Uncertainty-aware Optimization of Resource Provisioning, a Cloud

End-user Perspective

Masoumeh Tajvidi, Michael J. Maher and Daryl Essam

School of Engineering and Information Technology, UNSW, Canberra, Australia

Keywords:

Cloud Computing, Resource Provisioning, Two-stage Stochastic Programming.

Abstract:

Cloud computing offers a customer the possibility of the availability of large computational resources, while

paying only for the resources used. However, because of uncertainty in the customers future demand and the

future market price for the computational resources, obtaining these resources in a cost-effective and robust

way is a difﬁcult problem. The variety of pricing plans is a further complication. In this paper we solve

this problem using two-stage stochastic programming, for the ﬁrst time considering all three available pricing

plans, i.e. on-demand, reservation, and spot pricing. Through our experimental implementation, we ﬁnd that

our model can lower the total operational cost by up to 1.5 percent compared to other solutions.

1 INTRODUCTION

Resource provisioning problem in the cloud com-

puting environment can be viewed from different

perspectives. the Infrastructure as a Service (IaaS)

Provider, the Software as a Service (SaaS) provider,

and the cloud end-user. Each trying to maximize their

own proﬁt in the resource provisioning plan phase.

Due to different goals, requirements, and constraints,

the resource provisioning problem in the cloud com-

puting environment needs to be addressed separately,

for each stakeholder. In this paper we view this prob-

lem from the end-user point of view. The end-user is

an individual or an organization, aiming to rent com-

putational resources from a public cloud provider. In

cloud computing, provisioning of resources has to be

controlled by the end-user, which is a new and unfa-

miliar paradigm for such users, who are accustomed

to working with a ﬁxed set of resources they own. In-

stead, they encounter a complicated decision making

problem of choosing the most suitable type and num-

ber of VMs with the best pricing plans, for running

their application. There are also uncertain parame-

ters that make this optimization problem even more

complicated. Since the resource demand is highly dy-

namic in nature, its pattern cannot be known, or even

be accurately predicted, in advance. Moreover the

price of resources varies and is not easily predictable.

Numerous cloud providers offer various VM types,

namely reservation, on-demand, and spot pricing.

The reservation cost of resources per unit is typ-

ically the lowest, but under-provisioning can occur

when the reserved resources are unable to fully meet

the demand. However, by provisioning more re-

sources with either on-demand or spot plan for ex-

tra demand, this problem can be solved, although the

user may be charged a higher price. Another potential

issue is the over-provisioning problem, which occurs

when the reserved resources are more than the actual

demand and thence the reserved resources will be un-

derutilized. How to manage all these problems and

optimize cost is a critical issue the end-user must deal

with.

Although there are plenty research conducted on

resource provisioning from the IaaS (Chaisiri et al.,

2009) and SaaS (Li et al., 2015) cloud provider’s

view, There has been little work on solving this prob-

lem as it is in the real-world for the cloud end-users.

The paper closest to our work optimizes the cost of

VM provisioning in the cloud computing environ-

ment from the end-user’s point of view (Chaisiri et al.,

2012) by an optimal cloud resource provisioning al-

gorithm (OCRP). To make an optimal decision, de-

mand and price uncertainty are taken into account. A

stochastic integer programming approach with multi-

stage recourse is proposed for optimizing this prob-

lem. In this work, however, spot pricing and het-

eroginity of VMs were ignored. In (Adamuthe et al.,

2013), the authors solved this problem from the end-

user view in a two phase approach by using genetic

Algorithm (GA) and Particle Swarm Optimization

(PSO). Heterogeneity of VMs, uncertainty of param-

Tajvidi, M., Maher, M. and Essam, D.

Uncertainty-aware Optimization of Resource Provisioning, a Cloud End-user Perspective.

DOI: 10.5220/0006234103210328

In Proceedings of the 7th International Conference on Cloud Computing and Services Science (CLOSER 2017), pages 293-300

ISBN: 978-989-758-243-1

293

eters, and existence of various pricing plans were ne-

glected in this paper. In (Genaud and Gossa, 2011),

a satisfactory trade-off between cost and speed to

process a set of independent jobs is conducted from

the end-users’ side, but only the on-demand pricing

model is taken into account. The main focus of (Zhu

and Agrawal, 2010) is an automated and dynamic re-

source allocation approach, in the cloud environment,

based on control theory techniques. An autonomous

elasticity controller is proposed in (Ali-Eldin et al.,

2012), it changes the number of virtual machine al-

located to a service based on both monitored load

changes and prediction of future work.

Most of the existing literature, as mentioned above

focuses on deterministic formulations over ﬁxed hori-

zons where the scheduler has perfect foresight (Teng

and Magoules, 2010). Those that have considered

uncertainty in their problem, typically focus on just

one aspect (e.g. real-time pricing) (Chaisiri et al.,

2012), or use very simple and artiﬁcial data (Zafer

et al., 2012). Pricing and VM heterogeneity is also

neglected in most of them.

In this paper, we propose a mechanism to opti-

mize cost by choosing the most appropriate pricing

plans and VM types, while considering the applica-

tion’s demand uncertainty from the consumer side

and price uncertainty (on-demand and spot) from the

providers side. In order to take into account the un-

certainties, we model it as a two stage stochastic opti-

mization problem using the MiniZinc modelling lan-

guage (Nethercote et al., 2007). The results show that

our approach leads to a lower operational cost, com-

pared to previous relevant works.

The rest of the paper is organized as follows. The

problem description and formulation is discussed in

section II, then in section III is implementation and

experimental evaluation, followed by the result dis-

cussion in section IV. Finally in section V, conclu-

sions are stated.

2 SYSTEM MODEL AND

PROBLEM FORMULATION

The cloud end-user needs to rent a number of VMs

for running his application, using public cloud re-

sources with minimum cost. Amazon is a dominant

provider in the cloud service market and offers vari-

ous IaaS and Platform as a Service (PaaS) solutions.

The largest and best-known of these is the EC2 IaaS

solution (Amazon EC2, 2016). As it is one of the

most widely used IaaS providers in both academia

and industry, in this work we assume that the end-user

wishes to rent resources from the Amazon EC2.

2.1 System Model

Amazon EC2 provides various VM types with the dif-

ferent pricing plans of reservation, on-demand, and

spot. Reservation pricing refers to the advance reser-

vation of resources for a speciﬁc time period, while

securing a lower usage charge. It offers consumers

three purchasing variants, “all upfront”, “partial up-

front”, and “no upfront” to purchase reserved in-

stances. With the all-upfront variant, users pay for

the entire reserved instance with one upfront payment.

This variant provides the largest discount. With the

partial-upfront variant, users make a low upfront pay-

ment and are then charged a monthly rate for their

instances, even for instances that are not utilized in

this period of time. The no-upfront variant does not

require any upfront payment and provides a monthly

rate for the duration of the term. Amazon has recently

introduced convertible reserved VMs, which provide

customers with additional ﬂexibility to change the

VM family, OS, or tenancy, as long as the exchange

is for an equal or greater spend on the new convert-

ible reserved VMs. However in this paper we only

consider the standard Reservation.

On-Demand pricing lets customers pay for com-

pute capacity by the hour, with no long-term com-

mitments or upfront payments. Depending on the de-

mand of their application, users can simply increase

or decrease their compute capacity and only pay for

the speciﬁed hourly rate for the instances used. Al-

though this pricing model provides convenient ﬂexi-

bility and reliability, it charges customers higher rates

than other plans. The on-demand price is not a ﬁxed

price and the cloud provider can change it at any time.

Spot pricing enables users to bid for unused Amazon

EC2 capacity. This price ﬂuctuates periodically, de-

pending on the supply and demand for spot instances.

To acquire spot instances, the users place a spot re-

quest, specifying the instance type and the maximum

price they are willing to pay per hour per instance. If

the customer’s bid price meets or exceeds the current

spot price, the requested instances are granted and

they will run until either the user chooses to termi-

nate them or the spot price increases above the max-

imum bid price. In the latter case, the instances are

terminated immediately by the cloud providers with

2 minutes notice. The actual price users pay for their

instances is the spot market price, regardless of their

bid price. Due to the uncertain availability of spot in-

stances and the potential interruptions they may bring,

the spot instance plan is only practical for fault toler-

ant applications.

When it comes to spot instances, a big challenge

is choosing a good bidding strategy. There are various

CLOSER 2017 - 7th International Conference on Cloud Computing and Services Science

294

strategies proposed in the literature(Tang et al., 2012),

but generally one can bid high as a means of ensuring

to obtain instances with less volatility, or bid lower to

optimize costs and send any overﬂow to on-demand or

reserved instances. The most common strategy, how-

ever, is to bid on-demand price, called “always bid-

ding on-demand price”. With this strategy customers

ensure that they will get a discount over on-demand,

plus they have a lower chance to be interrupted. In

our model we use this simple and effective bidding

strategy.

The main issue of the resource provisioning prob-

lem for users, is the complexity of dealing with multi-

ple pricing plans, purchasing variants, and VM types,

as well as the uncertainty of on-demand and spot

prices. As reserved instances are reliable and cost ef-

fective resources, they can be considered one of the

best options for customers. However users need to

decide about them in advance, before running their

application, when the real workload and prices are not

known. This decision should be made carefully, be-

cause there is a long term commitment reserving VMs

(at least 1 year). Therefore, more information about

future workload can help. Based on this information,

a more accurate decision can be made and then, af-

ter starting the application, any excess demand can be

fulﬁlled using the more ﬂexible pricing plans of on-

demand and spot. As a result, the problem splits into

two steps: deciding on the number of reserved VMs,

before the uncertain parameters become known, and

then compensating for any under-provisioning with

on-demand or spot pricing plans.

Having split our uncertain problem into two

phases, one of the most appropriate techniques to

solve it, is stochastic programming (Birge and Lou-

veaux, 2011). Stochastic programming is an approach

for modelling optimization problems that involve un-

certainty. When the parameters are uncertain, but as-

sumed to lie in some given set of possible scenar-

ios, a good solution might be one that is feasible for

all possible parameter choices and optimizes a given

objective function. Stochastic programming models

are similar in style, but take advantage of the fact

that probability distributions of the uncertain data are

known or can be estimated. Often these models apply

to settings in which decisions are made repeatedly in

essentially the same circumstances, and the objective

is to come up with a decision that will, on average,

perform well. The most widely applied and studied

stochastic programming models are two-stage (linear)

programs. Here the decision maker takes some action

in the ﬁrst stage, after which a random event occurs

that affects the outcome of the ﬁrst-stage decision.

A recourse decision can then be made in the second

stage to compensate for any bad effects that might oc-

cur as a result of the ﬁrst-stage decision(Shapiro and

Philpott, 2007).

The ﬁrst stage decision, therefore, is deciding on

the number of reserved instance and the reservation

purchasing variants for a one hour time slot, based

on an estimation of the future workload. A recourse

decision in the second stage is acquiring more VMs

on On-demand or spot, if required, in the next hour

when the uncertain parameters become known. The

detailed explanation of the problem and its formula-

tion is discussed in the following section.

2.2 Problem Formulation

The objective of this problem is to minimize the to-

tal cost of provisioning resources. The decision vari-

ables are the number of each VM type provisioned

under different purchasing variants and pricing plans.

See Table 1 for notation. The decision variable x

the number of reserved VM type i, subscribed to pur-

chasing variant k in the ﬁrst stage, while x

denotes

the number of operating VM type i with purchasing

variant k in the second stage. The operating cost is

the hourly rate of the reserved VM’s utilization cost.

Also decision variables x

and x

, respectively, are

the number of on-demand and spot VMs of type i in

the second stage. We have four provisioning costs,

formulated as follows:

• The total Reservation Cost, or the upfront cost of

reserving resources, where c

is the price of VM

type i with purchasing variant k:

∑

(1)

• The total Operational cost, i.e. the hourly cost

of the reserved VMs actually used in the second

stage, where c

is the price of VM type i with

purchasing variant k:

∑

(2)

• The total On-demand cost, where c

is the price

of VM type i:

∑

(3)

• The total Spot cost, where c

is the price of VM

type i:

∑

(4)

The objective function z is the total expected pro-

visioning cost. It is the main objective function of this

problem.

Min z =

∑

+ IE

Ω

[Φ(x

, ω)] (5)

Uncertainty-aware Optimization of Resource Provisioning, a Cloud End-user Perspective

295

Table 1: Notation of the problem.

Symbol Description

I set of VM Types

R set of VM resources or features; CPU and Memory

T set of Tasks

Cap

CPU

CPU Capacity of VM type i

Cap

Memory

Memory Capacity of VM type i

Req

Memory

Amount of memory required for completing task t

Req

CPU

Amount of CPU required for completing task t

S set of scenarios

K Set of reservation purchasing variants, all-, partial-, or no-upfront

MaxBudget User’s maximum budget

Reservation Cost of VM type i subscribed purchasing variant k

Number of reserved Vms type i subscribed purchasing variant k

Operation Cost of VM type i, subscribed purchasing variant k

Number of Operation VM type i, subscribed purchasing variant k

On-demand Cost of VM type i

Number of on-demand VM type i

Spot Cost of VM type i

Number of Spot VM type i

subject to:

∈ N (6)

Where IE

Ω

[Φ(x

, ω)] is the expected cost under un-

certainty Ω, and Φ is the recourse optimization prob-

lem. The objective of Φ(x

, ω) is to minimize the cost

under uncertainty given scenario ω:

Minimize

∑

+ x

) (7)

subject to:

≤ x

(8)

z ≤ MaxBudget (9)

TotalCPU ≥

∑

Req

CPU

(10)

TotalMemory ≥

∑

Req

Memory

(11)

The ﬁrst constraint (8), limits the number of op-

erating reserved VMs (x

) of each type to be less

than or equal to the number of reserved VMs (x

As discussed earlier, the customer reserves a number

of VMs in the ﬁrst stage and pays an upfront fee for

them, then in the second stage these reserved VMs

can be used by the customer. So the number of used

VMs (operating VMs) in the second stage cannot be

greater than the number of reserved VMs in the ﬁrst

stage. The second constraint (9) states that the to-

tal provisioning cost, or the objective function z, can-

not be greater than the maximum budget the customer

speciﬁed for running their application.

Constraints (10) and (11) both ensure that the

amount of required resources for all tasks is satisﬁed

by the VMs acquired in the second stage. The in-

stance types comprise varying combinations of CPU

and memory, and give the customer the ﬂexibility to

choose the appropriate mix of resources for their ap-

plications. Therefore, each task can be run on mul-

tiple VMs simultaneously, just as each VM can host

multiple tasks of a particular application. TotalCPU

and TotalMemory are the available CPU and Memory

in the second stage, and are deﬁned as follows:

TotalCPU =

∑

Cap

CPU

∑

+ x

)Cap

CPU

(12)

TotalMemory =

∑

Cap

Memory

∑

+ x

)Cap

Memory

(13)

where Cap

CPU

and Cap

Memory

are the CPU and mem-

ory capacity of VM type i, speciﬁed by the cloud

provider.

CLOSER 2017 - 7th International Conference on Cloud Computing and Services Science

296

3 EXPERIMENTAL EVALUATION

3.1 Data Set

Two main characteristic of cloud workloads, relevant

to our work, are the job length and the resource uti-

lization (Di et al., 2012). In order to have a rep-

resentative data set for cloud, the jobs should ﬁnish

quickly, on the order of a few minutes: 55% of tasks

in cloud ﬁnish within 10 minutes and about 90% of

tasks’ lengths are shorter than 1 hour(Di et al., 2012).

In addition the jobs usually have low resource demand

for CPU and memory, as they are mostly interactive

and real-time, in contrast to scientiﬁc batch jobs (Di

et al., 2012).

Therefore, for evaluating the proposed approach

under realistic and various working conditions, we

found workload traces of the DAS-2 multi-cluster sys-

tem (DAS2, 2009) well-suited for our experiments.

This data set were obtained from Parallel Workload

Archive (Parallel Workload Archive, 2016) and con-

sist of over two hundred thousand small jobs with

short run-time period.

These data are real users’ request logs collected

from ﬁve different universities in the Netherlands. We

use twelve-month workloads on DAS-2 clusters in the

year 2003. The main characteristics of the data used

in this work include: Number of Allocated Proces-

sors, Used Memory, User ID and Group ID ﬁelds.

12 user groups with various jobs (different CPU and

Memory usage pattern) are extracted from the data

set. As our problem is viewed from the end-user’s

perspective, we use top 12 dominant users’ groups (in

terms of number of tasks) individually for evaluating

our work, further discussion on group behaviours are

made in the following sections.

The other data required for our experimental eval-

uation is the VM prices for all three pricing plans.

The VM prices of the prevalent IaaS cloud provider,

Amazon EC2 (Amazon EC2, 2016), i.e., the standard

reserved, operating, on-demand, and spot prices were

extracted from Amazon EC2s ofﬁcial website (Ama-

zon EC2, 2016) over May 2016.

3.2 MiniZinc Model

The model was implemented in the MiniZinc mod-

eling language (Nethercote et al., 2007), using the

G12 MIP solverWe model the problem in two sep-

arate MiniZinc models. The ﬁrst model solves the

problem of determining the number of reserved VM,

before the unknown parameters become known. The

workload probability distributions for the user group

are extracted from the DAS-2 data set (DAS2, 2009).

Figure 1: Workload patterns in cloud computing (Steve

Clayton, 2009).

To represent the uncertainty of parameters, 50 work-

load scenarios are chosen pseudo-randomly with a

uniform distribution from that range. Similarly, 50

cost scenarios for on-demand and spot prices were

generated based on the extracted data of May 2016.

The outcome of this model is the optimum number of

reserved VMs, and the expected total cost based on

the 50 scenarios.

In the second stage, the real workload and real

prices of on-demand and spot VMs become known.

A single set of workload demand is again pseudo-

randomly generated from our DAS-2 data set(DAS2,

2009) and is used with the prices captured from Ama-

zon EC2 (Amazon EC2, 2016). Based on these data

and determined number of reserved VMs from the

ﬁrst model, the outcome of the stage 2 model is the

optimal number of spot and on-demand instances as

well as the actual total cost.

The model contains some approximations. In gen-

eral, not all instances of a particular type perform to

exactly the same standards, because of variations in

the physical hardware that is allocated for them and

possible multi tenancy (Mao and Humphrey, 2012).

We use the minimum guaranteed performance of EC2

instances as the baseline to ensure that sufﬁcient re-

sources are available for each job.

We repeated the ﬁrst and second stage models 20

times, for each individual group independently and

for different options, that are described in section 3.4,

to see how total price varies. They all share the same

data and conﬁguration during each run and the over-

all MiniZinc execution time for each run is less than

1 minute.

3.3 Cloud Workload Patterns

Microsoft research (Steve Clayton, 2009) identiﬁed

four workload patterns as most suitable for cloud

computing applications, as shown in Fig 1. The work-

loads are:

Uncertainty-aware Optimization of Resource Provisioning, a Cloud End-user Perspective

297

On and off: Applications that have a relatively

short period of activity and after producing a result

they can be terminated ( such as image processing ap-

plications).

Predictable/unpredictable Bursting: In pre-

dictable bursting workload, the peak demand period

is roughly known. In unpredictable bursting work-

load, however, it is unknown when the peak demand

will be.

Growing Fast: This is the scenario of start-up

companies, when suddenly their services become suc-

cessful and the infrastructure they are running their

application on cannot cope.

3.4 Pricing Plan Options

We repeat the experiment for four different options

that are various combinations of Amazon EC2 pricing

plans. The options are:

• Reservation-Ondemand-Spot (ROS) option: This

is our main option; it considers all three pricing

plans. The ROS option is ideal for cloud users

with a “predictable bursting” workload. As we

will discuss later in the result section, a better pre-

diction of workload can lead to a more cost sav-

ing due to more accurate decisions made in the

ﬁrst stage on number of reserved VMs, and then

extra demand can be optimally satisﬁed with on-

demand and spot instances, if the application is

fault tolerant enough to deal with spot.

• Reservation-Ondemand (RO) option: Only reser-

vation and on-demand pricing are considered

for this option, it corresponds to the model of

(Chaisiri et al., 2012). When the user’s applica-

tion is time critical and deadline sensitive, the spot

instances cannot help much. So even if they have

the ideal “bursting” workload, they cannot con-

sider ROS. Instead they can apply the RO option.

• Ondemand-Spot (OS) option: The OS (no reser-

vation) option only considers on-demand and spot

pricing plans.

• Ondemand (O) option: In the O (all on-demand)

option, the only pricing plan is the on-demand

plan. With an application with “on and off” de-

mand that is deadline sensitive, the user has no

choice but the expensive on-demand instances.

Each option has its place and when used in the

correct manner savings can be made.

(a) Group 2 (b) Group 3

(e) Group 9 (f) Group 11

Figure 2: CPU usage probability distribution.

4 RESULTS

Figure 3 shows the average total cost of all groups for

all the above mentioned options. The ROS achieves

the lowest total cost for all 12 groups, while the O

yields the highest total cost due to the fact that on-

demand instances are the most expensive ones. The

next highest cost belongs to the OS and the RO op-

tions, respectively.

Comparing the total cost of the ROS to other op-

tions in average, there is a 70% and 53% cost sav-

ing over the O and the OS options, respectively. Also

there is an average of 1.53% cost reduction by using

the ROS option rather that the RO. In some groups,

the total costs of ROS and RO options are the same,

such as groups 1, 3, 5, and 8, where spot instances are

not needed. Whereas for groups 2, 4, 9, and 11 there

is a 6.6%, 7%, 4%, and 2% cost saving, respectively,

by using the ROS option. Therefore the ROS option

can be more or less beneﬁcial for users with different

demand attributes.

To get an idea of the group’s demand attributes,

Figure 2 shows the probability distribution for jobs’

CPU demand for 6 different user groups. Groups 3

and 8 have almost similar distribution patterns, their

density of the number of CPU demand is mostly

concentrated around a speciﬁc range (1 to 4 CPU

core). Other illustrated groups, group 2, 4, 9, and 11

have different probability distribution patterns, how-

ever they all have one thing in common: a large vari-

ety in the number of CPU cores required.

CLOSER 2017 - 7th International Conference on Cloud Computing and Services Science

298

Figure 3: Total Cost Comparison for all on-demand (O), no reservation (OS), no spot (RO), and the complete ROS options.

Figure 4: The difference (expected cost − actual cost) in $

for the ROS and RO options.

Consequently, we ﬁnd that the probability distri-

bution of CPU and Memory usage is a factor in cost

reduction by ROS, compared to RO. A more nar-

row demand distribution results in less cost saving,

whereas a wider range of job requirements leads to a

better cost saving. This is true for all groups, even

for the ones that are not shown in Figure 2. The un-

derlying reason appears to be that the workload of a

concentrated distribution is more predictable, as the

ﬁrst stage decision is made based on a set of work-

load scenarios that are more likely to be similar to the

real time workload of the second stage. That is why

the decision in the ﬁrst stage can be made more accu-

rately by the solver, and therefore there is less need to

handle jobs in the second stage, and in particular, less

need to employ spot instances.

The accuracy of the ﬁrst-stage decision can be cal-

culated as the the difference between expected cost in

the ﬁrst stage and the actual cost in the second stage.

The closer to zero this number is, the more accurate

was the decision for the number of reserved VMs in

the ﬁrst stage. Figure 4 shows the difference of to-

tal expected and total actual cost for the ROS and OS

options. In terms of overall accuracy on average, the

accuracy of the ROS is 5% better than the RO, while

for groups 2, 4, 9, and 11 this number is more signif-

icant. Accordingly, the total cost saving for them in

Figure 5: Number of Reserved VMs in ROS and RO op-

tions, average over 20 runs.

Figure 6: Total cost and number of reserved VMs in the RO

option.

the ROS is higher.

As depicted in Figure 5, for all groups, the num-

ber of reserved VMs with the RO option is greater

than or equal to the number of reserved VMs with

ROS, 4% greater on average. When there is not a low

cost spot VM available, the solver reserves more VMs

in the ﬁrst stage, to avoid paying for expensive on-

demand VMs later in the second stage. These extra

reserved VMs may not be used in the second stage,

therefore the user may pay for unused reserved in-

stances. Hence, the number of reserved VMs deter-

mined in the ﬁrst stage has an important impact on

the total price and leads to a higher price for the RO

model, as shown in Figure 6.

Generally, the total cost of our main option, ROS,

is the lowest cost among all other options, but specif-

Uncertainty-aware Optimization of Resource Provisioning, a Cloud End-user Perspective

299

ically it leads to more cost savings when the CPU de-

mand is more widely distributed or is less predictable.

The 1.5 percent cost saving by using spot instances

can be translated to a signiﬁcant amount of money

when a huge amount of resources is rented for the

cloud provider by a particular company. So by choos-

ing a cloud provider that offers spot instances, users

can beneﬁt from the potential huge discounts.

5 CONCLUSIONS

The resource provisioning problem in the cloud envi-

ronment is viewed from the end-user perspective, in

this paper. While there are uncertainties in the param-

eters and heterogeneity in VM type and prices, the

optimal number of VMs are determined using a two

stage stochastic optimization problem.

Our results show that in general, the proposed

ROS option is cheaper than the others. We saw that

user groups with almost uniform CPU requirements

do not pay a penalty when using the RO option, but

other user groups can pay a signiﬁcant penalty. Other

options are signiﬁcantly more expensive. Overall, our

results demonstrate and quantify the effects that job

mix and workload patterns can have on the resource

provisioning cost for cloud end-users.

We plan to extend this study by evaluating our

model with a real cloud dataset (Google Cluster

Dataset) and improve our model to a multi-stage

stochastic model for getting more precise results, and

also make the model more ﬂexible by considering the

convertible reserved VMs.

REFERENCES

Adamuthe, A. C., Bhise, V. K., and Thampi, G. (2013).

Solving resource provisioning in cloud using GAs and

PSO. In Engineering (NUiCONE), 2013 Nirma Uni-

versity International Conference on, pages 1–5. IEEE.

Ali-Eldin, A., Kihl, M., Tordsson, J., and Elmroth, E.

(2012). Efﬁcient provisioning of bursty scientiﬁc

workloads on the cloud using adaptive elasticity con-

trol. In Proceedings of the 3rd workshop on Scientiﬁc

Cloud Computing Date, pages 31–40. ACM.

Amazon EC2 (2016). Amazon Elastic Compute Cloud.

http://aws.amazon.com/ec2/.

Birge, J. R. and Louveaux, F. (2011). Introduction to

stochastic programming. Springer Science & Busi-

ness Media.

Chaisiri, S., Lee, B.-S., and Niyato, D. (2009). Opti-

mal virtual machine placement across multiple cloud

providers. In Services Computing Conference, 2009.

APSCC 2009. IEEE Asia-Paciﬁc, pages 103–110.

IEEE.

Chaisiri, S., Lee, B.-S., and Niyato, D. (2012). Opti-

mization of resource provisioning cost in cloud com-

puting. Services Computing, IEEE Transactions on,

5(2):164–177.

DAS2 (2009). The Distributed ASCI Supercomputer 2.

http://www.cs.vu.nl/das2/.

Di, S., Kondo, D., and Cirne, W. (2012). Characterization

and comparison of cloud versus grid workloads. In

2012 IEEE International Conference on Cluster Com-

puting, pages 230–238. IEEE.

Genaud, S. and Gossa, J. (2011). Cost-wait trade-offs in

client-side resource provisioning with elastic clouds.

In Cloud computing (CLOUD), 2011 IEEE interna-

tional conference on, pages 1–8. IEEE.

Li, S., Zhou, Y., Jiao, L., Yan, X., Wang, X., and Lyu, M. R.-

T. (2015). Towards operational cost minimization in

hybrid clouds for dynamic resource provisioning with

delay-aware optimization. Services Computing, IEEE

Transactions on, 8(3):398–409.

Mao, M. and Humphrey, M. (2012). A performance study

on the vm startup time in the cloud. In Cloud Com-

puting (CLOUD), 2012 IEEE 5th International Con-

ference on, pages 423–430. IEEE.

Nethercote, N., Stuckey, P. J., Becket, R., Brand, S., Duck,

G. J., and Tack, G. (2007). Minizinc: Towards a stan-

dard CP modelling language. In Proc. Int. Conf. on

Principles and Practice of Constraint Programming,

pages 529–543.

Parallel Workload Archive (2016). Logs of Real

Parallel Workloads from Production Systems.

http://www.cs.huji.ac.il/labs/parallel/workload/

logs.html.

Shapiro, A. and Philpott, A. (2007). A tutorial on stochastic

programming. Manuscript. Available at www2. isye.

gatech. edu/ashapiro/publications. html, 17.

Steve Clayton (2009). MSDN blog.

https://blogs.msdn.microsoft.com/stevecla01/2009/

11/26/optimal-workloads-for-the-cloud/.

Tang, S., Yuan, J., and Li, X.-Y. (2012). Towards optimal

bidding strategy for Amazon EC2 cloud spot instance.

In Cloud Computing (CLOUD), 2012 IEEE 5th Inter-

national Conference on, pages 91–98. IEEE.

Teng, F. and Magoules, F. (2010). Resource pricing and

equilibrium allocation policy in cloud computing. In

Computer and Information Technology (CIT), 2010

IEEE 10th International Conference on, pages 195–

202. IEEE.

Zafer, M., Song, Y., and Lee, K.-W. (2012). Optimal bids

for spot vms in a cloud for deadline constrained jobs.

In Cloud Computing (CLOUD), 2012 IEEE 5th Inter-

national Conference on, pages 75–82. IEEE.

Zhu, Q. and Agrawal, G. (2010). Resource provisioning

with budget constraints for adaptive applications in

cloud environments. In Proceedings of the 19th ACM

International Symposium on High Performance Dis-

tributed Computing, pages 304–307. ACM.

CLOSER 2017 - 7th International Conference on Cloud Computing and Services Science

300