Ehacig Cloud Computig Schedulig based o Queuig Models Mohamed Eisa Computer Sciece Departmet, Port Said Uiversity, 42526 Port Said, Egypt E. I. Esedimy Computer Sciece Departmet, Masoura Uiversity, Masoura, Egypt M. Z. Rashad Computer Sciece Departmet, Masoura Uiversity, Masoura, Egypt ABSTRACT This paper preseted a proposed model for cloud computig schedulig based o multiple queuig models. This allowed us to improve the quality of service by miimize executio time per jobs, waitig time ad the cost of resources to satisfy user s requiremets. By takig advatage of some useful proprieties of queuig theory schedulig algorithm is proposed to improve schedulig process. Experimetal results idicate that our model icreases utilizatio of global scheduler ad reduce waitig time. Keywords Cloud computig; Queuig models; Schedulig process. 1. INTRODUCTION Cloud Computig (CC) ca be defied as a ew style of computig i which dyamically scalable ad ofte virtualized resources are provided as a services over the iteret [1]. Cloud computig has become a sigificat techology tred, ad may experts expect that cloud computig will reshape Iformatio Techology (IT) processes ad the IT marketplace. The goal of CC is to provide ed users with a cosiderable processig power ad computig resources that allow them to ru the applicatios ad other user s requiremets. I geeral, CC depeds o the power ad resources of computer etworks. With this architecture, cliets have access to the resources provided by the cloud provider as described i their Service Level Agreemet (SLA). Clouds usig virtualizatio techology ad data ceters to allocate distributed resources for cliets as they eed. Ofte traditioal schedulig techiques [2, 3] ad allocatio strategies [4] caot be used i cloud computig, i which the umber of ed users requests icreases ad decreases over time i a upredictable way. This leads to difficulties of aalysis ad discover of iformatio from icomig requests to distribute the available resources accordig to user requiremets ad costraits of cloud provider. Similarly, upredictable requests due to the icreased costs of server load, maximum the total executio time of the task ad the difficulty of makig a optimal decisio i the whole group of tasks. Amazo EC2 [5], itroduce cloud services that allow users to acquire ad release resources o-demad. Amazo EC2 also allows workflow systems to icrease ad decrease the pool of available resources whe the demads chagig ad upredictable eeds of users are ivolved i the allocatio process. Several approaches are used for calculatig server s queue waitig time i cloud computig. I these traditioal approaches of cloud computig, oly a sigle server,called broker, serves all the etire ed users ad so the overload o that sigle server icreases which affects the system performace. Qiag Li ad Yike Guo [6] proposed a model for resource schedulig i the art of cloud computig based o liear programmig, but oe of these papers have bee take ito accout the cocept of server utilizatio, queue legth ad the respose time of the system. K.Mukherjee ad G.Sahoo, [7] preseted a mathematical model based o a Bee ad At coloy system for market-orieted cloud computig. Buyya et al. [8] have proposed a optimizatio algorithm that miimizes the respose time of ed users request s ad their cost i the cotext of cloud computig. Shirazi et al. [9] itroduce several schedulig algorithms based o distributed systems that assig the requests to the backed servers. Bryhi et al. [10] compare load balacig techiques for scalable web servers. Therefore, various queuig models are itroduced to address this problem based o waitig queues models for each broker i the cloud system that icrease system performace, reducig the average queue legth ad waitig time tha the traditioal approach of havig oly oe server. Also, the icomig request ot wait for alog period of time ad also queue legth eed ot be large. O the other had, there are differet strategies for effective distributio of the load amog the available servers. Radom, Roud Robi ad Least-coectio are differet strategies that balace the load amog distributed servers to miimize waitig times ad optimize system performace [11]. The most importat problem is how to build a model that ca maximize server utilizatio ad miimize waitig time i queuig models. Therefore, a mathematical model is proposed to deal with multiple tasks ad resources based o the basis of maximizig the beefit of the cloud provider ad decrease the respose time of the system. The mai objective of this paper is to improve the performace of cloud system usig queuig models as a tool. Furthermore, proposed model verified experimetally i several models that achieve higher utilizatio ad respose times compared to other models. Fially, schedulig algorithm that compute the lower ad upper waitig time for all jobs at the waitig queues is itroduced. The rest of this paper is structured as follows. Sectio 2 itroduces the prelimiaries ad otatios. Sectio 3 discusses our proposed model costructio. Sectio 4 describes the experimetatio carried out by discrete evet simulator ad presets the results. Sectio 5 cocludes the paper. 2. PRELIMINARIES AND NOTATIONS 2.1 Cloud Computig Cloud computig allows users to ru applicatios remotely, as show i Figure 1, the first is the public cloud services which ca be sold to ayoe o the Iteret (e.g., Amazo Elastic Compute Cloud (EC2) [5] ad Google App Egie [12] ). The secod type of cloud is a private cloud that supplies hosted services to a limited umber of customers (ed users). I the type of hybrid cloud the ifrastructure is a compositio of two 17
or more clouds (private, commuity or public) that remai uique etities but are boud together by stadardized or proprietary techology. I geeral, clouds are deployed to cliets by givig them three access levels: Software-as-a- Service (SaaS), Platform-as-a-Service (PaaS) ad Ifrastructure-as-a-Service (IaaS) [13].. 2.1.1 Software as a Service Software-as-a-Service (SaaS) is a software distributio model i which applicatios are accessible through a sigle iterface, like a web browser over the Iteret. Users do ot have to cosider the uderlyig cloud ifrastructure icludig servers, storage, platforms, etc. 2.1.2 Platform as a Service Platform-as-a-Service (PaaS) provides a high level of itegrated applicatios that cotrol of distributed applicatios ad their hostig eviromet cofiguratios. I geeral, developers accept all istructios o the type of software that ca be writte to chage built-i scalability. 2.1.3 Ifrastructure as a Service Ifrastructure-as-a-Service (IaaS) provides users with computatio processig, storage, etworks ad computig resources. IaaS users ca implemet a arbitrary applicatio which is able to grow up ad dow dyamically.also; IaaS seds programs ad related data, while the cloud provider does the computatio processig ad returs the result. 2.2 Queuig theory Queuig theory has emerged as a mathematical tool to deal with differet types of queues [14].Waitig queue is a abstract represetatio whose goal is to isolate the factors that affect the system's ability to respod to service requests whose occurreces ad duratios are radom. I geeral, models of simple queues are specified i terms of arrival process, service mechaism ad disciplie of the queue. The arrival process specifies the structure of the probabilistic way that service requests occur over time, the service mechaism describes the umber of servers ad the probabilistic structure of the period of time required to serve a user, ad queue disciplie specifies the order i which waitig users are selected from the queue for service. The ultimate goal of waitig queues aalysis is to uderstad the behavior of the uderlyig model so that itelliget ad iformed decisios ca be made i their maagemet. Therefore; the mathematical aalysis of models produce formulas that measurers system performace, such as average waitig time, server utilizatio, throughput, the probability of exceedig buffer, the distributio of waitig time, the period of activity server, etc. Waitig system was defied as, WS = S, R where S is a set of servers S =S 1,S 2,S 3,,S, R is a fiite set of requests R = R 1, R 2, R 3,, R, we assume that the types of requests ad Sevres s queue are radom, idepedet, idetically distributed, adapted accordig to their order i the sequece of o a First-Come-First-Served (FCFS). Public Cloud Computig Private Hybrid Fig. 1: Types of Cloud Computig. The maximum processig time of the cloud server s queue provider ca be computed usig the followig parameters; D = Total demad rate, R = Processig time rate, c o = Cost of processig uit, ad = Number of waitig jobs. As cloud computig itroduces ifiite resources so we are assumig that available processig time R will be large tha the total processig time requiremets D. Therefore; the idle processig time available is ( R-D ). If we ru schedulig process for t times ad place (R-D) available processig time 18
i ideal queue, the ideal queue at the ed of processig will be (R-D) t. will be Maximum ideal queue legth = (R-D) t (1) i=0 The total processig time available from cloud provider Q at a time t, the Q = Rt (2), ad the legth of the ideal queue t must be The, Q t= times R Q Maximum ideal queue legth = (R-D) ( ) i=0 R D Maximum ideal queue legth = (1- ) Q (4) i=0 R If we kow the cost of each processig time uits is c o (cost per processig uit) D Maximum ideal queue legth = (1- ) Qc o (5) i=0 R We fid that the probabilistic model is appropriated to cloud provider whose demad for public services arrived uexpectedly. For may waitig queues the arrivals requests arrive radomly ad idepedet of other requests, ad we caot predict whe a request arrive. I this case, the Poisso probability distributio provides a good distributio of the cofiguratio of arrival. The fuctio of the Poisso probability gives the probability of requests that arrive withi a period of time determied as follows. Where x -λ λ e p(x)= x! (3) (6) x = the umber of arrivals requests per time period, λ = the mea umber of arrivals per time period, e = 2.71828. 2.2.1 Sigle- queue -server (M / M / 1 Model) M / M / 1 model is a sigle server that has ulimited queue capacity ad ifiite requests, i which queue, service ad arrivals are Poisso distributio which arrivals ad service times follow the expoetial distributio. The mathematical ature of the expoetial distributio is a series of simple ratios ca be calculated for differet performace measures based o kowledge of arrival rate ad service rate. The mathematical method used to calculate the formulas for the sigle waitig queue model with Poisso arrivals ad expoetial service times. The followig formulas ca be used to calculate M / M/ 1 characteristic model for a sigle server queue with Poisso arrivals ad expoetial service times, where λ = the mea umber of arrivals per time period (the arrival rate) μ = the mea umber of services per time period (the service rate) The, the average umber of jobs i the waitig queue ca be calculated as the followig: 2 λ Lq = μ (μ-λ) Also, we ca compute the probability that a arrivig uit has to wait for service (7) λ P w = (8) μ Ad P w is called server utilizatio factor or traffic itesity The probability that o jobs are waitig i the system λ P o = 1- μ from the above formulas (8,9), we ca geeralized formula to compute the probability of waitig jobs i the queue by: λ P = ( ) Po μ (9) (10) 2.2.2 Multiple- queue- server (M / M/ S Model) Multiple servers cosists of two or more servers that are assumed to be idetical i terms of service capability. I the multiple servers, arrivig requests wait i a sigle waitig queue ad the move to the first available server to be served. We assume that icomig requests follow a Poisso probability distributio, the service time for each server follows a expoetial probability distributio, the service rate μ is the same for each server ad the icomig requests wait i a sigle waitig queue ad the move to the first idle server for service. The followig formulas ca be used to compute the operatig characteristics for multiple servers. This model is depicted i figure 2, where λ = The arrival rate for the system, μ = The service rate for each server, k = Number of servers, U(X) = The upper boud of waitig time for each queue q, i ad L(X) = The lower boud of waitig time for each queue q i 19
Fig. 2: Multiple queue servers, with service rate μ. The probability that o jobs are i the system be calculated as the followig: 1 p o = k-1 k (λ/μ) (λ/μ) kμ + ( ) =0! k! kμ-λ (11) Also, we ca compute the average umber of jobs i the waitig queue k (λ/μ) λμ Lq = p 2 0 (k-1)!(kμ-λ) (12) Let the maximum umber of job i the waitig queue is K, ad the maximum queue legth is k-1 the we ca be computed Maximum umber of jobs allowed i the system by computed the probability of the upper waitig time for each queue q i as the followig: k-1 k (λ /μ) (λ /μ) k μ U(X) = + ( ) (13) =0 k! k μ-λ 3. MODEL CONSTRUCTION Accordig to the aalysis of the behavior of the cloud computig etwork with multiple servers ad requests for service, the cloud ca be cosidered as a pool of resources. Proposed model depicted i figure 3. It cosists of four modules: multiple waitig queues for icomig requests, global scheduler based o SA algorithm, local schedulers ad waitig queues for each local scheduler. Submit requests (R 1, R 2,, R ) from differet sites are submitted to the Global Scheduler (GS). Each request is the trasported to the local cotroller via the commuicatio etwork ad the set to the local queue. Simulatio studies to examie the effectiveess of differet models withi this framework are used. Suppose a model i which may users submit a request for executio of the work by ay of a large umber of sites. At each site, two compoets are placed: a global scheduler (GS), who determie where to sed the jobs set to this site, a Local Scheduler (LS), resposible for determiig the order i which jobs is performed i this particular site. 3.1 Schedulig Algorithm (SA) The goal of this algorithm is to reduce waitig time at cloud provider by calculatig lower ad upper waitig time for each queue as preseted i Figure 4. The iput of the algorithm is the multiple waitig queues ad the output is the lower ad upper waitig time for each queue. Also, SA algorithm begis with samplig origial waitig queues ito sets ad assig each set to a local scheduler that compute lower ad upper waitig time. These lower ad upper calculated from all base local scheduler will be combied i a ew decisio system with low icosistet. SA algorithm is able to compute lower ad upper waitig time from waitig queues usig defiitios i 2.2.1 ad 2.2.2. This algorithm have three steps, i the first step it assigs each oe of this waitig queue to oe local scheduler that work based o queuig models methodology. The secod step is the core of algorithm where we compute the lower ad upper waitig time for each queue. The last step start by mappig the waitig job to appropriate queue. The 2 computatio time of SA algorithm is O ( k ) for waitig queues Also we ca compute the probability of the lower waitig time for each queue q i as the followig: L(X) = k-1 (λ /μ) k μ + ( ) (14) =0 k k μ-λ From the above formulas (11, 12), we ca geeralize formula to compute the probability of waitig jobs i the queue by: P = (λ/μ)! Po for k (15) (λ/μ) P = P (-k) o k!k for k (16) 20
Step 1: Iteratioal Joural of Computer Applicatios (0975 8887) Icomig requests Step 2: Global schedulig based o SA Global Scheduler Step 3: Local schedulers LS 1 LS 2 LS Step 4: Multiple waitig queues Fig. 3: Proposed Model. Algorithm: Schedulig Algorithm (SA) INPUT : Multiple waitig queues OUTPUT : Mappig jobs based o queue models //Costructig samplig waitig queues 1: For k=1 to N do 2: Create set Qi by samplig Q/N // N is the umber of waitig queues //Determie equivalece queues based o queue models 3: Let X { q 1, q 2,..., q } are the equivalece waitig queues 4: Set E( X ) ; E( X ) //Computig lower ad upper waitig time for each waitig job 5: Set LX ( ) ; U( X ) ; 6: For j = 1 to begi 7: if q j X the L ( X ) L ( X ) q j ; 8: Else if q j X the U ( X ) U ( X ) q j. 9: Ed if 10: Ed for 11: Ed for 12: MJ E ( X ) E ( X ) Fig. 4: Schedulig Algorithm (SA) based o queuig models. 21
4. EXPERIMENTAL RESULTS 4.1 Simulatio Settigs The proposed model based o discrete evet simulatio will simulate with Matlab [15, 16]. Requests eter the system radomly ad form separate queues for each cloud server. The iput flow of cliets is of type Poisso, ad that the service time distributio of the cloud servers is secod order Erlag. The cloud ceter cosists of 8 server idepedet that for performace issue ca accept globally a limited umber of requests i cocurret executio, i.e., they are allocated i a fiite capacity regio with the maximum umber of requests. A load balacer distributes the requests amog servers accordig to FCFS algorithm. 4.2. The discussio of the results I this sectio, we perform simulatios to evaluate the proposed model based o differet queuig models. Table1 shows the queue legth, residece time, utilizatio ad throughput for each model based o the same costraits. We first compare the performace betwee the proposed model ad other queuig models, i which the waitig time ad utilizatio for waitig queues ad servers are computed by proposed SA algorithm, where the arrival rates ad service time for proposed model are allocated equally. Compariso of the queue legth, residece time, utilizatio ad throughput betwee the proposed model based o SA algorithm ad the differet queuig models is show i table 1. From table 1, we ca see that the proposed model achieves much lower queue legth compared to the M / M / 1 Model ad M / M / S model uder the same costraits. Also, the proposed model allocates a large umber of waitig jobs i the computig servers, thus leadig to a higher utilizatio. We ext evaluate the system throughput betwee the proposed model ad the queuig models i the cloud system. We ru simulatio based o eight servers ad the previous parameters to illustrate the performace of the cloud system. We first compare the performace betwee the proposed optimal model, i which the jobs for schedule ad computatio are allocated optimally by SA algorithm ad the differet queuig models, i which the jobs for schedule ad computatio are allocated equally. Figure 5 shows the compariso of service respose time for each model. Table 1. Compariso betwee proposed model ad queuig models. Queue legth Residece time Utilizatio Throughput [jobs] [sec] [%] [jobs/sec] M / M / 1 Model Mi 0.373 2.836 0.076 4.996 Max 0.434 3.327 0.089 5.713 Avg 0.403 3.082 0.082 5.331 M / M / S model Mi 0.181 1.326 0.159 7.496 Max 0.216 1.495 0.185 8.606 Avg 0.199 1.410 0.172 8.013 proposed model Mi 0.080 0.882 0.276 13.067 Max 0.096 1.019 0.318 15.014 Avg 0.088 0.950 0.297 13.973 Table 2. The respose time ad throughput of proposed system model #of jobs System Respose Time [sec] System Throughput [job/sec] Mi 2.952 20.510 0.134 Max 3.047 21.413 0.149 Avg 3.00 20.961 0.141 22
Total Idle Time ToTal Busy Time Total Lost Time Fig. 5: Average respose time for differet combiatios of schedulig ad host utilizatio usig queuig models. From figure 6, we ca see that the proposed model takes less respose time tha the differet queuig models uder same costraits Fig. 6: Average respose time for proposed model uder same costraits. Proposed model performace icreased by reducig the mea queue legth ad waitig time. I additio, we observe that the proposed model is coveiet for global scheduler i which we eed to maximize the use, reducig waitig time ad deal with a ifiite umber of applicatios for cloud resources. O the other had, load balacig i global scheduler caot be achieved by M/M/1 model that itroduced a sigle chael for all requests. 5. CONCLUSION I this paper, the proposed model based o queuig models. routig icomig requests to the queue with the smallest workload reduced workload, respose time ad the average legth of the queue. These results idicate that our model icrease utilizatio of global scheduler ad decrease waitig time. The experimetal results idicated that proposed model decrease waitig time at global scheduler i cloud architecture. I the future work, proposed model will use cloud computig algorithms based o parallel algorithms to decrease the time of routig ed users requests. 6. REFERENCES [1] B. Furht, A. Escalate (eds.), "Hadbook of Cloud Computig", DOI 10.1007/978-1-4419-6524-0_1, Spriger Sciece + Busiess Media, LLC 2010. [2] Marti Radles, David Lamb, A. Taleb-Bediab, A Comparative Study ito Distributed Load Balacig Algorithms for Cloud Computig, 2010 IEEE 24th Iteratioal Coferece o Advaced Iformatio Networkig ad Applicatios Workshops, pp. 551-556. [3] T. Gopalakrisha Nair, M. Vaidehi, K. Rashmi, V. Suma, A Ehaced Schedulig Strategy to Accelerate the Busiess performace of the Cloud System, Proc. ICoINDIA 2012, AISC 132, pp. 461-468, Spriger- Verlag Berli Heidelberg 2012. [4] B. Rimal, E. Choi, I. Lumb, A taxoomy ad survey of cloud computig systems, i Proc. IEEE Fifth Iteratioal Joit Coferece o INC, IMS ad IDC, 2009, pp. 44 51. [5] Amazo.com, Elastic Compute Cloud (EC2) ; [6] Qiag Li, Yike Guo. Optimizatio of Resource Schedulig i Cloud Computig, 12th Iteratioal Symposium o Symbolic ad Numeric Algorithms for Scietific Computig, 978-0-7695-4324-6/10 IEEE, DOI 10.1109/SYNASC.2010.8. [7] K. Mukherjee, G. Sahoo, Developmet of Mathematical Model for Market-Orieted Cloud Computig, Iteratioal Joural of Computer Applicatios (0975 8887), Vol. 9, No. 11, November 2010. [8] R. Buyya, K. Sukumar Platforms for Buildig ad Deployig Applicatios for Cloud Computig, CSI Commuicatio, pp. 6-11, 2011 [9] Shirazi, B. A., K. Krisha, H. Ali. 1995. "Schedulig ad Load Balacig i Parallel ad Distributed Systems". Wiley-IEEE Computer Society Press. Voas, J., ad J. Zhag. 2009. Cloud Computig: New Wie or Just a New Bottle, IT Professioal 11: 15-17. [10] Bryhi, H., E. Klovig, O. Kure. 2000. "A Compariso of Load Balacig Techiques for Scalable Web Servers", IEEE NETWORK 14: 58-64. [11] T. Helmy, A. Dekdouk Burst Roud Robi: As a Proportioal-Share Schedulig Algorithm", IEEE Proceedigs of the fourth IEEE-GCC Coferece o towards Techo-Idustrial Iovatios, pp. 424-428, 11-14 November, 2007. [12] Google App Egie. http://code.google.com/appegie/ (accessed o October 25, 2011). [13] B. Furht, A. Escalate, Hadbook of cloud computig, Cloud computig fudametals" writte by B. Furht, Spriger, 2010. [14] L. Breuer, D. Baum "A Itroductio to Queueig Theory", Spriger Verlag, 2005. [15] Itegratig MATLAB, Simulik ad State flow Compoets i a SimEvets odel: www.mathworks.com/wbr15638 [16] Averill M. Law, W. David Kelto, McGraw-Hill 2000 "Simulatio Modelig ad Aalysis" (3rd Editio). IJCA TM : www.ijcaolie.org 23