DynamicSecurityExchangeSchedulingModelforBusiness ...downloads.hindawi.com/journals/scn/2020/8886640.pdfstandard enterprise operations [2]. Business process occurs at all organizational

Research ArticleDynamic Security Exchange Scheduling Model for BusinessWorkflow Based on Queuing Theory in Cloud Computing

Rongbin Xu12 Jianguo Wu2 Yongliang Cheng2 Zhiqiang Liu1 Yuanmo Lin1 andYing Xie 1

1College of Information Engineering Putian University Putian China2School of Computer Science and Technology Anhui University Hefei China

Correspondence should be addressed to Ying Xie xieyingahueducn

Received 3 March 2020 Revised 11 June 2020 Accepted 31 July 2020 Published 28 August 2020

Academic Editor Benjamin Aziz

Copyright copy 2020 Rongbin Xu et al )is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

With the rapid development of e-business large volume of business processes need to be handled in a constrained time )ere isalways a security issue related to on-time completion in many applications in the economic fields So how to effectively manage andorganize business processes became very important By using cloud computing instance-intensive processes can be handled moreeffectively by applying just-right virtual machines Hence the management of cloud resources became an important issue that manyresearchers focus on to fully utilize the advantage of cloud In this paper we mainly discuss the queuing theory and put forward ournovel dynamic process schedulingmodel based on queuing theory which is namedMGkl-P for business processes)ismodel cansolve the issue of allocating appropriate number of cloud resources based on the number of tasks and execution stages to ensurewhether the numbers of cloud resources are sufficient and adequate or not which can improve the security issue for business process)e service discipline in our model can provide a dynamic process by setting different priorities to improve the experience of usersEvaluations prove that the queuing model of MGkl-P can work very well for business workflow scheduling

1 Introduction

Business processes are the series of interactions betweenbusinesses and their users vendors and other relatedpartners [1] A business workflow is an instance of well-defined business process that is often repeated as a part ofstandard enterprise operations [2] Business process occursat all organizational levels and may not be visible to thecustomers A business process may often be visualized ormodeled as a flowchart of a sequence of activities with in-terleaving decision points which can also be viewed as aprocess matrix of a sequence of activities with relevance rulesbased on data in the process [3] )e benefits of usingbusiness processes mainly concentrate on improving thesatisfaction of customer and improving agility for reacting torapid market change [4 5] With intensified globalizatione-business is in the process of rapid growth which ofteninvolves processing large numbers of instance-intensivebusiness processes within a constrained period of time [6]

A typical motivating instance-intensive business ex-ample is security exchange in the stock market that involvesa large number of transactions between different organi-zations and each of them is a relatively short workflowinstance with only a few steps [7] A stock depository andclearing corporation in the stock market need to check andproduce money transfer details in the night-time for eachclient who makes deals during the daytime before corre-sponding money transfers can be processed between theclearing corporation and the designated banks )e re-quiring allocation of cloud and edge resources is a typicaldynamic process depending on the number of transactions[8] )e clearing process and transferring money in stockmarket may need to be finished before a deadline for ex-ample 3 00 am each weekday [9]

By utilizing the novel infrastructure of cloud and edgecomputing instance-intensive processes can be solved easily toapply enough virtual machines for the elastic property of cloudenvironment [10 11] All the users can access those services for

HindawiSecurity and Communication NetworksVolume 2020 Article ID 8886640 12 pageshttpsdoiorg10115520208886640

running their software applications in pay-as-you-go fashion toavoid huge capital investment energy consumption and systemmaintenance [12] However at the same time of meeting thetemporal requirement for examole deadline of businessworkflow [13] cost is another factor we should focus on )eproper allocation of cloud resources can improve the efficiencyof virtual machines so that there is no waste [14 15] In thispaper we apply queuing model for the allocation of cloudresources based on the process of dynamic management whichcan be regarded as a very efficient method for cloud allocationAs demonstrated in our evaluation the queuingmodel ofMGkl-P is an effective solution for business workflow scheduling

)ere are mainly three contributions in our paperFirst it is the first time that we employ queuing theory

for business workflow scheduling )ere are a large numberof tasks that need to be scheduled in business workflowswhich are convenient to operate virtual machines as serversby queuing theory in cloud environment

Second our modelMGkl-P applies cloud resources ina dynamic process which can dynamically manage thenumber of virtual machines based on service time distri-bution so there is no much waste

)ird the service discipline in our modelMGkl-P cansignificantly improve the Quality of Service (QoS) inbusiness processes We apply two service disciplines besidesthe default one in our model so that the tasks in businessprocesses with high priority can be served first based on thedifferent demands of users

)e remainder of this paper is organized as followsSection 2 introduces the related work Section 3 proposes amotivating example of time-constrained instance-intensivebusiness processes in stock market and gives the detailedproblem analysis Section 4 presents some preliminarycontents of queuing theory Section 5 discusses some clas-sical queuing models and puts forward our novel queuingmodel of MGkl-P for business processes Section 6 pro-vides a set of results for evaluation of our queuing modelFinally section 7 concludes our contributions and points outthe future work

2 Related Work

Matching abundant business tasks to machines andscheduling the execution order of these tasks are referred tomapping)is problem of mapping has been proved to be anNP-complete issue in [15ndash17] A shortest tree algorithm isdescribed in [15] that minimizes the sum of execution andcommunication costs for arbitrarily connected distributedsystems with arbitrary numbers of processors )is algo-rithm uses a dynamic programming approach to solve theproblem for n tasks and m processors in O(m2n) time Ascheduling risk assessment framework [16] is developed tomodel the uncertainties in duration and observe their impacton project objectives such as completion time and cost Itprovides some important propositions or guidelines forproject management practitioners An Analytics-as-a-Ser-vice (AaaS) platform [17] is proposed to deliver on-demandservices at low cost in an easy use manner In this paper wepropose a model that effectively admits data analytics

requests dynamically provisions resources and maximizesprofit for AaaS providers while satisfying QoS requirementsof queries with Service Level Agreement guarantees It canenhance profits reduce resource costs increase query ad-mission rates and decrease query response times All thesealgorithms mainly focus on minimizing execution andcommunication costs However these algorithms have notfully considered the specific scenarios with large amounts ofbusiness workflow tasks In our paper queuing theory isemployed for scheduling large number of business workflowtasks so it is convenient to operate cloud servers for no wasteof resources

In cloud environments scheduling decisions can bemade in the shortest time which are possible for utilizing adistributed suite of different high-performance machinesCloud computing can offer powerful on-demand andelastic computing resources which is an ideal hosting en-vironment for running a large batch of parallel businessprocesses [18] Many algorithms have been proposed toschedule the business workflow applications in heteroge-neous distributed system environments Reference [19] isdevoted to improving the performance for cloud serviceplatforms by minimizing uncertainty propagation inscheduling workflow applications that have both uncertaintask execution time and data transfer time Moreover anovel scheduling architecture is designed to control thecount of workflow tasks directly waiting on each serviceinstance Yu et al [20] propose several challenges forscheduling workflow applications in grid environment andsome are hard to resolve for example the grid resources arenot under the control of the scheduler )ey also classifyworkflow scheduling into two major types best-effort-basedand QoS-constraint-based scheduling However these al-gorithms do not fully utilize the dynamic characteristic ofcloud resources In our paper the allocation of cloud re-sources can be a dynamic process based on the initializednumber of tasks and execution stage First the executionprocesses are prioritized by different demands of users)en our MGkl-P can dynamically manage the usage ofvirtual machines based on service time distribution

)ere are some existing researches which focus on dy-namic resource allocation )ey mostly draw attention onenergy consumption by using multiple virtual machines andmake great contributions to computer science Reference[21] proposes a cloud resource allocation model based on animperfect information Stackelberg game (CSAM-IISG) us-ing a hidden Markov model in cloud computing environ-ment )is strategy increases the profit of both the resourcesuppliers and applicants Reference [22] presents a queuingmodel that buffers the same type of VM jobs in one virtualqueue )e queuing model then divides the VM schedulinginto two parallel low-complexity algorithms that is intra-queue buffering and interqueue scheduling )is model canachieve low delay performance in terms of average jobcompletion time and high throughput performance in termsof job hosting ratio Reference [23] provides a QoS-metric-based resource provisioning technique that can cater toprovisioned resource distribution and scheduling of re-sources )is technique is efficient in reducing execution

2 Security and Communication Networks

time and cost of cloud workloads along with other QoSparameters Reference [24] uses virtualization technology toallocate data center resources dynamically based on appli-cation demands and supports green computing by opti-mizing the number of servers Waiting time is considered asan important parameter for the evaluation of queuingtheory )is strategy combines different types of workloadsnicely and improves the overall utilization of server re-sources All these strategies have set up a more specificsituation and solve the problem of resource allocationHowever these scheduling strategies almost have not con-sidered service discipline to prove high QoS )e queuingmodel in our MGkl-P can reduce the number of thevirtual machines and significantly improve the QoS in twoaspects dynamically manage the usage of virtual machinesand set different service disciplines for the demands of users

3 Motivating Business Workflow Example andExisting Problem

Security exchange is a typical time-constrained commercialevent and any failures of the on-time completion for moneytransfer in stock market may cause huge financial lossesbecause unsuccessful timely money transfer could result inthe failure of making deals which is definitely a disastroussituation in the stock market Security exchange is also atypical multistep process and most steps are executed inparallel For the clearing process there are six major stageswhich contain some steps as shown in Figure 1

For an example of security organization in China thereare tens of thousands of users and their information includeaccount password transaction balance of account and soon All these involve threat protection encryption dataprotection and archiving

More than one hundred security corporations that mayhave a great number of branches in security exchangemarket which is a typical instance-intensive business pro-cess Customers may choose a certain branch to deal with thesecurity transactions so the system of security exchange isextremely complex Figure 1 is just a very simple model thatwe use to interpret our business workflow schedulingprocesses Step 1 in Figure 1 may involve various validationprocesses and they all log on security stock trading center toconduct transactions Millions of client entrustments can berequested by clients all over the country All of them areprocessed concurrently in more than 4000 branches [25]Steps 2 and 3 check the raw entrustment data that clientsmake deals and generate the balance of trades [26] Howeverafter settling all the trading processes during trading daybefore 3 00 pm (closing time) the real fund settlementsshould be cleared within three levels as shown in steps 4ndash6which are the most important steps for security trading )efirst level clearing is between clearing corporations andsecurity corporations the second one is between securitycorporations and their branches and then the third one isbetween branches and users)ese three steps involve a largenumber of capital flow and money transfer in stock marketthat need to be finished before 3 00 am of each weekdaywhich are typical time-constrained tasks Any failures of on-

time completion for money transfer in stock market maycause huge financial losses because unsuccessful timelymoney transfer could result in the failure of making dealswhich is definitely a disastrous situation in the securityexchange market )e final step that is step 6 is to produceclearing files Security corporations and designated banksshould produce the clearing files for clearing corporation)e balance of all transferred capital should be set to zero atthe clearing corporation level [27]

As shown in Figure 1 the six steps have a sequentialrelationship)ere is a large number of works to schedule allthe security exchange transactions in limited constrainedtime )e amount of transactions may be much biggerduring some special days than common time like the firstday and the weekend of a week and there are more taskswhich should be scheduled in the night Meanwhile themultistep transactions are always short-duration activities)e execution time of short-duration activities is normallymuch smaller than traditional scientific long-duration ac-tivities and every activity can be handled and responded in ashort time Based on all these characteristics in stock marketit is well suited to apply cloud environment to schedulesecurity exchange transactions because cloud computing canoffer on-demand elastic and cost-effective resource asshown in Figure 2

However due to the dynamic characteristics of cloudcomputing how to allocate cloud resources dynamically inthe initiation and execution stages so that the cloud re-sources can be efficiently utilized without much waste is anextremely complex issue because the allocation of cloudresources should be dynamically adjusted based on thearrival tasks First what we need to do is allocating ap-propriate number of cloud resources based on the initializednumber of tasks )en execution process of businessworkflow should be monitored in real time to ensure that thenumber of cloud resources is sufficient and adequate It isreally a dynamic usage process of cloud resources In thispaper we apply queuing modelMGkl-P for the allocationof cloud resources )e novel queuing model can be provedas a very efficient method based on our evaluations Fur-thermore we apply different service disciplines in ourqueuing model so that it can offer a dynamic schedulingprocess by setting different priorities to the tasks based onthe requirements of users

4 Preliminary of Queuing Theory

Queuing theory is a mathematical research of waiting linesor queues which focuses on identifying and managing theresponse time of users for services Queuing theory wascreated to describe the Copenhagen telephone exchangeoriginally and the ideas had seen applications includingtelecommunication [28] traffic engineering [29] computingand the design of factories [30] shops offices and hospitals[31])e theory allows cloud system to be scaled optimally toguarantee the QoS for response time It can also plan properdeployment and removal of virtual machines according tothe system load [32] So it is very applicable to be used forour instance-intensive workflow scheduling which also aims

Security and Communication Networks 3

to get an excellent scheduling result in the response time ofvarious kinds of tasks dynamically )e queuing model isconstructed in advance so that the queue length and waitingtime can be predicted by queuing theory (httpsenwikipediaorgwikiQueueing_theory-cite_note-sun-1)It isgenerally considered as a branch of process managementresearch because the results are often used when makingbusiness decisions about the required resources to provide agood service

Queuing systems can be characterized by variousprobabilistic properties such as complex input processservice time distribution number of servers buffer size andqueue discipline)ese properties can be described as shownin Figure 3 which is the fundamental form for differentkinds of queuing theories

)e aim of investigations in queuing system is to get themain measures of the system which are the probabilisticproperties of following random variables number of tasks inthe system number of waiting tasks in each server responsetime of tasks waiting time of a task and utilization of allservers To fully utilize these properties of queuing system ininstance-intensive business processes wemainly apply inputprocess as the incoming flow and service time as the exe-cution time of scheduling tasks We also employ a number ofservers as the virtual machines in cloud environment Buffersize represents the quantitative restriction of virtual ma-chines which can be unlimited based on the dynamicalproperty of cloud Queue discipline is the basic schedulingrule by which a task will be selected)emost common rules

are First In First Out (FIFO) and Random Serve by usingqueuing theory and we aim at adjusting the number ofvirtual machines dynamically to control the length ofwaiting queue and response time It is an effective way tosave the cost of using cloud resources

As shown in Figure 3 there can be many kinds of formsby using different properties in different queuing theoriesCommonly used characters for ldquocomplex input processrdquo andldquoservice time distributionrdquo in the shorthand notation are D(Deterministic) M (Markovian-Poisson for the arrivalprocess or exponential for the service time distributionrequired by each task) G (General) GI (General and In-dependent) and Geom (Geometric) [33] ldquoNumber ofserversrdquo can be a fixed number or a variable ldquoBuffer sizerdquoand ldquoqueue disciplinerdquo are designated as yellow color inFigure 3 which means that they can be omitted if they areunnecessary ldquoBuffer sizerdquo is not used if the waiting room isunlimited ldquoQueue disciplinerdquo is not used for the case of theFirst Come First Serve queue discipline

5 Queuing Models for Business Workflow

51 Classical Models of Queuing (eory )ere are somecommon forms of queuing systems GG1 is the mostgeneral FIFO Single-Server Queue (SSQ) considered inqueuing theory where both the arrival and service processesare based on general distribution G denotes a generaldistribution for both interarrival time and service time Onedenotes that the model has a single server )e evolution of

P1

P2

Pmhellip hellip

hellip hellip

hellip helliphellip hellip

hellip hellip

hellip hellip

Step 11 Step 12 Step 16


Step i1 Step i2 Step i6

Step j1 Step j2 Step j6

Step n1 Step n2 Step n6

hellip

hellip

hellip

hellip

hellip

Task 1

Task 2

Task i

Task j

Task n

Scheduler

Figure 2 Scheduling model for a batch of parallel business tasks

Entrustment 1

Entrustment 2

Entrustment n

Settle the trade 1 Transfer capital 1


Settle the trade m Transfer capital m

Fit and make deal

Generate feeand balance

Produceclearing fileshellip

helliphellip

helliphellip

hellip

helliphellip

hellip

Figure 1 Simplified flowchart of multistep process of security exchange


this queue can be described by the Lindley equation [34]which is a discrete-time stochastic process An where n is aninteger value Here we set An to be the interarrival timebetween the nth and (n + 1)th tasks Bn represents theservice time of the nth task )e process of execution can beused to describe the waiting time experienced by tasks in aqueue or evolution of a queue length over time Let W

represent mean waiting time and we apply Wn to be thewaiting time of the nth task So the execution time of Un canbe described as

Un Bn minus An (1)

Based on formula (1) we can figure out the waiting timeof tasks in a recursion form

Wn+1 max0

Wn + Un1113896 st nge 1 (2)

where W1 0 represents that the first task does not need towait Subsequent tasks have to wait if they arrive at a timebefore the previous task has been served Different inter-arrival and service time are considered to be independent sothat sometimes the model is denoted as GIGI1 to em-phasize the independent characteristic

By considering the straightforward case of deterministicqueues we will discuss another form of queuing modelwhere the interarrival and service time are nondeterministicMM1 represents the queue length in a system which has asingle server where interarrival is determined by a Poissonarrival process and task service time is based on an expo-nential distribution with infinite buffer )is model is themost elementary queuing system which is an attractiveobjective of study as closed-form expressions that can beobtained for many metrics of interest in this model Anextension of this model with more than one server is theMMk queue

)e MM1 model is a stochastic process whose statespace is the set 0 1 2 3 where the value corresponds tothe number of tasks in the system Arrivals of tasks occur atrate λ according to the Poisson process andmove the processfrom state i to state i + 1 Service times of tasks have anexponential distribution with parameter 1μ in the MM1queue where μmeans service rateMM1 is a special case ofGG1 so all the results which are applicable to GG1 arealso applicable to MM1 Here one important measure forperformance of queuing system is the utilization which isdenoted as ρMM1 It is the proportion of time that a server isbusy on average )e other probability of n tasks is denotedas pn Here

ρMM1 λμ

(3)

By this utilization we can get a balance equation whichdescribes the probability flux associated with aMarkov chainin and out of states or set of states in MM1 model )ebalance equations of all tasks are shown as the followingsituations

Situation 1

μ1P1 λ0P0 (4)

Situation 2

λ0P0 + μ2P2 λ1 + μ1( 1113857P1 (5)

Situation n

λnminus 1Pnminus 1 + μn+1Pn+1 λn + μn( 1113857Pn (6)

So we can obtain the probability of P0 in MM1 modelby those balance equations

PMM10

11 + 1113936

infinn1 1113937

nminus 1i0 λiμi+1( 1113857

(7)

MM1 is the simplest Markovian queue A single ma-chine is used to serve the first task at a time from the front ofthe queue according to FIFO discipline When the service isfinished the task leaves the queue and the number of tasks inthe system is decreased by one Assuming that the MM1queue-size process starts at state 0 it will stay in state 0 for aperiod of time that is exponentially distributed with pa-rameter λ and then it moves to state 1)e buffer is of infinitesize so there is no limit on the number of tasks )e modelcan be described as a continuous Markov chain withtransition rate matrix on the state space

QMM1

minus λ λ

μ minus (μ + λ) λ


⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠ (8)

Generally state space transition diagrams are used torepresent a system as a collection of states and activitiesassociated with various relationships among the statesQueuing systems are modeled by continuous Markov chainsthat are often described by their state transition diagramwhich provides the complete information of their detailedbalance equations )e state space transition diagram of MM1 is shown in Figure 4

)e diagram shows how the systemmoves from one stateto another and the rate of movements between different

Complex input process Service time distribution Number of servers Buffer size Queue discipline

Figure 3 Fundamental form of queuing theory


states )e state space transition diagram has many appli-cations related to the design and analysis of real-time andobject-oriented systems

52 MGkl-P Model As the business workflow exampledescribed in Section 3 there are tens of thousands of securitytransactions that need to be scheduled and handled in a fixedperiod of time So it is convenient to apply virtual machinesas servers in cloud environment In many cloud systemsserver is paid for its usage time regardless whether it is busy ornot Normally the time that transmission capacity is not usedand this is time during whichmoney is spent but no revenue isearned )erefore it is important to design systems that willmaintain high utilization for cloud resources Hence we needto consider the waiting lengths of different models for variousvirtual machines so we use l to represent the length of waitingqueue Finally we add a service discipline in our model so itcan be presented as MGkl-P

First we will continuously discuss the first three basiccomponents of MGkl-P Based on the above MM1model in subsection 51 we can get the queuing model ofMMk when the applied number of servers is more than 1)e model can also be described as a continuous Markovchain with complex transition rate matrix on the state space

QMMk

minus λ λ


2μ minus (2μ + λ) λ

⋮

kμ minus (kμ + λ) λ


⋮

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(9)

)e state space transition diagram ofMMk is shown inFigure 5

)ere is a key difference betweenMM1 andMMk sincethe system has m servers which refers to the number of linksbetween source and destination nodes Let P represent theprobabilities of n tasks in the system S represent the numberof times of entering state n and L represent the number oftimes of leaving state n where S and L have the followingrelation |S minus L| isin 0 1 when the system arrives at a steadystate Using the same calculation process withMM1 we canget the probability of p0 inMMkmodel Here the utilizationof k servers forMMk is denoted as ρMMk where ρMMk lt 1

PMMk0 1113944

kminus 1

i0

1i

λμ

1113888 1113889

i

+1k

11 minus ρMMk

λμ

1113888 1113889

k

⎡⎣ ⎤⎦

minus 1

(10)

)en the mean waiting time of MMk model can bepredicted so we can obtain the mean waiting time for alltasks of WMMk in formula (11) ρMMk λkμ M meansMarkov that tasks arrive according to Poisson process

WMMk

kρMMk( 1113857

kρMMk

k 1 minus ρMMk( 11138572λ

PMMk0 (11)

As the dynamic nature of business process most of thetasks may be served in a period of time which is an arbitraryprobability distribution )e distribution and mean numberof busy servers are also insensitive to the shape of servicetime distribution So we applyMGkmodel to schedule thebusiness processes instead of MMk

MGk queue is a queuing model where task arrivalshave an exponential distribution with infinite buffer Grepresents service time process which is arbitrary k rep-resents the number of virtual machines that we apply incloud environment )e model is an extension of theMMkqueue where service time must be generally distributedbased on MG1 queue with a single server Using the samecalculation process with MMk we can get the probabilityof p0 in MGk model Here the utilization of k servers forMGk is denoted as ρMGk where ρMGk lt k

PMGk0 1 + 1113944

kminus 1

i0

(k minus 1) k minus ρMGk( 1113857

i ρMGk( 1113857(kminus 1)

⎡⎣ ⎤⎦

minus 1

(12)

Here we make it clear that the insensitivity propertydoes not extend to the arrival process )e distribution ofbusy servers and blocking probability is insensitive to theshape of the service time distribution So we concentrate onservice time of different models )ere are some elementsthat we need to use for illustrating the waiting time ofMGksuch as expectation and variance )ey are denoted as E andV in the following formula

WMGk

V + E

2

2E k minus ρMGk( 1113857P

MGk0 (13)

)e expectation of waiting time for MGk model is alsobased on MMk )e main difference between them is theservice time distribution So we compare both of the ex-pectation for MMk and MGk in the following formula

λ λ

micro micro

0 1

λ λ

micro micro

n n + 1

λ λ

micro micro

i

λ

micro

Figure 4 State space transition diagram of MM1


E WMGk

1113960 1113961 C2

+ 12

E WMMk

1113960 1113961 (14)

Here C2 is a variable coefficient of service time distri-bution and C is less than 1 So we can figure out that thevalue of (C2 + 1)2 is less than 1 It means that the expec-tation of MGk will be less than MMk based on formula(14)

)en we add l to represent the length of waiting queue inour model by considering the waiting length of differentmodels

l λV + λE

2


MGk0 (15)

Finally the most important factor we consider in thispaper is the service discipline )is can significantly influ-ence the Quality of Service (QoS) in instance-intensivebusiness processes )ere are various scheduling policiesthat can be used at queuing nodes However both the FIFOand Random Serve may result in quite long waiting timewhich can seriously influence the service time for most oftasks In order to prove that all the business tasks can bescheduled in a constrained time period we add the priorityproperty which is represented by P in our queuing modelSo our model is described as MGkl-P which means thattasks in instance-intensive business processes with highpriority are served first

Here priority queues can be set into two typesnonpreemptive and preemptive Nonpreemptive means atask in service cannot be interrupted and preemptivemeans a task in service can be interrupted by a higherpriority task So the waiting queue in our MGkl-P isdynamical based on different priorities of tasks and thiscan be called as dynamic process scheduling )e dy-namic mechanism can satisfy some high QoS of userswhen they need to execute their tasks in a short time Italso can be used in the scenario that all tasks should becompleted in a constrained time As we discuss in Section3 that security exchange is a typical instance-intensivebusiness process there are a large number of securityexchange transactions need to be scheduled in a con-strained time Security company should prove that all thetasks are scheduled in the constrained time If there is anyerror in the execution process which may cause executioncongestion in a certain virtual machine )en the priorityof tasks in waiting queue should be changed based on ourdynamic process So it can adjust the execution processin real-time )is also can avoid the execution failure bythe congestion which may cause huge financial losses

Based on the dynamic mechanism ofMGkl-P if thereis just one task in the system the service rate of the system isμ1 and only one virtual machine works in the schedulingprocess It means the other virtual machines are all in idlestate If there are two tasks in the system then the service rateof the system is 1113936

2j1 μj )e service rate reaches the highest

value when the task number reaches k which means all theservers are put into operation So the state space transitiondiagram of Figure 6 is different with Figures 4 and 5

We set four indicators like urgency degree occupationdegree waiting time and defrayment of tasks as x1 x2 x3and x4 So the priority of task can be set as

yi max4i1 xi( 1113857 minus xi

max4i1 xi( 1113857 minus min4i1 xi( 1113857 (16)

)en the proportion of the four indicators will be addedbased on formula (16) Finally all the tasks are set intopreemptive and nonpreemptive by our queuing theoryBased on the above discussion a concrete process for MGkl-P model is described in Algorithm 1 as the servicediscipline is applied in MGkl-P that the tasks will bescheduled with different priorities )e normal time com-plexity is O(nm) in Algorithm 1 by nonpreemptive waywhich is a very good result for scheduling When some taskshave high priorities and need to preempt the resources ofother tasks the time complexity will be up to O(nm2) in theworst case

6 Evaluation

61 Experimental Setting In this section we will present oursimulation based on different parameters such as arrivaltime waiting time and response time for different tasks totest the effectiveness of our queuing model )e arrival timeof tasks such as in security exchange will be different andfollow a certain arrival rate )e clearing process in securityexchange is a typically time-constrained and real-timesystem All the tasks in security exchange must be completedbased on a certain temporal expectation However there arethousands of security corporations which may have a greatnumber of branches in security exchange market Aftersettling all the transaction processes during the trading daythe real fund settlement should be generated and clearedwithin a certain constrained time which is most importantfor security exchange )e trading numbers of differentsecurity corporations may not be the same in differenttrading time of a certain day So the arrival rate of tasks willnot be monotonous but in different range It is appropriateto use our MGkl-P queuing model because the task ar-rivals have an exponential distribution in our model which

λ λ

micro 2micro

0 1

λ λ

kmicro kmicro

k k + 1

λ

kmicro

k + m

λ λ

imicro (i + 1)micro

i

λ

kmicro

Figure 5 State space transition diagram of MMk


can represent the real service time process in security ex-change As depicted in Figure 7 massive business processesare mapped into workflow instances in a short period oftime )e same type of cloud server is set in the waitingqueue system for obtaining service

Waiting time is also a most important parameter becausesecurity exchange is a real-time system Each task needs to behandled as soon as it comes into the system to ensure the real-time requirement of the trading systemWaiting time is greatlyinfluenced by the arrival time of tasks However waiting timecan be totally different by various queuing systems So wemainly demonstrate our simulations to test the parameter ofwaiting time in this part )e other parameter we focus on isresponse time which depends on the tasksrsquo arrival time waitingtime and service time in the queuing system )e values ofwaiting time are expected to be small enough to satisfy therequirements of security exchange system )en these pa-rameters will be carried out in different experiments and thecontrast methods are First Come First Serve (FCFS) queuesystems [35] and dynamic programming (DP) algorithm [36]

Our experiments are conducted based on various sim-ulations to satisfy different requirements and conditions ofsecurity exchange systems We compare various simulationresults by different arrival rates temporal expectationwaiting time and response time )e simulation environ-ment is based on Win 10 OS (32GB memory32Hz CPU)

and MATLAB 2015 )e execution time in our simulationcan be considered as standard time unit

62 Experimental Results Based on our queuing model MGkl-P the total waiting time is influenced by differentarrival rate λ service rate μ and temporal expectation of allthe tasks If the temporal expectation is too small then thenumber of servers needs to be more So we set a largetemporal expectation first to avoid using large volume ofservers as shown in Table 1 Here the temporal expectationis set to 30 time units

As shown in Table 1 the total waiting time is very highwhen both the arrival rate and service rate are very low)ere is very short waiting time when the service rate is largeenough Generally service rate should not be smaller thanarrival rate so that waiting queue will not exceed the buffersize which can avoid the overflow of waiting queue

)en some representative and comprehensive temporalexpectations and service rates are applied to get convictiveresults in the following figures )e temporal expectation isset to 15 which is a relatively small number in Figure 8 to geta high demand result In addition the arrival rate is also setto a small number which can avoid a rather long waitingqueue in the system

As shown in Figure 8 five servers at least are requiredto deal with all the tasks because the total waiting time for

λ λ

micro1 micro1 + micro2

0 1

λ λ

summicrok summicrok

k k + 1

λ

summicrok

k + m

λ λ

summicroi summicro(i+1)

i

λ

summicrok

Figure 6 State space transition diagram of MGkl-P

Businessprocess

Business workflow instance

Workflow activity

Mapping

Parallelworkflowinstances

Queuingsysten

CloudserverWaiting queue

MGK1ndashP model

Figure 7 Queuing model for business workflows


all tasks will be very high if less than four servers areapplied be it in FCFS DP MDk MMk or our MGkl-P However the total waiting time decreases sharplywhen more servers are applied Meanwhile we can seethat our MGkl-P performs much better than the othermethods regardless of how many servers are applied forscheduling

Moreover the total waiting time is also lower Howeverif the arrival rate λ of tasks increases to 08 as shown inFigure 10 we can see that the total waiting time is higherthan that in Figure 9 Specifically when the number ofservers is one or two the waiting time in Figure 10 is muchhigher than that in Figure 9 because most of the tasks willswarm into the waiting queue at the beginning and theprocessing capacity cannot keep up with the demand ofusers when the arrival rate reaches to 08 So most of thetasks need to wait for a long time when the applied serversare too few )is situation will cause a poor experience ofQoS for users In order to solve this problem we can applysuitable number of servers according to the high arrival rateof 08 as shown in Figure 10 )e waiting time is as much asthat in Figure 9 by ourMGkl-P when applying more thantwo servers Also the waiting time obtained byMGkl-P ismuch lower than the other methods

Input )e arrival states of business workflow examplesOutput )e finished business workflow examples

(1) for i⟶ 1 in k do(2) l λV + λE22E(i minus ρ)P0(3) yi max4i1(xi) minus ximax4i1 minus min4i1(xi)(4) ifyi gt 1 do(5) select the example of this priority to process(6) update l and yi(7) else(8) for u⟶ 1 in queue do(9) if u in l then(10) u is selected to process(11) update l and yi(12) break(13) P [1 + 1113936

kminus 1i0 (k minus 1)(k minus ρ)iρkminus 1]minus 1

(14) W V + E22E(k minus ρ)P(15) update P and W(16) end

ALGORITHM 1 MGkl-P model

Table 1 Total waiting time by MGkl-P model with different arrival and service rates for all tasks

λ 01 02 03 04 05 06 07 08 0901 833 mdash mdash mdash mdash mdash mdash mdash mdash02 333 417 mdash mdash mdash mdash mdash mdash mdash03 214 234 278 mdash mdash mdash mdash mdash mdash04 159 167 182 208 mdash mdash mdash mdash mdash05 126 130 138 149 169 mdash mdash mdash mdash06 105 107 111 118 126 139 mdash mdash mdash07 90 91 94 98 103 109 119 mdash mdash08 78 79 79 83 87 91 97 104 mdash09 71 71 71 73 75 78 82 86 93

FCFSDPMMk

MDkMGkl-P

0

50

100

150

200

250

Wai

ting

time

5 6 7 8 9 10 114Number of servers

Figure 8 Total waiting time within the temporal expectation of 15time units and arrival rate of 04 for all tasks


Based on our model MGkl-P we can see that thewaiting time is relatively small when applying a suitablenumber of servers which influences the performance of thequeuing model Meanwhile it can monitor the waiting timeunder different number of servers to dynamically adjust thenumber for queuing model So MGkl-P can dynamicallymanage the number of virtual machines and waiting queuebased on service time distribution to avoid much waste ofcloud resources

As we described in our queuing model MGkl-Pservice discipline is also an important factor that willsignificantly influence the experience of users )e defaultservice discipline is FCFS and we set certain priorities toimprove the QoS of users As shown in Figure 11 the

discipline of short-task preemptive performs better inwaiting time than any other two disciplines when thearrival rate is lower than 09 Although the waiting time oflong-task preemptive discipline is higher than the othermodels as shown in Figure 11 it can offer high priority forlong task to avoid serving in queuing model at lastHence our queuing model MGkl-P can meet thedifferent demands of queuing question by consideringcorresponding service disciplines

Figure 12 illustrates the changing process of total re-sponse time when the arrival rate increases In this exper-iment increasingly low values for the number of servers hasa great impact on reducing the response time when theapplied number of servers is less than four Also the re-sponse time can stabilize quickly when the number of serversincreases So four servers are applied to see the variationtrend when arrival rate increases by our queuing model MGkl-P as shown in Figure 12 It demonstrates that theresponse time is highly influenced by arrival rate Howeverthe waiting time is smoothly influenced Moreover thewaiting time has been reduced in large extent which meansour queuing model MGkl-P actually improves the effi-ciency greatly

Based on the above discussions our model MGmk-P can perform better thanMDk andMMkmodels Wecan know that the impact of arrival rate is smaller thantime expectation in our model All the experiments fromFigures 8ndash11 indicate thatMDk MMk andMGkl-Pget close performance while the applied numbers ofservers are large enough because the differences betweenthese models will be small and the redundant hardwareresources will compensate for the lack of traditionalmodels when applying more servers However these maycause huge waste to apply too much cloud servers So weproved that our model MGkl-P can get the best resultscompared with others as shown from Figures 8ndash11 when weapply appropriate number of cloud servers )is feature

0

50

100

150

200

250

300

Wai

ting

time

FCFSDPMMk

MDkMGkl-P

2 3 4 51Number of servers


FCFSShort-task preemptiveLong-task preemptive

76

80

84

88

92

96

Wai

ting

time

06 07 08 0905Arrival rate

Figure 11 Total waiting time with different service disciplines

0

20

40

60

80

100

120

140

160

180W

aitin

g tim

e

FCFSDPMMk

MDkMGkl-P




ensures that our queuing model MGkl-P can be wellapplied on the scenario of security exchange and showsgreat advantage compared with traditional models Ourqueuing model MGkl-P can provide correct and quickclearing process for large numbers of security transactionsand save much execution cost for security exchangecompanies

7 Conclusion and Future Work

)e paper introduces a typical motivating instance-intensivebusiness example in the stock market It involves a largenumber of transactions which can be scheduled by queuingtheory )en we put forward our novel model of queuingsystem based on queuing theory which is MGkl-P forbusiness processes Our model can handle the issue of al-locating appropriate number of cloud resources dynamicallyto ensure that the number of cloud resources is sufficient andadequate We also set different priorities for tasks based onthe demands of users so it can improve the experience ofusers Various simulations in our paper prove thatMGkl-P performs very well for instance-intensive business process

To the best of our knowledge this is the first paper thatschedules the instance-intensive business processes byqueuing theory )e results presented in this paper promise anew research direction in the area of business workflowsHowever there are at least two research topics that we need toaddress in the near future First the service rate should belarger than arrival rate so that the waiting queue would notexceed the size of buffer in ourmodelMGkl-P Also we canset a dynamical buffer in the future to relax this constraintSecond the service discipline can be more flexible in thefuture so that the queuing model can perform even better

Data Availability

)e authors declare that materials described in the manu-script including all relevant raw data will not be available toany scientist

Conflicts of Interest

)e authors declare that they have no financial and personalrelationships with other people or organizations that caninappropriately influence their work )ere is no professional

or other personal interest in any product and service thatcould influence the position presented in this manuscript

Acknowledgments

)e research was partly supported by the National NaturalScience Foundation of China (61602005) MOE YouthProject of Humanities and Social Sciences of China(20YJCZH197) Natural Science Foundation of AnhuiProvince (1808085MF199) Natural Sciences ResearchProject in Universities of Anhui Province (KJ2018A0016)Putian Technology Planning Project (2019GP0011) andStarting funds of Putian University (2019020 2019021) )eauthors are grateful to Professor Y Yang Australia Swin-burne University of Technology for editing the Englishlanguage of the manuscript

References

[1] X Wang L T Yang X Xie J Jin and M J Deen ldquoA cloud-edge computing framework for cyber-physical-social ser-vicesrdquo IEEE Communications Magazine vol 55 no 11pp 80ndash85 2017

[2] X Xu R Mo F Dai W Lin et al ldquoDynamic resourceprovisioning with fault tolerance for data-intensive meteo-rological workflows in cloudrdquo IEEE Transactions on IndustrialInformatics vol 16 no 9 pp 6172ndash6181 2020

[3] L Qi Y Chen Y Yuan S Fu et al ldquoA QoS-aware virtualmachine schedulingmethod for energy conservation in cloud-based cyber-physical systemsrdquo World Wide Web vol 23no 2 pp 1275ndash1297 2019

[4] H Wu W J Knottenbelt and K Wolter ldquoAn efficient ap-plication partitioning algorithm in mobile environmentsrdquoIEEE Transactions on Parallel and Distributed Systems vol 30no 7 pp 1464ndash1480 2019

[5] X Xu Q Liu Y Luo K Peng et al ldquoA computation off-loading method over big data for IoT-enabled cloud-edgecomputingrdquo Future Generation Computer Systems vol 95pp 522ndash533 2019

[6] R Xu Y Wang H Luo F Wang et al ldquoA sufficient andnecessary temporal violation handling point selection strategyin cloud workflowrdquo Future Generation Computer Systemsvol 86 pp 464ndash479 2018

[7] X Liu D Wang D Yuan F Wang and Y Yang ldquoWorkflowtemporal verification for monitoring parallel business pro-cessesrdquo Journal of Software Evolution and Process vol 28no 4 pp 286ndash302 2016

[8] X Xu Y Xue L Qi Y Yuan X Zhang et al ldquoAn edgecomputing-enabled computation offloading method withprivacy preservation for internet of connected vehiclesrdquoFuture Generation Computer Systems vol 96 pp 89ndash1002019

[9] R Xu Y Wang W Huang D Yuan et al ldquoNear-optimaldynamic priority scheduling strategy for instance-intensivebusiness workflows in cloud computingrdquo Concurrency andComputation Practice and Experience vol 29 no 18p e4167 2017

[10] F Amato and F Moscato ldquoExploiting cloud and workflowpatterns for the analysis of composite cloud servicesrdquo FutureGeneration Computer Systems vol 67 pp 255ndash265 2017

[11] S M Nithya and V R Uthariaraj ldquoIdentity-based publicauditing scheme for cloud storage with strong key-exposure

005 01 015 02 025 03 035 04 045 05Arrival rate λ

0102030405060708090

Resp

onse

tim

e

Figure 12 Total response time by MGkl-P model


resiliencerdquo Security and Communication Networks vol 2020Article ID 4838497 13 pages 2020

[12] A Watanabe K Ishibashi T Toyono K Watanabe et alldquoWorkflow extraction for service operation using multipleunstructured trouble ticketsrdquo IEICE Transactions on Infor-mation and Systems vol E101D no 4 pp 1030ndash1041 2018

[13] X Matsuo and H Wu ldquoSpatio-temporal representation withdeep neural recurrent network in MIMO CSI feedbackrdquo IEEEWireless Communications Letters vol 9 no 5 pp 653ndash6572020

[14] B Cha P Sun J Kim et al ldquoInternational network perfor-mance and security testing based on distributed abyss storagecluster and draft of data lake frameworkrdquo Security andCommunication Networks vol 2018 Article ID 174680914 pages 2018

[15] S H Bokhari ldquoA shortest tree algorithm for optimal as-signments across space and time in a distributed processorsystemrdquo IEEE Transactions on Software Engineering vol SE-7no 6 pp 583ndash589 1981

[16] R K Chakrabortty A Abbasi and M J Ryan ldquoA risk as-sessment framework for scheduling projects with resourceand duration uncertaintiesrdquo IEEE Transactions on Engi-neering Management vol 4 no 10 pp 1ndash15 2019

[17] Y Zhao R N Calheiros G Gange et al ldquoSLA-based profitoptimization resource scheduling for big data analytics-as-a-service platforms in cloud computing environmentsrdquo IEEETransactions on Cloud Computing vol 6 no 1 pp 1ndash12 2018

[18] V Nallur and R Bahsoon ldquoA decentralized self-adaptationmechanism for service-based applications in the cloudrdquo IEEETransactions on Software Engineering vol 39 no 5pp 591ndash612 2013

[19] H Chen X Zhu G Liu and P Witold ldquoUncertainty-Awareonline scheduling for real-time workflows in cloud serviceenvironmentrdquo IEEE Transactions on Services Computingvol 8 no 7 pp 98ndash110 2019

[20] Yu Jia R Buyya and K Ramamohanarao ldquoWorkflowscheduling algorithms for grid computingrdquo in Metaheuristicsfor Scheduling in Distributed Computing Environmentspp 173ndash214 Springer Berlin Germany 2008

[21] W Wei X Fan H Song X Fan and J Yang ldquoImperfectinformation dynamic stackelberg game based resource allo-cation using hidden Markov for cloud computingrdquo IEEETransactions on Services Computing vol 11 no 1 pp 78ndash892018

[22] M Guo Q Guan W Chen et al ldquoDelay-Optimal schedulingof VMs in a queueing cloud computing system with het-erogeneous workloadsrdquo IEEE Transactions on ServicesComputing vol 10 no 9 pp 90ndash102 2019

[23] S Singh and I Chana ldquoQ-aware Quality of service basedcloud resource provisioningrdquo Computers amp Electrical Engi-neering vol 47 pp 138ndash160 2015

[24] Z Xiao W Song and Q Chen ldquoDynamic resource allocationusing virtual machines for cloud computing environmentrdquoIEEE Transactions on Parallel and Distributed Systems vol 24no 6 pp 1107ndash1117 2013

[25] H Luo J Liu X Liu and Y Yang ldquoPredicting temporalviolations for parallel business cloud workflowsrdquo SoftwarePractice and Experience vol 48 no 4 pp 775ndash795 2018

[26] C Wang Z Chen K Shang and H Wu ldquoLabel-removedgenerative adversarial networks incorporating withK-Meansrdquo Neurocomputing vol 361 pp 126ndash136 2019

[27] TMatsubara R Akita and K Uehara ldquoStock price predictionby deep neural generative model of news articlesrdquo IEICE

Transactions on Information and Systems vol E101D no 4pp 901ndash908 2018

[28] J Liu M Sheng Y Xu J Li and X Jiang ldquoEnd-to-end delaymodeling in buffer-limited MANETs a general theoreticalframeworkrdquo IEEE Transactions on Wireless Communicationsvol 15 no 1 pp 498ndash511 2016

[29] Y Xiang V Aggarwal Y-F R Chen and T Lan ldquoDiffer-entiated latency in data center networks with erasure codedfiles through traffic engineeringrdquo IEEE Transactions on CloudComputing vol 7 no 2 pp 495ndash508 2019

[30] D A Chekired L Khoukhi and H T Mouftah ldquoIndustrialIoT data scheduling based on hierarchical fog computing akey for enabling smart factoryrdquo IEEE Transactions on In-dustrial Informatics vol 14 no 10 pp 4590ndash4602 2018

[31] S Guo and M Huang ldquoSimulation design of shop materialsupply based on queuing theoryrdquo in Proceedings of the IEEEInternational Conference on Software Quality Reliability andSecurity Companion (QRS-C) pp 258ndash263 Lisbon PortugalJuly 2018

[32] H Pourvaziri and H Pierreval ldquoDynamic facility layoutproblem based on open queuing network theoryrdquo EuropeanJournal of Operational Research vol 259 no 2 pp 538ndash5532017

[33] C Kim A Dudin O Dudina and S Dudin ldquoTandemqueueing system with infinite and finite intermediate buffersand generalized phase-type service time distributionrdquo Euro-pean Journal of Operational Research vol 235 no 1pp 170ndash179 2014

[34] F Ferreira A Pacheco and H Ribeiro ldquoMoments of lossesduring busy-periods of regular and nonpreemptive oscillating$$MXG1n$$ M XG1n systemsrdquo Annals of OperationsResearch vol 252 no 1 pp 191ndash211 2017

[35] M Wang W Chen and A Ephremides ldquoReal-time recon-struction of A counting process through first-come-first-servequeue systemsrdquo IEEE Transactions on Information (eoryvol 66 no 7 pp 4547ndash4562 2020

[36] Q He R Zhou X Zhang et al ldquoEfficient keyword search forbuilding service-based systems based on dynamic program-mingrdquo in Proceedings of the 15th International Conference onService-Oriented Computing pp 462ndash470 Malaga SpainNovember 2017


running their software applications in pay-as-you-go fashion toavoid huge capital investment energy consumption and systemmaintenance [12] However at the same time of meeting thetemporal requirement for examole deadline of businessworkflow [13] cost is another factor we should focus on )eproper allocation of cloud resources can improve the efficiencyof virtual machines so that there is no waste [14 15] In thispaper we apply queuing model for the allocation of cloudresources based on the process of dynamic management whichcan be regarded as a very efficient method for cloud allocationAs demonstrated in our evaluation the queuingmodel ofMGkl-P is an effective solution for business workflow scheduling

)ere are mainly three contributions in our paperFirst it is the first time that we employ queuing theory

for business workflow scheduling )ere are a large numberof tasks that need to be scheduled in business workflowswhich are convenient to operate virtual machines as serversby queuing theory in cloud environment

Second our modelMGkl-P applies cloud resources ina dynamic process which can dynamically manage thenumber of virtual machines based on service time distri-bution so there is no much waste

)ird the service discipline in our modelMGkl-P cansignificantly improve the Quality of Service (QoS) inbusiness processes We apply two service disciplines besidesthe default one in our model so that the tasks in businessprocesses with high priority can be served first based on thedifferent demands of users

)e remainder of this paper is organized as followsSection 2 introduces the related work Section 3 proposes amotivating example of time-constrained instance-intensivebusiness processes in stock market and gives the detailedproblem analysis Section 4 presents some preliminarycontents of queuing theory Section 5 discusses some clas-sical queuing models and puts forward our novel queuingmodel of MGkl-P for business processes Section 6 pro-vides a set of results for evaluation of our queuing modelFinally section 7 concludes our contributions and points outthe future work

2 Related Work

Matching abundant business tasks to machines andscheduling the execution order of these tasks are referred tomapping)is problem of mapping has been proved to be anNP-complete issue in [15ndash17] A shortest tree algorithm isdescribed in [15] that minimizes the sum of execution andcommunication costs for arbitrarily connected distributedsystems with arbitrary numbers of processors )is algo-rithm uses a dynamic programming approach to solve theproblem for n tasks and m processors in O(m2n) time Ascheduling risk assessment framework [16] is developed tomodel the uncertainties in duration and observe their impacton project objectives such as completion time and cost Itprovides some important propositions or guidelines forproject management practitioners An Analytics-as-a-Ser-vice (AaaS) platform [17] is proposed to deliver on-demandservices at low cost in an easy use manner In this paper wepropose a model that effectively admits data analytics

requests dynamically provisions resources and maximizesprofit for AaaS providers while satisfying QoS requirementsof queries with Service Level Agreement guarantees It canenhance profits reduce resource costs increase query ad-mission rates and decrease query response times All thesealgorithms mainly focus on minimizing execution andcommunication costs However these algorithms have notfully considered the specific scenarios with large amounts ofbusiness workflow tasks In our paper queuing theory isemployed for scheduling large number of business workflowtasks so it is convenient to operate cloud servers for no wasteof resources

In cloud environments scheduling decisions can bemade in the shortest time which are possible for utilizing adistributed suite of different high-performance machinesCloud computing can offer powerful on-demand andelastic computing resources which is an ideal hosting en-vironment for running a large batch of parallel businessprocesses [18] Many algorithms have been proposed toschedule the business workflow applications in heteroge-neous distributed system environments Reference [19] isdevoted to improving the performance for cloud serviceplatforms by minimizing uncertainty propagation inscheduling workflow applications that have both uncertaintask execution time and data transfer time Moreover anovel scheduling architecture is designed to control thecount of workflow tasks directly waiting on each serviceinstance Yu et al [20] propose several challenges forscheduling workflow applications in grid environment andsome are hard to resolve for example the grid resources arenot under the control of the scheduler )ey also classifyworkflow scheduling into two major types best-effort-basedand QoS-constraint-based scheduling However these al-gorithms do not fully utilize the dynamic characteristic ofcloud resources In our paper the allocation of cloud re-sources can be a dynamic process based on the initializednumber of tasks and execution stage First the executionprocesses are prioritized by different demands of users)en our MGkl-P can dynamically manage the usage ofvirtual machines based on service time distribution

)ere are some existing researches which focus on dy-namic resource allocation )ey mostly draw attention onenergy consumption by using multiple virtual machines andmake great contributions to computer science Reference[21] proposes a cloud resource allocation model based on animperfect information Stackelberg game (CSAM-IISG) us-ing a hidden Markov model in cloud computing environ-ment )is strategy increases the profit of both the resourcesuppliers and applicants Reference [22] presents a queuingmodel that buffers the same type of VM jobs in one virtualqueue )e queuing model then divides the VM schedulinginto two parallel low-complexity algorithms that is intra-queue buffering and interqueue scheduling )is model canachieve low delay performance in terms of average jobcompletion time and high throughput performance in termsof job hosting ratio Reference [23] provides a QoS-metric-based resource provisioning technique that can cater toprovisioned resource distribution and scheduling of re-sources )is technique is efficient in reducing execution




















P1

P2

Pmhellip hellip

hellip hellip


hellip hellip

hellip hellip






hellip

hellip

hellip

hellip

hellip

Task 1

Task 2

Task i

Task j

Task n

Scheduler


Entrustment 1

Entrustment 2

Entrustment n




Fit and make deal



helliphellip

helliphellip

hellip

helliphellip

hellip





Un Bn minus An (1)


Wn+1 max0

Wn + Un1113896 st nge 1 (2)




ρMM1 λμ

(3)


Situation 1

μ1P1 λ0P0 (4)

Situation 2

λ0P0 + μ2P2 λ1 + μ1( 1113857P1 (5)

Situation n



PMM10

11 + 1113936

infinn1 1113937


(7)


QMM1

minus λ λ



⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠ (8)









QMMk

minus λ λ



⋮



⋮

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(9)



PMMk0 1113944

kminus 1

i0

1i

λμ

1113888 1113889

i

+1k

11 minus ρMMk

λμ

1113888 1113889

k

⎡⎣ ⎤⎦

minus 1

(10)


WMMk

kρMMk( 1113857

kρMMk


PMMk0 (11)



PMGk0 1 + 1113944

kminus 1

i0



⎡⎣ ⎤⎦

minus 1

(12)


WMGk

V + E

2


MGk0 (13)


λ λ

micro micro

0 1

λ λ

micro micro

n n + 1

λ λ

micro micro

i

λ

micro



E WMGk

1113960 1113961 C2

+ 12

E WMMk

1113960 1113961 (14)



l λV + λE

2


MGk0 (15)










6 Evaluation


λ λ

micro 2micro

0 1

λ λ

kmicro kmicro

k k + 1

λ

kmicro

k + m

λ λ

imicro (i + 1)micro

i

λ

kmicro











λ λ


0 1

λ λ

summicrok summicrok

k k + 1

λ

summicrok

k + m

λ λ


i

λ

summicrok


Businessprocess


Workflow activity

Mapping


Queuingsysten


MGK1ndashP model












FCFSDPMMk

MDkMGkl-P

0

50

100

150

200

250

Wai

ting

time









0

50

100

150

200

250

300

Wai

ting

time

FCFSDPMMk

MDkMGkl-P




76

80

84

88

92

96

Wai

ting

time



0

20

40

60

80

100

120

140

160

180W

aitin

g tim

e

FCFSDPMMk

MDkMGkl-P








Data Availability





Acknowledgments


References












005 01 015 02 025 03 035 04 045 05Arrival rate λ

0102030405060708090

Resp

onse

tim

e

















































P1

P2

Pmhellip hellip

hellip hellip


hellip hellip

hellip hellip






hellip

hellip

hellip

hellip

hellip

Task 1

Task 2

Task i

Task j

Task n

Scheduler


Entrustment 1

Entrustment 2

Entrustment n




Fit and make deal



helliphellip

helliphellip

hellip

helliphellip

hellip





Un Bn minus An (1)


Wn+1 max0

Wn + Un1113896 st nge 1 (2)




ρMM1 λμ

(3)


Situation 1

μ1P1 λ0P0 (4)

Situation 2

λ0P0 + μ2P2 λ1 + μ1( 1113857P1 (5)

Situation n



PMM10

11 + 1113936

infinn1 1113937


(7)


QMM1

minus λ λ



⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠ (8)









QMMk

minus λ λ



⋮



⋮

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(9)



PMMk0 1113944

kminus 1

i0

1i

λμ

1113888 1113889

i

+1k

11 minus ρMMk

λμ

1113888 1113889

k

⎡⎣ ⎤⎦

minus 1

(10)


WMMk

kρMMk( 1113857

kρMMk


PMMk0 (11)



PMGk0 1 + 1113944

kminus 1

i0



⎡⎣ ⎤⎦

minus 1

(12)


WMGk

V + E

2


MGk0 (13)


λ λ

micro micro

0 1

λ λ

micro micro

n n + 1

λ λ

micro micro

i

λ

micro



E WMGk

1113960 1113961 C2

+ 12

E WMMk

1113960 1113961 (14)



l λV + λE

2


MGk0 (15)










6 Evaluation


λ λ

micro 2micro

0 1

λ λ

kmicro kmicro

k k + 1

λ

kmicro

k + m

λ λ

imicro (i + 1)micro

i

λ

kmicro











λ λ


0 1

λ λ

summicrok summicrok

k k + 1

λ

summicrok

k + m

λ λ


i

λ

summicrok


Businessprocess


Workflow activity

Mapping


Queuingsysten


MGK1ndashP model












FCFSDPMMk

MDkMGkl-P

0

50

100

150

200

250

Wai

ting

time









0

50

100

150

200

250

300

Wai

ting

time

FCFSDPMMk

MDkMGkl-P




76

80

84

88

92

96

Wai

ting

time



0

20

40

60

80

100

120

140

160

180W

aitin

g tim

e

FCFSDPMMk

MDkMGkl-P








Data Availability





Acknowledgments


References












005 01 015 02 025 03 035 04 045 05Arrival rate λ

0102030405060708090

Resp

onse

tim

e






































P1

P2

Pmhellip hellip

hellip hellip


hellip hellip

hellip hellip






hellip

hellip

hellip

hellip

hellip

Task 1

Task 2

Task i

Task j

Task n

Scheduler


Entrustment 1

Entrustment 2

Entrustment n




Fit and make deal



helliphellip

helliphellip

hellip

helliphellip

hellip





Un Bn minus An (1)


Wn+1 max0

Wn + Un1113896 st nge 1 (2)




ρMM1 λμ

(3)


Situation 1

μ1P1 λ0P0 (4)

Situation 2

λ0P0 + μ2P2 λ1 + μ1( 1113857P1 (5)

Situation n



PMM10

11 + 1113936

infinn1 1113937


(7)


QMM1

minus λ λ



⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠ (8)









QMMk

minus λ λ



⋮



⋮

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(9)



PMMk0 1113944

kminus 1

i0

1i

λμ

1113888 1113889

i

+1k

11 minus ρMMk

λμ

1113888 1113889

k

⎡⎣ ⎤⎦

minus 1

(10)


WMMk

kρMMk( 1113857

kρMMk


PMMk0 (11)



PMGk0 1 + 1113944

kminus 1

i0



⎡⎣ ⎤⎦

minus 1

(12)


WMGk

V + E

2


MGk0 (13)


λ λ

micro micro

0 1

λ λ

micro micro

n n + 1

λ λ

micro micro

i

λ

micro



E WMGk

1113960 1113961 C2

+ 12

E WMMk

1113960 1113961 (14)



l λV + λE

2


MGk0 (15)










6 Evaluation


λ λ

micro 2micro

0 1

λ λ

kmicro kmicro

k k + 1

λ

kmicro

k + m

λ λ

imicro (i + 1)micro

i

λ

kmicro











λ λ


0 1

λ λ

summicrok summicrok

k k + 1

λ

summicrok

k + m

λ λ


i

λ

summicrok


Businessprocess


Workflow activity

Mapping


Queuingsysten


MGK1ndashP model












FCFSDPMMk

MDkMGkl-P

0

50

100

150

200

250

Wai

ting

time









0

50

100

150

200

250

300

Wai

ting

time

FCFSDPMMk

MDkMGkl-P




76

80

84

88

92

96

Wai

ting

time



0

20

40

60

80

100

120

140

160

180W

aitin

g tim

e

FCFSDPMMk

MDkMGkl-P








Data Availability





Acknowledgments


References












005 01 015 02 025 03 035 04 045 05Arrival rate λ

0102030405060708090

Resp

onse

tim

e

































Un Bn minus An (1)


Wn+1 max0

Wn + Un1113896 st nge 1 (2)




ρMM1 λμ

(3)


Situation 1

μ1P1 λ0P0 (4)

Situation 2

λ0P0 + μ2P2 λ1 + μ1( 1113857P1 (5)

Situation n



PMM10

11 + 1113936

infinn1 1113937


(7)


QMM1

minus λ λ



⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠ (8)









QMMk

minus λ λ



⋮



⋮

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(9)



PMMk0 1113944

kminus 1

i0

1i

λμ

1113888 1113889

i

+1k

11 minus ρMMk

λμ

1113888 1113889

k

⎡⎣ ⎤⎦

minus 1

(10)


WMMk

kρMMk( 1113857

kρMMk


PMMk0 (11)



PMGk0 1 + 1113944

kminus 1

i0



⎡⎣ ⎤⎦

minus 1

(12)


WMGk

V + E

2


MGk0 (13)


λ λ

micro micro

0 1

λ λ

micro micro

n n + 1

λ λ

micro micro

i

λ

micro



E WMGk

1113960 1113961 C2

+ 12

E WMMk

1113960 1113961 (14)



l λV + λE

2


MGk0 (15)










6 Evaluation


λ λ

micro 2micro

0 1

λ λ

kmicro kmicro

k k + 1

λ

kmicro

k + m

λ λ

imicro (i + 1)micro

i

λ

kmicro











λ λ


0 1

λ λ

summicrok summicrok

k k + 1

λ

summicrok

k + m

λ λ


i

λ

summicrok


Businessprocess


Workflow activity

Mapping


Queuingsysten


MGK1ndashP model












FCFSDPMMk

MDkMGkl-P

0

50

100

150

200

250

Wai

ting

time









0

50

100

150

200

250

300

Wai

ting

time

FCFSDPMMk

MDkMGkl-P




76

80

84

88

92

96

Wai

ting

time



0

20

40

60

80

100

120

140

160

180W

aitin

g tim

e

FCFSDPMMk

MDkMGkl-P








Data Availability





Acknowledgments


References












005 01 015 02 025 03 035 04 045 05Arrival rate λ

0102030405060708090

Resp

onse

tim

e


































QMMk

minus λ λ



⋮



⋮

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(9)



PMMk0 1113944

kminus 1

i0

1i

λμ

1113888 1113889

i

+1k

11 minus ρMMk

λμ

1113888 1113889

k

⎡⎣ ⎤⎦

minus 1

(10)


WMMk

kρMMk( 1113857

kρMMk


PMMk0 (11)



PMGk0 1 + 1113944

kminus 1

i0



⎡⎣ ⎤⎦

minus 1

(12)


WMGk

V + E

2


MGk0 (13)


λ λ

micro micro

0 1

λ λ

micro micro

n n + 1

λ λ

micro micro

i

λ

micro



E WMGk

1113960 1113961 C2

+ 12

E WMMk

1113960 1113961 (14)



l λV + λE

2


MGk0 (15)










6 Evaluation


λ λ

micro 2micro

0 1

λ λ

kmicro kmicro

k k + 1

λ

kmicro

k + m

λ λ

imicro (i + 1)micro

i

λ

kmicro











λ λ


0 1

λ λ

summicrok summicrok

k k + 1

λ

summicrok

k + m

λ λ


i

λ

summicrok


Businessprocess


Workflow activity

Mapping


Queuingsysten


MGK1ndashP model












FCFSDPMMk

MDkMGkl-P

0

50

100

150

200

250

Wai

ting

time









0

50

100

150

200

250

300

Wai

ting

time

FCFSDPMMk

MDkMGkl-P




76

80

84

88

92

96

Wai

ting

time



0

20

40

60

80

100

120

140

160

180W

aitin

g tim

e

FCFSDPMMk

MDkMGkl-P








Data Availability





Acknowledgments


References












005 01 015 02 025 03 035 04 045 05Arrival rate λ

0102030405060708090

Resp

onse

tim

e































E WMGk

1113960 1113961 C2

+ 12

E WMMk

1113960 1113961 (14)



l λV + λE

2


MGk0 (15)










6 Evaluation


λ λ

micro 2micro

0 1

λ λ

kmicro kmicro

k k + 1

λ

kmicro

k + m

λ λ

imicro (i + 1)micro

i

λ

kmicro











λ λ


0 1

λ λ

summicrok summicrok

k k + 1

λ

summicrok

k + m

λ λ


i

λ

summicrok


Businessprocess


Workflow activity

Mapping


Queuingsysten


MGK1ndashP model












FCFSDPMMk

MDkMGkl-P

0

50

100

150

200

250

Wai

ting

time









0

50

100

150

200

250

300

Wai

ting

time

FCFSDPMMk

MDkMGkl-P




76

80

84

88

92

96

Wai

ting

time



0

20

40

60

80

100

120

140

160

180W

aitin

g tim

e

FCFSDPMMk

MDkMGkl-P








Data Availability





Acknowledgments


References












005 01 015 02 025 03 035 04 045 05Arrival rate λ

0102030405060708090

Resp

onse

tim

e







































λ λ


0 1

λ λ

summicrok summicrok

k k + 1

λ

summicrok

k + m

λ λ


i

λ

summicrok


Businessprocess


Workflow activity

Mapping


Queuingsysten


MGK1ndashP model












FCFSDPMMk

MDkMGkl-P

0

50

100

150

200

250

Wai

ting

time









0

50

100

150

200

250

300

Wai

ting

time

FCFSDPMMk

MDkMGkl-P




76

80

84

88

92

96

Wai

ting

time



0

20

40

60

80

100

120

140

160

180W

aitin

g tim

e

FCFSDPMMk

MDkMGkl-P








Data Availability





Acknowledgments


References












005 01 015 02 025 03 035 04 045 05Arrival rate λ

0102030405060708090

Resp

onse

tim

e








































FCFSDPMMk

MDkMGkl-P

0

50

100

150

200

250

Wai

ting

time









0

50

100

150

200

250

300

Wai

ting

time

FCFSDPMMk

MDkMGkl-P




76

80

84

88

92

96

Wai

ting

time



0

20

40

60

80

100

120

140

160

180W

aitin

g tim

e

FCFSDPMMk

MDkMGkl-P








Data Availability





Acknowledgments


References












005 01 015 02 025 03 035 04 045 05Arrival rate λ

0102030405060708090

Resp

onse

tim

e




































0

50

100

150

200

250

300

Wai

ting

time

FCFSDPMMk

MDkMGkl-P




76

80

84

88

92

96

Wai

ting

time



0

20

40

60

80

100

120

140

160

180W

aitin

g tim

e

FCFSDPMMk

MDkMGkl-P








Data Availability





Acknowledgments


References












005 01 015 02 025 03 035 04 045 05Arrival rate λ

0102030405060708090

Resp

onse

tim

e



































Data Availability





Acknowledgments


References












005 01 015 02 025 03 035 04 045 05Arrival rate λ

0102030405060708090

Resp

onse

tim

e



























































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DynamicSecurityExchangeSchedulingModelforBusiness ...downloads.hindawi.com/journals/scn/2020/8886640.pdfstandard enterprise operations [2]. Business process occurs at all organizational