advances, Systems and Applications (2019) 8:15 Page 8 of 13

Figures 5 shows that as the computing demand in-creases, the optimal interoperability cost, z*, decreaseswith more investment in the interoperability enhance-ment, G. The decline of the per-unit interoperabilitycost is more rapid when the demand is smaller andthe decline slows down as the demand increases.Figure 6 shows that as the demand level increases,

the difference gets wider between the total cost of thesimultaneous cloud-interoperability and that of the noinvestment decision. The simultaneous cloud-interoperability dominates no investment at all de-mand levels. Figure 7 shows that the total cost of thesequential cloud-interoperability investment is higherthan that of the no investment decision when the de-mand level is small, but becomes lower than that ofthe no investment decision as the demand gets larger.The analysis indicates that an organization with a

large cloud demand level would achieve a greater costadvantage from the interoperability enhancement thanan organization with a small demand, since a mar-ginal increase of the investment in the interoperabilityenhancement generates large savings for the totalcloud cost when the demand is high. On the otherhand, many small and medium-sized companies mayfind the use of a third-party cloud broker to be morecost effective than an in-house development of inter-operability technologies. Small and medium-sizedcompanies may also reap benefits from cloud pro-viders which offer standardized interoperable cloudtechnologies.

Return on investment of an interoperabilityprojectAs in many other IT projects, one of the barriers tothe investment in cloud technologies is difficulty inmeasuring the potential return on investment (ROI).ROI is one of the most crucial criteria for companies

to consider when investing in a new technology. ROIanalyses have been used in various technology evalua-tions [44]. For example, Lee [45] develops cost/benefitmodels to measure the impact of RFID-integratedquality improvement programs and to predict theROI. Using these models, the decision makers decidewhether and how much to invest in quality improve-ment projects. An ROI model was developed for aneconomic evaluation of cloud computing investment[27].While a formula for calculating ROI is relatively

straightforward, the ROI method is more suitable whenboth the benefits and the costs of an investment areeasily traceable and tangible. Since an investment incloud technologies is a capital expenditure, the invest-ment is likely to be under scrutiny of senior manage-ment for the budget approval. The investmentevaluation and decision model in the previous sectionsidentifies the optimal investment point where the mar-ginal cost saving equals the marginal investment. How-ever, it is possible that the optimal solution does notnecessarily meet the ROI threshold rate imposed by theorganization. The ROI threshold rate is the minimumROI level for which a company will make investments.The ROI threshold rate is usually tied to the cost ofcapital and is used to screen out low productivity pro-jects under financial constraints. This section derives aformula to identify the target ROI of the interoperabil-ity enhancement project.To illustrate the calculation of the ROI, suppose the total

cloud cost without investment in interoperability is $100m.Assume that with the investment of $10 million, the totalcloud cost including the investment is $99m. In this casethe ROI is 10% (i.e., ($100m-$99m)/$10m). If the ROIthreshold rate of the company is 20%, the project would berejected even though the investment of $10 million reducesthe total cloud cost. The basic ROI formula is given as:

Fig. 5 Change of Computing Demand and and Optimal Interoperability Cost

Lee Journal of Cloud Computing: Advances, Systems and Applications (2019) 8:15 Page 9 of 13

ROI ¼ Total Cost without investment−Total cost with investmentInvesment

� �� 100

ð20Þ

Since the optimal investment, G*, is the point wherethe marginal cost saving equals the marginal invest-ment, it is expected that the decrease of the invest-ment amount increases the ROI. Equation (21) isused to measure the ROI.

I− k � cþ qpt þ qzt þ 1−qð Þkatð Þ 1λe−λc

� �þ G

� �

G¼ r

ð21Þ

where I is the total cloud cost without investment ininteroperability and r is the ROI target threshold.To find the target ROI using the Newton-

Raphson method in one variable, the following isformulated:

f Gð Þ ¼ I− k � cþ qpt þ qzt þ 1−qð Þkatð Þ 1λe−λc

� �þ G

� �−rG

ð22ÞThen, the first derivative of f(G) is:

f0Gð Þ ¼ − qz

0t

� � 1λe−λc

� �−1−r ð23Þ

where z′ = − β(W −U)e−βG.To begin the search for the target ROI, r, set G0 at G*

found in Eq. (19).

G1 ¼ G0−f G0ð Þf0G0ð Þ ð24Þ

The process is repeated as:

Gnþ1 ¼ Gn−f Gnð Þf0Gnð Þ ð25Þ

until a sufficiently accurate value of G is reached.As an illustration of the above Newton-Raphson

method, assume that the target ROI is 20%. Using the

Fig. 6 Change of Computing Demand and Total Costs by Simultaneous Investment and No Investment

Fig. 7 Change of Computing Demand and Total Costs by Sequenctial Investment and No Investment

Lee Journal of Cloud Computing: Advances, Systems and Applications (2019) 8:15 Page 10 of 13

base parameters given in “Sensitivity analysis of cloud-interoperability investment decision” section, G0 is set at$932,129. G1 is $690,836 and ROI is 14.83%. G2 is $620,350 and ROI is 18.72%. G3 is $612,780 and ROI is 19.87%.G4 is $612,690 and ROI is 19.9985%. After only four itera-tions of Eqs. (24) and (25), a sufficiently accurate value ofG is obtained to achieve the target ROI of 20%. Comparedto a time-consuming linear search for the G for the targetROI, the Newton-Raphson method is shown to achievetremendous efficiency in the cloud investment decisionand can be a useful performance management technique.A sensitivity analysis is conducted to investigate the rela-

tionship between the ROI and G. Note that to minimizethe total cloud cost, the optimal investment should be$932,129 and the ROI is 14.82%. Figure 8 shows that thedecrease of the investment from $932,129 generates higherROIs, but the increase of the investment from $932,129 de-creases the ROIs. If the ROI threshold rate of the companyis higher than 14.82%, they need to decrease the investmenteven though the total cloud cost is the lowest at the invest-ment of $932,129. With the ROI, managers would be ableto develop a strong justification for the investment.Diminishing return applies to the ROI of the interoper-

ability investment. A corporate cloud customer can findthat for their given computing demand distribution, thereis an optimal level of interoperability investment that min-imizes the total cloud cost. Up to the optimal level of in-vestment, any additional investment will increase thereturn. However, over that optimal level of investment,any additional investment will continue to diminish thereturn. The corporate cloud customer may have an ROIthreshold rate which is equal to the company’s minimumacceptable ROI rate. If the ROI at the optimal total cloudcost is greater than or equal to the ROI threshold rate,then the interoperability investment level needed for theoptimal total cloud cost is justified. However, if the ROI atthe optimal total cloud cost is less than the ROI thresholdrate, the company needs to lower the interoperability

investment to the point where the ROI equals their ROIthreshold rate.

ConclusionAccording to Forrester [46], in 2018, cloud computingbecame a must-have technology for every enterprise.Nearly 60% of North American enterprises are usingsome type of public cloud platform. Furthermore, privateclouds are also growing fast, as companies not onlymove workloads to the public cloud but also developon-premises private cloud in their own data centers.Therefore, this paper predicts that the corporate adop-tion of hybrid cloud computing for corporate cloud cap-acity management is an irreversible trend. The demandfor the hybrid cloud will continue to grow in the futureas big data, smart phones, and the Internet of Things(IoT) technologies require highly scalable infrastructureto meet the growing but fluctuating computing demand.Advances in cloud computing hold great promise for

lowering computing costs and speeding up new businessdevelopments. However, despite the popularity of cloudcomputing, no significant investment evaluation modelsare available. The existing body of studies are mostly de-scriptive in nature. The optimal cloud capacity invest-ment has been elusive and therefore investments havebeen based on gut feelings rather than solid decisionmodels. Hence, this paper presented a capacity evalu-ation and investment decision model for the hybridcloud. A closed form solution was derived for the opti-mal capacity decision. This model provides a solid foun-dation to evaluate investment decisions for various cloudtechnologies, moving beyond the existing descriptivevaluation studies to normative studies, the outcomes ofwhich should be able to guide cloud professionals toplan on how much they need to invest in different cloudtechnologies and how they can enhance the investmentbenefits from a corporate customer’s perspective.

Fig. 8 Change of the ROI over the Investment in Interoperability

Lee Journal of Cloud Computing: Advances, Systems and Applications (2019) 8:15 Page 11 of 13

While there is widespread cloud adoption and techno-logical breakthrough, the interoperability issue remains abarrier. To address the interoperability issue in the hy-brid cloud, this paper also developed the cloud-interoperability evaluation and investment model by ex-tending the basic model. This model derives the optimalinvestment levels for both the cloud capacity and theinteroperability enhancement simultaneously. The rela-tionship between the investment in the interoperabilityenhancement and ROI was also investigated.This study is the first effort in developing an analytical

cloud capacity evaluation and investment decision modelfor the hybrid cloud, and analyzing the impact of the inter-operability investment on the cost savings and ROI. Thismodel can be easily adapted to a variety of investment situ-ations in both for-profit organizations and non-profit orga-nizations such as hospitals, governments, and libraries thathave similar computing demand and cost structures.Like many studies, this study has several limitations. First,

it is noted that the successful use of these models would re-quire accurate estimation of the model parameters and theuse of various modeling techniques. Future research mayexplore various estimation techniques of the model param-eters to develop more realistic models. Second, future stud-ies need to investigate additional variables for the model.For example, different cloud providers employ differentschemes and models for pricing [47] and the diversity inthe pricing models makes price comparison difficult [48].Incorporation of this variable price may be a worthwhile fu-ture research. The interoperability costs may include notonly tech architecture or wrappers, but also data transportcosts. The future model may include the data transportcosts in the cloud capacity decision. Lastly, despite an in-creased focus on cloud cost management, only a minorityof companies have implemented policies to minimizewasted cloud resources such as shutting down unusedworkloads or rightsizing instances [5]. Implementation ofwell-defined cloud governance and adaptive cloud schedul-ing techniques may help companies minimize the wastedcloud resources and avoid overinvestment in cloud cap-acity. Researchers are encouraged to explore the above-mentioned limitations of this study in their future research.

AbbreviationsRFID: Radio Frequency Identification; ROI: Return on investment

AcknowledgementsNot applicable.

Authors’ contributionsIn Lee is the sole author of this study. The author read and approved thefinal manuscript.

Authors’ informationNot applicable.

FundingNot applicable.

Availability of data and materialsData sharing not applicable to this article as no datasets were generated oranalyzed during the current study.

Competing interestsThe author declares that he has no competing interests.

Received: 29 March 2019 Accepted: 15 October 2019

References1. Varghese B, Buyya R (2018) Next generation cloud computing: new trends

and research directions. Future Gener Comput Syst 79(Part 3):849–8612. Birje MN, Challagidad PS, Goudar RH, Tapale MT (2017) Cloud computing

review: concepts, technology, challenges and security. Int J Cloud Comput6(1):32–57

3. Hentschel R, Leyh C, Petznick A (2018) Current cloud challenges inGermany: the perspective of cloud service providers. J Cloud Comput 7:5.https://doi.org/10.1186/s13677-018-0107-6

4. Opara-Martins J, Sahandi R, Tian F (2016) Critical analysis of vendor lock-inand its impact on cloud computing migration: a business perspective. JCloud Comput Adv Syst Appl 5:4. https://doi.org/10.1186/s13677-016-0054-z

5. RightScale (2019). State of the cloud report. Available from: https://www.rightscale.com/lp/state-of-the-cloud?campaign=RS-HP-SOTC2019

6. Lee I (2017) Determining an optimal mix of hybrid cloud computing forenterprises. UCC ‘17 companion. In: Proceedings of the10th internationalconference on utility and cloud computing, pp 53–58

7. Azumah KK, Sørensen LT, Tadayoni R (2018) Hybrid cloud service selectionstrategies: a qualitative meta-analysis. In: 2018 IEEE 7th internationalconference on adaptive science & technology (ICAST), Accra, Ghana

8. Litoiu M, Wigglesworth J, Mateescu R (2016) The 8th CASCON workshop on cloudcomputing. In: Proceeding CASCON ‘16 proceedings of the 26th annual internationalconference on computer science and software engineering, pp 300–303

9. Computerweekly (2018) Available from: https://www.computerweekly.com/news/252452059/Uber-backs-hybrid-cloud-as-route-to-business-and-geographical-expansion. Accessed 21 January 2019.

10. Alashoor T (2014) Cloud computing: a review of security issues andsolutions. Int J Cloud Comput 3(3):228–244

11. Khazaei H, Misic J, Misic VB (2011) Modelling of cloud computing centersusing M/G/m queues. In: 2011 31st international conference on distributedcomputing systems workshops, Minneapolis, MN, USA, pp 87–92

12. Moreno I, Garraghan P, Townend P, Xu J (2013) An approach forcharacterizing workloads in google cloud to derive realistic resourceutilization models. In: Proceedings of 7th international symposium onservice oriented system engineering (SOSE), Redwood City, CA, pp 49–60

13. Magalhães D, Calheiros RN, Buyya R, Gomes DG (2015) Workload modelingfor resource usage analysis and simulation in cloud computing. ComputElectr Eng 47:69–81

14. Rochman Y, Levy H, Brosh E (2017) Dynamic placement of resources incloud computing and network applications. Perform Eval 115:1–37

15. Gupta V, Harchol-Balter M, Sigman K, Whitt W (2007) Analysis of join-the-shortest-queue routing for web server farms. Perform Eval 64(9–12):1062–1081

16. Yang B, Tan F, Dai Y, Guo S (2009) Performance evaluation of cloud serviceconsidering fault recovery. In: First Int’l conference on cloud computingCloudCom, Beijing, China, pp 571–576

17. Xiong K, Perros H (2009) Service performance and analysis in cloud computing.In: IEEE 2009 world conference on services, Los Angeles, CA, pp 693–700

18. Patch B, Taimre T (2018) Transient provisioning and performance evaluation forcloud computing platforms: a capacity value approach. Perform Eval 118:48–62

19. Wolski R, Brevik J (2014) Using parametric models to represent private cloudworkloads. IEEE Trans Serv Comput 7(4):714–725

20. Grid Workloads Archive (2017) Available from: http://gwa.ewi.tudelft.nl/.Accessed 21 January 2019.

21. Araujo J, Maciel P, Andrade E, Callou G, Alves V, Cunha P (2018) Decisionmaking in cloud environments: an approach based on multiple-criteriadecision analysis and stochastic models. J Cloud Comput Adv Syst Appl 7:7.https://doi.org/10.1186/s13677-018-0106-7

22. López-Pires F, Barán B (2017) Cloud computing resource allocationtaxonomies. Int J Cloud Computing 6(3):238–264

23. Balaji M, Kumar A, Rao SVRK (2018) Predictive cloud resource managementframework for enterprise workloads. J King Saud Univ Comput Inf Sci 30(3):404–415

Lee Journal of Cloud Computing: Advances, Systems and Applications (2019) 8:15 Page 12 of 13

24. Wang CF, Hung WY, Yang CS (2014) A prediction based energy conservingresources allocation scheme for cloud computing. In: 2014 IEEE internationalconference on granular computing (GrC), Noboribetsu, Japan, pp 320–324

25. Han Y, Chan J, Leckie C (2013) Analysing virtual machine usage in cloudcomputing. In: 2013 IEEE ninth world congress on services, Santa Clara, CA,USA, pp 370–377

26. Deng D, Lu Z, Fang W, Wu J (2013) CloudStreamMedia: a cloud assistantglobal video on demand leasing scheme. In: 2013 IEEE internationalconference on services computing, Santa Clara, CA, USA, pp 486–493

27. Misra SC, Monda A (2011) Identification of a company’s suitability for theadoption of cloud computing and modelling its corresponding return oninvestment. Math Comput Model 5(3/4):504–521

28. de Assunção MD, di Costanzo A, Buyya R (2010) A cost-benefit analysis of usingcloud computing to extend the capacity of clusters. Clust Comput 13(3):335–347

29. Gmach D, Rolia J, Cherkasova L, Kemper A (2007) Capacity managementand demand prediction for next generation data centers. In: IN: IEEEinternational conference on web services, Salt Lake City, UT, USA, pp 43–50

30. Laatikainen G, Mazhelis O, Tyrvainen P (2016) Cost benefits of flexible hybridcloud storage: mitigating volume variation with shorter acquisition cycle. JSyst Softw 122:180–201

31. Guo T, Sharma U, Shenoy P, Wood T, Sahu S (2014) Cost-aware cloudbursting for enterprise applications. ACM Trans Internet Technol (TOIT)13(3):10 22 pages

32. Clemente-Castelló FJ, Mayo R, Fernández JC (2017) Cost model and analysisof iterative MapReduce applications for hybrid cloud bursting. In: CCGrid ‘17Proceedings of the 17th IEEE/ACM international symposium on cluster,cloud and grid computing, Madrid, Spain, pp 858–864

33. Weinman J (2016) Hybrid cloud economics. IEEE Cloud Comput 3(1):18–2234. Toosi AN, Sinnott RO, Buyya R (2018) Resource provisioning for data-

intensive applications with deadline constraints on hybrid clouds usingAneka. Future Gener Comput Syst 79(Part 2):765–775

35. Petcu D (2011) Portability and interoperability between clouds: challengesand case study. In: Abramowicz W, Llorente IM, Surridge M, Zisman A,Vayssière J (eds) Towards a service-based internet. ServiceWave 2011.Lecture notes in Computer Science, vol 6994. Springer, Berlin, pp 62–74

36. Edmonds A, Metsch T, Papaspyrou A, Richardson A (2012) Toward an opencloud standard. IEEE Internet Comput 16(4):15–25

37. Henneberger M (2016) Covering peak demand by using cloud services - aneconomic analysis. J Decis Syst 25(2):118–135

38. Fan TJ, Chang XY, Gu CH, Yi JJ, Deng S (2014) Benefits of RFID technologyfor reducing inventory shrinkage. Int J Prod Econ 147(Part C):659–665

39. 451 Research (2017) Can private cloud be cheaper than public cloud?Available from: https://www.vmware.com/content/dam/digitalmarketing/vmware/en/pdf/products/vrealize-suite/vmware-paper1-can-private-cloud-be-cheaper-than-public-cloud.pdf

40. Mansour I, Sahandi R, Cooper K, Warman A (2016) Interoperability in theheterogeneous cloud environment: a survey of recent user-centric approaches.In: ICC ‘16 proceedings of the international conference on internet of thingsand cloud computing, Article No. 62, Cambridge: ACM, New York.

41. Toosi AN, Calheiros RN, Buyya R (2014) Interconnected cloud computingenvironments: challenges, taxonomy, and survey. ACM Comput Surv 47(1):7 47 pages

42. Zhang Z, Wu C, Cheung DWL (2013) A survey on cloud interoperability: taxonomies,standards, and practice. ACM SIGMETRICS Perform Eval Rev 40(4):13–22

43. Morpheus (2016) If cloud bursting is so great, why aren’t more companiesdoing it? Available from: https://www.morpheusdata.com/blog/2016-10-26-if-cloud-bursting-is-so-great-why-aren-t-more-companies-doing-it

44. Sarac A, Absi N, Dauzère-Pérès S (2010) A literature review on the impact ofRFID technologies on supply chain management. Int J Prod Econ 128(1):77–95

45. Lee HH (2008) The investment model in preventive maintenance in multi-level production systems. Int J Prod Econ 112(2):816–828

46. Forrester (2018) Predictions 2019: Cloud computing comes of age as thefoundation for enterprise digital transformation. Available from: https://go.forrester.com/blogs/predictions-2019-cloud-computing/

47. Al-Roomi M, Al-Ebrahim S, Buqrais S, Ahmad I (2013) Cloud computingpricing models: a survey. Int J Grid Distr Comput 6(5):93–106

48. Lehmann S, Buxmann P (2009) Pricing strategies of software vendors. BusInf Syst Eng 1(6):452–462

Publisher’s NoteSpringer Nature remains neutral with regard to jurisdictional claims inpublished maps and institutional affiliations.

Lee Journal of Cloud Computing: Advances, Systems and Applications (2019) 8:15 Page 13 of 13