Guaranted QOS with Profit Maximization Scheme in CloudComputing

Guaranted QOS with Profit Maximization Scheme in CloudComputing

Sindhu P Nandish Kumar D

Dept. of CSE Assoc. Prof., & Head, Dept. of CSE GMIT, Bharathinagar GMIT, Bharathinagar

AbstractAs an effective and efficient way to provide computing resources and services to customers on demand, cloud computing has become more and more popular. From cloud service providers perspective, profit is one of the most important considerations, and it is mainly determined by the configuration of a cloud service platform under given market demand. However, a single long-term renting scheme is usually adopted to configure a cloud platform, which cannot guarantee the service quality but leads to serious resource waste. In this paper, a double resource renting scheme is designed firstly in which short-term renting and long-term renting are combined aiming at the existing issues. This double renting scheme can effectively guarantee the quality of service of all requests and reduce the resource waste greatly. Secondly, a service system is considered as an M/M/m+D queuing model and the

performance indicators that affect the profit of our double

A

1 IN TRO D U C T IO N

S an effective and efficient way to consolidat e co mput – ing resources and co mput ing services, clouding com-

put ing has become more and more popu la r [1]. Cloud com- puting cent ra lizes man age ment of resources and services, and delive rs hosted services over the Internet . The hard- ware, softwa re, d atabases, in fo rmat ion, and all resources a re concentrated and prov id ed to consu me rs on -de ma nd [2]. Cloud comput ing turns in fo rmat ion te chno logy into ordi- nary commod it ies and utilities by the the pay-per-use pric- ing model [3, 4, 5]. In a cloud co mput ing env iron ment , th ere are always three tiers, i.e., in frastructure provide rs, services prov ide rs, and custo me rs (see Fig. 1 and its elabo rat ion in Section 3.1). An infrastructu re prov id er ma inta ins the basic hard ware and softwa re facilities. A service prov id er rents resources from the infrastru cture p rov id ers and provid es services to custome rs. A custo mer sub mits its request to a service prov ide r and pays for it based on the a mo unt a nd the qua lity of the p rov id ed service [6]. In this paper, we aim at research ing the mu lt iserve r con figuration of a service prov id e r such that its profit is ma ximize d.

Like all business, the profit of a service provid e r in cloud co mput ing is related to two parts, which are the cost and the revenu e. For a service prov ide r, the cost is the rent ing

renting scheme are analy zed, e.g., the average charge, the ratio of requests that need temporary servers, and so forth. Thirdly, a profit ma ximizat ion proble m is formulated for the double renting scheme and the optimized configuration of a cloud platform is obtained by solving the profit ma ximization proble m. Fina lly , a series of calculat ions are conducted to compare the profit of our proposed scheme with that of the single renting scheme. The results show that our scheme can not only guarantee the service quality of all requests, but also obtain more profit than the latter.

Index Te rmsCloud computing, guaranteed service quality, mu ltiserver system, profit ma ximization, queuing model, service-level ag ree ment, wa iting time.

cost paid to the infrastru cture prov ide rs plus the electric ity cost caused by energy consu mpt ion , and the revenue is the service charge to custome rs. In genera l, a service prov id er rents a certain nu mb er of serve rs from the infrast ruct ure prov ide rs and builds diffe rent mu lt iserve r syste ms for dif- ferent applicat ion do ma ins. Each mu lt iserve r syste m is to execute a special type of service requests and applic ations. Hence, the rent ing cost is propo rt iona l to the numbe r of servers in a mu lt iserve r syste m [2]. The powe r consu mpt ion of a mu lt ise rver syste m is line arly propo rt iona l to the nu m- ber of servers and the server utilizat ion, and to the square of e xecut ion speed [7, 8]. The revenue of a service provide r is re lated to the a mount of service and the quality of service. To summa rize , the profit of a service prov id er is ma in ly dete rmin ed by the configurat ion of its service platfo rm.

To configure a cloud service platfo rm, a service prov id er

usually ad opts a single renting scheme. Thats to say, the servers in the service system are all long -te rm rent ed. Be- cause of the limited n u mbe r of servers, some of the inco m- ing service requests cannot be processed immed iately. So they are first inserted into a queue until they can hand led by any availab le server. Howev er, the wa it ing time of the service requests cannot be too long. In orde r to satisfy quality-of-serv ice requ ire ments, the wa it ing time of each inco ming service request should be limited with in a certa in range, which is dete rmine d by a service -level ag ree ment (SLA). If the quality of service is guarant eed , the service is fully charged, othe rwise, the service provide r serves the request for free as a pena lty of low qua lity. To obtain high er revenue , a service provid e r shou ld rent more servers fro m the infrastructu re prov id ers or scale up the server e xecut ion speed to ensure that more service requests are processed with high service qualit y. Ho wev er, doing this wou ld lead to

sharp inc rease of the renting cost or the electric ity cost. Such inc reased cost may counte rwe ig ht the gain from pena lty reduct ion. In conc lusion, the single renting scheme is not a good scheme for service provide rs. In this pape r, we p ropose a novel renting scheme for service provide rs, which not only can satisfy quality-of-serv ice require ments, but also can obtain more profit. Our contribut ions in this pape r can be su mma rize d as follo ws.

• A novel double rent ing scheme is proposed fo r service provid ers. It co mb ines long-t erm rent ing with short-term rent ing, which can not only satisfy quality -of-serv ice requ ire me nts unde r the vary ing system wo rkload, but also reduce the resource waste great ly.

• A mu lt ise rve r syste m adopt ed in our pap e r is mod – eled as an M/M/m+ D queu ing model and the perfo r- mance indic ators are a na ly zed such as the avera ge service charge, the ratio of requests that need short- term serve rs, and so forth.

• The optima l con figurat ion p rob le m of servic e prov ide rs for profit ma xi mizat ion is fo rmu lated an d two kinds of optima l solutions, i.e., the ideal solu- tions and the actual solutions, are obtain ed respec- tive ly.

• A series of comp arisons are given to verify the per- formanc e of our scheme. The results show that the proposed Doub le -Qua lity -Gu aranteed (DQG) rent – ing scheme can achieve more profit than the com- pare d Sing le-Qua lity -Ungua ra nteed (SQU) rent ing scheme in the pre mise of gua rant ee ing the service quality co mp lete ly.

The rest of the paper is org an ized as follows. Section 2 revie ws the related work on profit aware prob le m in c loud co mputing. Section 3 presents the used mode ls, inc lud ing the three-t ie r cloud co mput ing mod e l, the mult iserve r sys- tem mod el, the revenue nd cost mo de ls. Section 4 pro- poses our DQG rent ing scheme and formu lates the profit optimizat ion p rob le m. Section 5 introduces the methods of find ing the optima l so lut ions for the profit optimizat ion prob le m in two scenarios. Section 6 de monst rates the perfor- mance of the proposed scheme through co mpa rison with the trad it ion a l SQU rent ing scheme. Finally, Section 7 concludes the wo rk.

1. RELA T ED WO R K

   In this section, we rev ie w recent works relevant to the profit of cloud service provid ers. Profit of service providers is re lated with many factors such as the price, the ma rket de man d, the system configu rat ion, the custome r satisfaction and so forth. Service provide rs natura lly wish to set a higher price to get a highe r profit marg in; but doing so wou ld decrease the custome r satisfa ction , which leads to a risk of discou ra g ing de mand in the future. Hence, selecting a rea- sonable p ric ing strategy is impo rt ant for service prov ide rs.

   The pric ing strateg ies are div ided into two categories,

   i.e., static pric ing and dynamic pric ing . Static pric ing me ans that the price of a service request is fixed and kno wn in advance, and it does not change with the conditions. With dynamic p ric ing a service prov ide r de la ys the pric ing

   decis ion until after the custo me r de ma nd is revea led, so that the service prov ide r can adjust prices according ly [9]. Static pric ing is the dominant st rateg y which is wid e ly used in real wo rld and in research [2, 10, 11]. Gha mkha ri et al. [11] ado pte d a flat-rate pric ing strat egy and set a fixed price for all requ ests, but Odly zko in [12] a rg ued that the predo mi- nant flat-rate pric ing en courages waste and is incomp atib le with service different iat ion . Anothe r kind of static pric ing strategies are usage-based pric ing . For e xa mple, the price of a service request is propo rt iona l to the service time and task e xecut ion requ ire ment (measure d by the nu mber of instruct ions to be exe cuted) in [10] and [2], respective ly. Usage-b ased pric ing reveals that one can use resources more efficiently [13, 14].

   Dyna mic p ric ing e merges as an attractiv e a lte rnat ive

   to better cope with unpred ictab le custo me r d e mand [15]. Mac´as et al. [16] used a genetic algo rith m to iterat ive ly optimize the pric ing policy. A ma zon EC2 [17, 18] has in- trodu ced a spot pric ing featu re, whe re the spot price for a virtua l instance is dyn a mic a lly up date d to match supply and dema nd. Ho weve r, c onsu mers dislike prices to change, especially if they perceive the changes to be unfa ir [19, 20]. After comp arison, we select the usage-based p ric ing strate- gy in this pap e r since it agrees with the concept of cloud co mput ing mostly.

   The second factor affecting the profit of service prov ide rs is custome r satisfact ion which is deter mined by the quality of service and the charge. In order to imp rove the customer satisfaction level, there is a service-leve l agree ment (SLA) bet ween a service prov ide r and the custome rs. The SLA adopts a price co mpe nsation mechan is m for the custome rs with low service quality. The mechan is m is to guarantee the service qua lity and the custome r satisfact ion so that more custome rs are attracte d. In previo us resea rch, different SLAs are adopted. Gha mkha ri et al. [11] ado pte d a stepwise charge function with two stages. If a service request is hand led before its deadline , it is no rma lly ch a rg ed; but if a service request is not hand le d before its deadline , it is dro pp ed and the prov id e r pays for it due to penalty. In [2, 10, 21], charge is decre ased cont inu ously with the inc reas ing wa iting time until the charge is free. In this pape r, we use a two-step charge funct ion, whe re the service requests served with high qua lity are no rma lly cha rged, otherwise, are serv ed for free.

   Since profit is an impo rta nt concern to cloud service prov ide rs, many works have been done on how to boost their profit. A large body of works have recent ly focused on reducing the energy cost to increase profit of service prov ide rs [22, 23, 24, 25], and the idle server turn ing off strategy and dynamic CPU clock frequency scaling are adopt- ed to reduc e ene rgy cost. Ho weve r, only reduc ing en ergy cost cannot obtain profit ma xi mizat ion. Many researche rs invest igate d the trad e-o ff bet wee n min imizing cost and ma xi mizing rev enue to optimize profit. Both [11] and [26] adjusted the nu mb e r of switched on servers pe riod ic ally using diffe rent strateg ies and different profit ma xi mizat ion mod els were built to get the numb e r of s wit ched on servers. Ho wever, these works did not consider the cost of resource configurat ion .

   Ch iang and Ouy ang [27] cons ide red a cloud server

   system as an M/M/R/K queu ing syste m whe re all service

   requests that exceed its ma ximu m cap ac ity are rejected. A a set of services in the form of virtua l ma ch ine (VM). In fras-

   profit ma ximi zat ion fun ction is defined to find an optimal co mb inat ion of the server size R and the queue capac ity K such that the profit is ma ximi zed. Ho weve r, this strategy has furthe r imp licat ions other than just losing the revenue

   from some services, because it also implies loss of reputat ion

   and therefo re loss of future custo me rs [3]. In [2], Cao et al. treated a cloud service plat fo rm as an M/M/m model, and the proble m of opt ima l mu ltise rve r con figurat ion for profit ma ximi zat ion was formu lated and solved. This work is the most relevant work to ours, but it ado pts a single rent ing scheme to configure a mu lt iserve r syste m, wh ich cannot adapt to the vary ing ma rket d e mand and leads to low service quality and great resource waste. To overcome this wea kn ess, another resource manage me nt strategy is used in [28, 29, 30, 31], which is cloud federation. Us- ing federat ion , d iffe rent prov id ers run n ing services that have comp le menta ry resource requ ire ments over time can mutua lly co llabo rate to share their respect ive resou rces in orde r to fulfill each ones de mand [30]. Ho weve r, p rov ide rs should make an inte lligent de cis ion about utilizat ion of the fed erat ion (either as a contributor or as a consumer of resourc es) dep end ing on different condit ions that they might face, which is a comp licated p rob le m.

   In this pape r, to overco me the shortco mings ment io ned above, a double rent ing scheme is designe d to configure a cloud service platfo rm, which can guarantee the service quality of all requ ests and reduce the resource waste greatly. Moreover, a profit ma xi mizat ion prob le m is fo rmu lated and solved to get the optima l mu lt iserv er con figu rat ion wh ich can product more profit than the optima l con figuration in [2].

2. TH E MO D ELS

   In this section, we first describe the three-t ier cloud co mput- ing structure. Then, we introduce the related mode ls used in this paper, inc lu ding a mu lt iserve r syste m mode l, a revenue mode l, and a cost mode l.

   1. A Cloud S yste m Mo del

      The cloud structure (see Fig. 1) consists of three typical part ies, i.e., in frastru cture prov ide rs, service prov ide rs and custome rs. This three-t ie r stru cture is used co mmon ly in existing lite rat ures [2, 6, 10].

      Fig. 1: The three -t ier cloud structure.

      In the three-t ie r structu re, an in frastructu re p rov ide r the basic hard ware and software facilities. A service provid er rents resources from in frastructu re p rov ide rs and prepa res

      tructu re p rov id ers p rov id e two kinds of resource rent ing schemes, e.g., long -te rm rent ing and short-term rent ing . In genera l, the rental price of long-term rent ing is much cheap- er than that of short-term rent ing . A custo me r sub mits a service request to a service provide r which delive rs services on de ma nd. The custo me r receives the desired result ro m the service provid er with certain service -level agre e ment, and pays for the service based on the a mount of the service and the service quality. Service prov ide rs pay infrast ruct ure prov ide rs for rent ing their physica l resources, and charge custo me rs for processing their service requests, which gen- erates cost and revenue, respect ive ly. The profit is generated from the gap between the revenu e and the cost.

   2. A Multiserver Model

      In this paper, we consider the cloud service platform as a mu lt iserve r syste m with a service request queue. Fig. 2 g ives the sche mat ic d iag ra m of cloud co mput in g [32].

      Fig. 2: The sche mat ic d iag ra m of c loud comput ing .

      In an actual cloud co mput ing p lat form such as Ama zon EC2, IBM blue cloud, and private c louds, there are many work nodes man aged by the cloud manag ers such as Eu- calyptus, Open Nebu la, and Nimbus. The clouds provide resources for jobs in the form of virtua l mach in e (VM). In add it ion, the users sub mit their jobs to the cloud in which a job queuing syste m such as SGE, PBS, or Condo r is used. All jobs are schedu led by the job schedule r and assigned to different VMs in a centralized way. Hence, we can con- sider it as a service request queue . For e xa mple, Condor is a specia lized worklo ad ma nage ment syste m for co mpute- intensive jobs and it provides a job queue ing mech anis m, scheduling policy, priority scheme, resource mon ito ring, and resource manag e ment. Users sub mit their jobs to Con- dor, and Condo r places them into a queue, chooses when and whe re to run them based upon a policy [33, 34]. Hence, it is reasonable to abstract a cloud service platfo rm as a mu l- tiserve r model with a service request queue , and the mode l is wide ly ado pted in existing lit e ratu re [2, 11, 35, 36, 37].

      In the three-tie r structu re, a cloud service prov ide r serv es custome rs service requests by using a mu lt iserve r syste m

      Fig. 3: The mult iserver system mode l, where serv ice requests are first placed in a queue before they are processed by any servers.

      which is rented from an infrast ructu re prov id er. Assu me that the mu lt iserve r syste m consists of m long-te rm rented ident ica l serve rs, and it can be scaled up by te mpo ra rily rent ing short -te rm serv ers from infrastructu re p rov ide rs. The servers in the system have ident ica l e xecut ion speed s (Unit: billion instructions per second). In this paper, a mu l- tiserve r syste m e xc lud ing the short-term se rve rs is mode led as an M/M/m queuing syste m as follows (see Fig. 3). There is a Poisson strea m of service requests with arriva l rate , i.e., the intera rriva l times are indep end ent and identica lly dist ribut ed (i.i.d.) e xponent ia l rando m va riab les with mean 1/. A mu lt iserve r syste m ma inta ins a qu eue with infin ite capacity. When the inco ming service requests cannot be pro- cessed imme d iate ly after they arrive, they are firstly placed in the queue until they can be handle d by any availab le server. The first-co me-first-served (FCFS) queu in g d isc ip line is adopted. The task e xecut ion requ ire ments (me asured by the nu mb er of instruct ions) are inde pen den t and identica lly distribut ed e xpon ent ia l rando m v ariab les r with mean r (Unit: billion instructions). Therefore, the e xecution times of tasks on the mu lt iserver syste m are also i.i.d. e xponent ia l random variables x = r/s with mean x = r/s (Unit: second). The averag e service rate of each server is calcu lat ed as µ = 1/x = s/r, and the system ut ilizat ion is

   3. Re ve nue Mo deling

      The revenue model is determin ed by the pric ing st rategy and the server-leve l ag ree ment (SLA). In this paper, the usage-based p ric ing strat egy is adopted , since cloud com- puting p rov ides services to customers and charges them on de man d. The SLA is a negotiation bet ween service prov ide rs and custome rs on the service quality and the price. Because of the limit ed serve rs, the service requests that cannot be hand led immed iate ly after ente ring the system must wait in the queue until any server is availab le. Ho wev er, to satisfy the quality-of-serv ice requ ire ments, the wa it ing time of each service request should be limited with in a certain range which is deter mined by the SLA. The SLA is wid e ly used by many types of businesses, and it adopts a price compensa- tion mechan is m to guarantee service qualit y and customer satisfaction. For e xa mp le, China Post gives a service time co mmit ment for do mestic e xpress mails. It pro mises that if a do mestic e xp ress mail does not arrive with in a dea d- line, the ma iling charge will be refun ded . The SLA is also ado pte d by many real wo rld c loud service provide rs such as Rackspace [39], Joyent [40], Microsoft Azure [41], and so on. Taking Joyent as an e xa mp le, the custome rs order Smart Machines, Smart Appliances, and/or Virtual Machines fro m Joyent, and if the availab ility of a custo mer s services is less than 100%, Joyent will credit the custome r 5% of the mont h ly fee for each 30 min utes of downti me up to 100% of the custome rs month ly fee for the affected server. The only difference is that its performa nce metric is availab ility and ours is wait ing t ime.

      In this paper, the service level is refle cted by the wa it ing time of requests. Hence, we define D as the ma xi mu m wait in g time here that the service requests can tolerate, in other wo rds, D is their dead line . The service charge of each task is related to the a mou nt of a service and the service- level agree ment . We define the service charge function for a service request with execut ion requ ire ment r and wait ing

      defined as = / mµ = / m × r/s.

      time W

      { in Eq. (2),

      Because the fixed co mput ing capa c ity of the service system is limited, some requests wou ld wait for a long time

      R(r, W ) =

      ar, 0 W D; 0, W > D.

      (2)

      before they are served. Acco rd ing to the queuing theory, we have the follo wing th eorem about the wa it ing time in an M/M/m queuing syste m.

      Theorem 3.1. The cu mu lat ive d istrib utio n fun ction (cdf) of the wa iting time W of a service request is

      wh ere a is a constant, which ind icates the price per one billion instructions (Unit: cents per one billion instructions). When a service request starts its execut ion before wait ing a fixed time D (Unit: second), a service provid er cons ide rs that the service request is processed with high quality-o f-

      service and charges a custome r ar. If the wait ing time of a

      FW (t) = 1 m emµ(1)t , (1) service request exceeds deadline D, a service prov id e r must

      wh ere

      1

      [m 1

      = (m)m (m)k (m)m

      ]1

      serve it for free. Similar revenue mode ls have been used in many existing research such as [2, 11, 42].

      According to Theorem 1, it is easy to know that the

      m m!

      k =0

      k ! + m!(1 ) .

      probab ility that the wait ing time of a service request e xceeds its deadline D is

      Proof 3.1. We have kno wn that the probab ility d istribut ion

      funct ion (pdf) of the wa it ing time W of a service request is

      P (W D) = 1 FW (D) =

      m emµ(1 )D . (3)

      1

      fW (t) = (1 Pq

      )u(t) + mµ m

      e (1) mµt ,

   4. Cost Modeling

      The cost of a service provide r consists of two major pa rts,

      wh ere Pq = m /(1 ) and u (t ) is a unit impu lse funct ion [2, 38]. Then, FW (t ) can be obtained by stra ight – forward ca lcu lat ion.

      i.e., the rental cost of physica l resources and the utility cost of energy consu mpt ion. Many existing resea rch such as [11, 43, 44] only consider the power consu mpt ion cost. As a major differenc e between their mode ls and ours, the

      resource rental cost is considered in this pape r as well, since it is a major part which affects the profit of service prov ide rs. A similar cost model is adopted in [2]. The resources can be rented in two ways, long-term renting and short-term rent ing, and the rental price of long-term rent ing is much cheape r than that of short-te rm renting . This is reasonable and co mmon in the real life. In this paper, we assu me that the long-te rm rental price of one server for unit of time is (Unit: cents per second) and the short-term rental price of one server for unit of time is (Unit: cents per second), wh ere < .

      The cost of energy consu mpt ion is dete rmine d by the electric ity price and the a mount of ene rgy consu mpt ion . In this paper, we ad opt the follo wing dyn a mic po we r mode l, which is adopt ed in the lit erature such as [2, 7, 45, 46]:

      Pd = Nsw CL V 2 f, (4)

      whe re Ns w is the average gate switc hing factor at each clock cycle, C L is the loading capac itanc e, V is the supply vo ltage , and f is the clock frequency [45]. In the ideal case, the re lat ionsh ip bet we en the clock frequency f and the supply

      voltage V is V f for some constant > 0 [46]. The server execut ion speed s is line arly p ropo rt iona l to the clock frequen cy f , na me ly, s f . Hence, the powe r c onsu mpt ion is Pd Nsw CL s2 +1 . For ease of discussion, we assu me that Pd = bNsw CL s2 + 1 = s where = bNsw C L a nd

      = 2 + 1. In this paper, we set Nsw CL = 7.0, b = 1.3456 and = 0.5. Hence, = 2.0 and = 9.4192. The value of power consu mpt ion ca lcu lated by Pd = s is close to the value of the Intel Pent iu m M processor [47]. It is reasonable that a server still consu mes some a mo unt of static powe r [8],

      denote d as P (Unit: Watt), wh en it is idle. For a busy server,

      the average a mou nt of energy consu mpt ion per unit of time is P = s + P (Unit: Watt). Assume that the price of

      energy is (Unit: cents per Watt).

3. A QUA L I T Y -GUA R A N T EED SC H EM E

   The tradit io na l single resource rent ing scheme cannot guar- antee the quality of all requ ests but wastes a great a mount of resources due to the unce rta inty of syste m worklo ad. To overco me the wea kness, we propose a d oub le rent ing scheme as follows, which not only can guarante e the quality of service co mp lete ly but also can reduce the resource waste great ly.

   1. The Propos e d Sche me

      In this section, we first propose the Double -Qua lity- Gu a rante ed (DQG) resource renting scheme which com- bines long-te rm rent ing with short-te rm rent ing. The ma in co mput ing c apac ity is prov ide d by the long-te rm rented servers due to their low price. The short-term rented se rve rs prov ide the extra capacity in peak perio d. The detail of the scheme is shown in Algo rith m 1.

      The proposed DQG scheme adopts the trad it ion a l FCFS queueing disc ip lin e. For each service request ente ring the system, the system re cords its wait ing time. The requests are assigned and e xecuted on the long-te rm rented se rve rs in the orde r of arriva l times. Once the wa iting time of a request reaches D, a te mp o ra ry server is rent ed from infrastruct ure

      Algorithm 1 Double-Qua lity-Gu aranteed (DQG) Sche me

      1: A multis erver syst em with m servers is running and w ait- ing for the events as follows

      2: A queue Q is initializ ed as empty

      3: Event A service request arrives 4: Search if any server is available 5: if true then

      6: Assign the service request to one available s erver

      7: else

      8: Put it at the end of queue Q and record its w ait ing t ime

      9: end if

      10: End Event

      11: Event A server becomes idle 12: Search if the queue Q is empty 13: if true then

      14: Wait for a new service request

      15: else

      16: Take the first service request from queue Q and assign it to the idle s erver

      17: end if

      18: End Event

      19: Event The deadline of a request is achieved

      20: Rent a temp orary server to execute the request and releas e the temp orary server when the request is complet ed

      21: En d Event

      prov ide rs to process the request. We consider the novel ser- vice model as an M/M/m+ D queuing model [48, 49, 50]. The M/M/m+ D model is a special M/M/m queuing model with impat ient custo me rs. In an M/M/m+ D mode l, the requests are impat ient and they have a ma xi ma l to le rab le wa it ing time. If the wa it ing time e xceeds the tolerable wa iting t ime, they lose patience and leave the system. In our scheme, the impat ient requests do not leave the system but are assigned to tempo ra ry rent ed se rve rs.

      Since the requests with wa it ing time D are all assigned

      to temp orary serve rs, it is appa re nt that all service requests can guarantee their dead line and are charged based on the wo rkload acc ord ing to the SLA. Hence, the revenue of the service provider in cre ases. Ho wev er, the cost increases as well due to the temp ora rily re nted se rve rs. Mo reov e r, the a mount of cost spent in rent ing te mpo ra ry se rve rs is deter- min ed by the comput ing c apac ity of the long-term rented mu lt iserve r syste m. Since the revenue has been ma xi mized using our scheme, min imizing the cost is the key issue for profit ma xi mizat ion. Ne xt, the tradeoff bet we en the long- term rental cost and the short-term rental cost is considered, and an optima l prob le m is formu lated in the follo win g to get the optima l long -te rm con fig urat ion such that the profit is ma xi mized.

   2. The Profit Opti mizati on Pr oble m

Assume that a cloud service platfo rm consists of m long- term rented serve rs. It is kn o wn that part of requests nee d te mpo ra ry se rve rs to serve, so that their quality can be guarante ed. De noted by pext (D) the steady-state p robab ility that a request is assigned to a te mpo ra ry server, or put diffe rently, pext (D) is the long-run fract ion of requests whose wait in g times exceed the deadlin e D. pext (D) is d ifferent from FW (D). In c alcu lat in g FW (D), a ll service requests, wheth er e xceed the deadlin e, will be wa it ing in the queue. Ho wever, in ca lcu lat ing pext (D), the requests whose wa iting

times are equal to the deadlin e will be assigned to the te mpo ra ry se rve rs, which will redu ce the wa it ing time of the follo wing requests. In general, pext (D) is much less than FW (D). Refer to [50], we can kno wn that pext(D) is:

(1 )(1 FW

NCETEIT – 2017 Conference Proceedings

The theorem is proven.

The profit of a service prov ide r in one unit of time is obtain ed as

Profit = Revenue Clong Cshort, (9)

0.24

0.21

0.18

0.15

pext(D) =

( D)) .

a ver _r = 1

1 (1 FW ( D))

(5)

wh ere Revenue = a r,

Clong = m( + ((1 pext (D)) s + P )),

r

and

s

Cshort = pext (D) ( + ( s + P )).

We aim to choose the optima l n u mbe r of fixed serve rs m

and the optima l e xe cut ion speed s to ma xi mize the profit:

p

ext

0.12

Profit(m, s) = ar p

ext

(D) r ( + ( s + P ))

s

(10)

0.09

0.06

m( + ((1 p

ext

( D)) s + P )).

0.03

0

0 5 10 15 20 25 30 35 40 45 50

D ea dli ne

Fig. 4: The probab ility of wa it ing time e xceed ing D.

That is to say, there are about pext (D) service requ ests in one unit of time which need short-te rm rented serv ers. Fig. 4 gives the probab ility ve rsus d iffe re nt de ad line wh ere = 5.99, r = 1, m = 6 and s = 1. Hence, the cost on short-te rm rented serve rs in one unit of time is calcu lat ed

as: r

Fig. 5 gives the gra ph of funct ion Profit(m, s) where = 5.99, r = 1, D = 5, a = 15, P = 3, = 2.0, = 9.4192,

= 1.5, = 3, and = 0. 3.

50

0

Profit

50

100

Cshort = pext (D)

s ( + P ), (6)

150 30

where r is the average e xe cution time of eah request.

3 2 20

1 10

s

A mong the requests ente ring the service syste m, a bout

0 0

The S erv er S p e e d

The S erv er S i ze

pext (D) percentage requests are not e xecuted by the m long- term rented se rve rs. Hence, the system ut ilizat ion of the m servers is (1 pext (D)). Since the powe r for spe ed s is s , the average a mount of ene rgy consu med by a

long -te rm re nted server in one unit of time is Plong = (1 pext(D))s + P . Hence, the cost of the long-te rm rented serv ers in one unit of time is calculated as:

Clong = m( + Plong). (7) The follo wing theorem gives the expe cted charge to a

Fig. 5: The funct ion Profit(m, s).

From the figure, we can see that the profit of a service prov id e r is vary ing with different server size and different e xecut ion speed. Therefo re, we have the proble m of select- ing the optima l server size and/or server speed so that the profit is ma xi mized . In the following section, the solutions to this proble m are proposed.

service request.

5 OP T I M A L SO LU T IO N

Theorem 4.1. The expe cted charge to a service request is ar.

r

Proof 4.1. Because the wa iting time W of each request is less than or equal to D, the e xpected charge to a service request with e xecut ion requ ire ment r is ar accord ing to the SLA. Since r is a rando m va riab le, ar is also rando m variab le. It is kno wn that r is an e xpon ent ia l ra ndo m variab le with mean r, so its probab ility d istribut ion funct ion is fr (z) = 1 ez/ r . The e xpected charge to a

service request is

In this section, we first develo p an ana lyt ic a l me thod to solve our optimizat ion prob le m. Using the analytica l met hod, the ideal optima l so lutio ns are obtained. Because the server size and the server speed are limited and discrete, we give an algorith mic meth od to get the actual solut ions based on the ideal optimal ones.

1. An Analytical Method for Ideal S ol uti ons

   1

   z/ r

   We firstly solve our optimizat ion proble m ana lytica lly, as-

   fr (z )R(r, z)dz =

   0 a

   r e

   0

   azdz

   su ming that m and s are continuous variab les. To this end, a closed-form e xp ression of pext (D) is needed . In this

   = e z/ r zdz = a

   r

   zde z/ r

   pape r, we use the same closed-form e xpression as [2], which

   is m1 (m) m

   0[

   0 ] k =0 k ! e

   . This exp ression is very accurate

   = a ze z/ r

   ez/ r dz (8) when m is not too small and isnot too large [2]. Since

   0 0 Stirlings appro xi mat ion of m! is 2 m( m )m , one closed-

   [ form e xp ression of is e

   = a

   z ez/ r ]

   + rez/ r

   m

   1

   0 0 m

   ,

   = a r. 2 m(1)( ee )m +1

   and

   (1 )e mµ (1 )D

   NCETEIT – 2017 Conference Proceedings

   90

   pext(D)

   80

   e

   1+ 2 m(1 )( e )m .

   e mµ(1 )D 70

   For convenience, we re write p ext (D) (1)K1 , wh ere 60

   K1 = emµ (1 )D , and K2

   K2 K1

   Profit

   = 1 + 2 m(1 ), whe re 50

   = (e /e)m .

   In the follo wing, we solve our optimizat ion p rob le ms based on above closed-form e xpression of pext ( D).

   Given , r, a, P , , , , , , D, and s, our objective is to find m such that Profit is ma xi mized. To ma xi mize Profit, m must be found such that

   40

   30 lamda =4.9 9

   20 lamda =5.9 9

   lam da =6.99 10 lamda =7.9 9

   1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

   The Server Siz e

   Fig. 6: Net profit ve rsus m and .

   Profit = Clong Cshort = 0,

   wh ere

   m

   Clong

   m m

   lamda =4.9 9

   lam da =5.99

   lam da =6.99 lam da =7.99

   50

   1 p (D)

   = + P

   r s

   ext ,

   m

   and

   m 40

   Optimal Size

   Cshort = ( + P ) r pext (D) + r s1 pext (D) . 30

   m

   Since

   s m m

   20

   ln = m ln(e /e) = m( ln 1),

   and 10

   we have

   = r

   m m2 s

   = ,

   m

   0

   0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

   The Server Speed

   and

   1 = ( ln 1) + m(1

   m

   1. ) m

      = ln ,

      1. Optimal size versus s and .

         90

         m

         80

         = ln .

         70

         Maximal Profit

         Then, we get 60

         K 1 = µ D K , 50

         m 1 40

         and

         K

         (

         ) 30

         lamda =4.9 9

         2 = 1

         2 m

         (1 + ) ln (1

         ) . 20

         lamda =5.9 9

         m 2m

         lam da =6.99

         10 lam da =7.99

         pext (D)

         1 [

         =

         1K (2K 1K

         0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

         The Server Speed

         ) m (K2 K 1 )2 m

         + ( 1)µ DK1 K2

         (1 + ) K 1

         2m]

         (K 2 1)

      2. Maximal profit versus s and .

   Fig. 7: Opt ima l size and ma xima l profit vs. s and .

   + (1 )K1 (ln )(K2 1) .

   We cannot get a closed-form solut ion to m, but we can get the nume ric al solut ion to m. Since Pro fit/ m is not an increasing or dec reas ing funct ion of m, we need to find the decreasing region of m, and then use the standard bisect ion met hod. If there are more than one ma xi ma l va lu es, they are co mpa red and the ma xi mu m is selected. When using the bisect ion method to find the e xtre me point, the iterat ion

   accuracy is set as a unifie d value 1010 .

   In Fig. 6, we d e monstrate the net profit in one unit of time as a function of m and where s = 1, r = 1, and the other para met ers are same as with those in Fig. 5. We notice that there is an optima l choice of m such that the net profit is ma xi mized . Using the analyt ica l method , the optima l va lue of m such that Pro fit / m = 0 is 4.8582, 5.8587, 6.8590,

   7.8592 for = 4.99, 5.99, 6.99, 7.99, respective ly. When the nu mbe r of servers m is less than the optima l value, the service prov ide r needs to rent more te mporary serve rs to execute the requests whose wa iting times are equal to the

   deadlin e; hence, the extra cost increases, even surpassing the gained revenu e. As m increases, the wait in g times are

   significant ly redu ced, but the cost on fixed servers increases great ly, which also surpasses the gained revenu e too. Hence, there is an optima l choice of m which ma xi mizes the profit.

   In Fig. 7, we de monst rate the optima l size and ma xima l profit in one unit of time as a function of s and . It means, for each co mb inat ion of s and , we find the optima l nu mb er of servers and the ma xima l profit. The para mete rs are same

   NCETEIT – 2017 Conference Proceedings

   9

   as those in Fig. 6. From the figures we can see that a 0

   high e r

   speed leads to a less nu mb e r of servers needed for each ,

   and diffe rent va lues have diffe rent o pt ima l co mb inat ions

   80 of spe ed and size. In addit ion , the greater the is, the more

   70 the ma xima l profit can be

   obtain ed .

   Profit

   60 50

   1. Optimal Speed

      Given , r, a, P , , , , , , D, and m, our objective is 30

      lam da =4.99

      to find s such that Profit is ma xi mized . To ma xi mize Profit, s lam da =5.99

      must be found such that

      20 lam da =6.99

      lam da =7.99

      wh ere

      = = 0, 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

      s s s

      The Server Speed

      Clong [ p (D) ]

      lamda =4.9 9

      lamda =5.9 9

      lam da =6.99

      lam da =7.99

      ,

      s = rs2

      ( 1)(1 pext (D)) s

      ext

      s

      Fig. 8: Net profit ve rsus s and .

      (

      and

      ) 1.6

      Cshort = r( + P )

      s s2

      [

      s pext (D) pe xt ( D)

      s ]

      1.4

      Optimal Speed

      1.2

      + r s 2

      s pext (D ) + ( 1)p (D) ,

      Since

      =

      s

      r

      = ,

      ext 1

      0.8

      0.6

      and

      s ms2 s

      0.4

      1 = m(1

      s

      1 ) , s

      0.2

      0

      1 3 5 7 9 11 13 15 17 19 21 23 25

      we have

      m

      The Server Siz e

      Now, we get

      s =

      s (1 ). (a) Optimal spe e d ver sus m and .

      ,

      90

      and

      K2

      K1 = DK m 80

      Maximal Profit

      1

      s r 70

      60

      s =

      2 m( + m(1 )2 )

      s

      . 50

      40

      pext (D)

      1 [

      = K

      K )

      30 lamd a=4.9 9

      20 lamd a=5.9 9

      (K s (K2 K 1 )2 s lamda =6.9 9

      + ( 1)K1

      2

      10 lamda =7.9 9 0

      1 3 5 7 9 11 13 15 17 19 21 23 25

      s

      2m( + m(1 ) )

      m ]

      + ( 1) DK1 K2 r .

      Similarly, we cannot get the closed-form e xpression of s, so we can use the same metho d to find the nu meric al solut ion of s. In Fig. 8, we de monstrate the net profit in one unit of time as a function of s and , whe re m = 6. The rest para mete rs are the same as that in Figs. 6 and 7. We notice that there is an optima l choice of s such that the net profit is ma xi mize d. Using the ana lyt ica l met hod, the optima l value of s such that respective ly. When the servers run at a slower speed than the optima l speed, the wait in g times of service requests will be long and exceed the deadlin e. So, the revenue is small and the profit is not optima l. When s increases, the energy consu mpt ion as we ll as the electricity cost increases. Hence, the incre ased revenue is much less than the increased cost. As a result, the profit is reduced. Therefo re, there is an optima l choice of s such that the net profit is ma ximi zed.

      In Fig. 9, we de mo nstrat e the optima l speed and ma xi- mal profit in one unit of time as a function of m and . The

      The Server Siz e

      (b) Maximal profit versus m and .

      Fig. 9: Opt ima l speed and ma xi ma l profit ve rsus m and .

      para mete rs are same as that in Figs. 68. From the figures we can see that if the nu mb er of fixed serve rs is great, the servers must run at a lower speed, which can lead to an optima l profit. In addit ion , the optima l speed of servers is not faster than 1.2, that is because the increased electric ity cost surpasses the increased cost that rents extra servers. The figure also shows us that different va lu es have differe nt optima l co mb inat ions of speed and size.

   2. Optimal Size and Speed

      Given , r, a, P , , , , , , D, our th ird p rob le m is to find m and s such that Profit is ma xi mize d. Hence, we need to find m and s such that Pro fit/ m = 0 and Pro fit/ s = 0, whe re Pro fit/ m and Pro fit/ s have been deriv ed in the

      Algorithm 2 Find ing the optima l size

      55

      ISSN: 2278-0181

      Input: s, , r, a, P , , ,NC, E,TE, IaTnd- 2D017 Conference Proceedings

      50 Output: the optimal number Opt size of fixed s ervers

      1: Profit max

      0

      ction

      Profit

      45 2: find the server size m using the analytical met hod in

      Se

      5

      m=3

      m=4

      m=5

      m=6

      . 1

      . 1

      40 3: m

      l m, m

      u

      m

      4: Profitl Prof it (ml , s), Prof itu Prof it (mu, s )

      l

      35 5: if Profit > Profit then

      u

      30 6: Profit max Pro fitl

      l

      7: Opt size m

      25 8: else

      0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

      The Server Speed

      9: Profit max Pro fitu

      u

      10: Opt size m

      Fig. 10: Net profit versus m and s.

      11: end if

      lam da =4.99 lam da =5.99

      lam da =6.99

      lam da =7.99

      16 0

      14 0

      Maximal Profit

      12 0

      10 0

      80

      60

      40

      optima l e xe cutio n speed of all se rve rs such that the profit is ma xi mized . The metho d is shown in Algo rith m 3.

      Algorithm 3 Find ing the optima l sp eed

      Input: m, , r, a, P , , , , , , and D Output: the optimal server sp eed Opt s p eed 1: Profit max 0

      2: find the server sp eed s using the analytical method in

      Section 5.1.2

      l

      u

      l u s if si < s si+1

      l

      20 4: Profitl

      Profit(m, s), Profitu

      Profit(m, s )

      0

      0.5 0.75 1 1.25 1.5 1.75 2

      Average r

      5: if Profitl > Pro fitu then 6: Profit max Pro fitl 7: Opt speed s

      9: Profit max Pro fit

      u

      Fig. 11: Maximal profit ve rs us and r. 8: else

      10: Opt speed su

      11: end if

      last two sections. The two equations are solved by using the same met hod as [2]. In Fig. 10, we de mo nstrat e the net profit in one unit of time as a function of m and s. Here is 5.99, and r = 1. The optima l value is m = 6.2418 and s = 0.9386, which result in the ma xima l profit 58.0150. In Fig. 11, we de monstrat e the ma xi ma l profit in one unit of time in d ifferent co mb inat ions of and r. The figure shows that the service prov ide rs can obtain more profit when the service requests are with gre ate r and r.

2. An Algorithmic Method for Actual S ol uti ons

In above subsection, the optima l so lutions find using the ana lyt ica l meth od are ideal solutions. Since the number of rented serv ers must be integer and the server speed leve ls

are discrete and limited in real syste m, we need to find the

5.2.3 Optimal Size and Speed

In this subsection, we solve the third prob le m, which is to find the optimal co mb inat ion of m and s such that the profit is ma xi mize d. Given , r, a, P , , , , , , and D, the

me thod is sho wn in Algo rith m 4.

Algorithm 4 Find ing the optima l size and speed

Input: , r, a, P , , , , , , and D

Output: the optimal number Opt size of fixed s ervers and the optimal execut ion speed Opt speed of s ervers

1: Profit max 0

2: find the server size m and speed s using the analytical method in Section 5.1.3

3: m m, m m

optima l so lut ions for the disc ret e sc ena rios . Assu me th at

l u

4: find the optimal sp eel d s

anud s

using Algorithm 3 w it h

l and mu, respectively

i

S = {s |1 i n} is a discrete set of n speed levels with inc reas ing order. Ne xt, different situ ations are discussed an d

the correspond ing methods are given as follo ws.

5: sPerrovfeitr sizePrmofit(m

l

6: if Profitl Pro fitu lt,hsel n), Profit

7: Profit max Pro fitu

Profit(m , s )

u u

u

8: Opt size m , Opt speed s

1. Optimal Size

   Assume that all servers run at a given execut ion speed s.

   Given , r, a, P , , , , , , and D, the first proble m is to find the nu mb er of long -te rm rente d se rve rs m such that the profit is ma xi mize d. The method is shown in Algo rith m 2.

2. Optimal Speed

   u u

   9: else

   10: Profit max Profi tl

   l , Opt speed sl

   11: Opt size m

   12: end if

1. Com parison of Two Kinds of S ol uti ons

   AsVsoulmume etpa,tIstshuee 2se0rvice prov ide r rents m servers. PGuivbelinshed, by,InwwTwab.iljeesrt.1co, m2, and 3, the ideal optima l solut ions and the9

   r, a, P , , , , , , and D, the second prob le m is to find the actual optimal solut ions are co mpa red for three different

   cases. Table 1 comp ares the ideal optima l size and the actual optima l size u nd er the given server speed. Table 2 co mpa res the ideal optima l speed and the actual optima l sp eed und e r the given server size. In Table 3, two kinds of solutions a re compared for d ifferent co mb inat ions of and r. Here, m can be any positive intege r, and the availab le speed lev els

   are S = { 0.2, 0.4, · · · , 2.0}. Acco rding to the co mpa risons

   Therefore, the e xpNecCteEdTcEhIaTrg- e20t1o7 aCsoenrfveirceencreeqPuroecseteidsinthges

   e xpect ed value of R(r):

   R(r)

   = fr (z )R(z )dz

   0 1

   = e z/ r az(1 P e (1 )mµD )dz

   we can see that the ideal ma xi ma l profit is greate r than 0 r q

   a

   the actual ma xima l profit. In the tables, we also list the = r (1 P qe (1 )mµD ) ez/ r zdz

   relative difference (RD) between the ideal optima l profit and the actual optima l profit, which is calcu lated as

   Idep Actp

   0

   = ar(1 Pq e (1)mµD ).

   The theorem is proven.

   RD = Actp ,

   wh ere Idep and Actp are the ma xi ma l profit in ideal and

   By the above theore m, the profit in one unit of time us ing the SQU rent ing scheme is calculated as:

   actua l scenarios. From the resu lts we kno w th at the re lat ive

   difference is a lways small e xcept some cases in Table 2. That is because a small diffe rence of speed wou ld lead to a big difference of profit whe n the server size is la rge.

1. PER FO R M A N C E CO M PA R IS O N

   ar(1 Pq e (1 )mµD ) m( + ( s + P )). (11) Using the SQU rent ing scheme, a service prov ide r must rent more servers or scale up the server speed to ma inta in a high quality -gu arante ed ratio. Assumed that the required qua lity-gua rant eed ratio of a service prov id er is and the

   dead line of service requests is D. By solving equatio n

   Using our resource rent ing scheme, te mpo ra ry serv ers are

   F (D) = 1 m e mµ (1 ) D

   W

   1

   rent ed for all requests whose wa it ing time are equal to the dead line , which can guarantee that all requests are served with high service quality. Hence, our scheme is superior to the trad it iona l resource rent ing scheme in terms of the service quality. Ne xt, we cond uct a series of calculations to comp are the profit of our renting scheme and the rent- ing scheme in [2]. In order to disting u ish the proposed scheme and the co mpa red scheme, the proposed scheme is rena med as Doub le -Qua lity -Gua rante ed (DQG) rent ing scheme and the co mpa red scheme is rena med as Single- Qu a lity-Ungua rante ed (SQU) re nting scheme in this pape r.

   1. The Compare d Sche me

      Firstly, the average charge of the using the SQU rent ing scheme is analy zed .

      Theorem 6.1. The exp ected charge to a service request usin g the SQU rent ing scheme is

      ar(1 Pq e (1)mµD ).

      Proof 6.1. Recall that the probability distribut ion fun ction o f the wa iting time W of a service request is

      fW (t) = (1 Pq )u(t) + mµ m e (1) mµt .

      Since W is a rando m va riab le , so R(r, W ) is also a ran- dom variab le . The exp ected charge to a service request with e xecut ion requ ire ment r is

      R(r) = R(r, W )

      = fW (t )R(r, t)dt

      with given m or s, we can get the correspond ing s or m such that the requ ired qua lity -g ua rante ed ratio is achieved .

   2. Profit Comparison under Different Quality- Guar antee d Rati o

      Let be 5.99 and the other para me te rs be the same as those in Section 5. In the first exa mp le, for a given nu mbe r of servers, we co mpa re the profit using the SQU renting scheme with quality -gua ra nteed ratio 100%, 99%, 92%, 85% and the optima l profit using our DQG rent ing scheme. Be-

      cause the quality -gua rant eed ratio 100% cannot be achieved using the SQU rentin g scheme, hence, we set 99.999999% 100%. The results are shown in Fig. 12. From the figure, we

      can see that the profit obtained using the proposed scheme is always great er than that using the SQU rent ing scheme, and the five curves reach the peak at diffe rent sizes. In addition, the profit obtain ed by a service prov ide r inc reases when the qualt iy -gua rantee d ratio increases from 85% to 99%, but decreases when the ratio is greater than 99%. That is because more service requests are charged with the inc reas ing rat io from 85% to 99%; but once the ratio is greate r than 99%, the cost to expand the server size is greater than the revenue obta ined from the extra qualtiy -gua rante ed requests, hen ce, the total profit is reduced.

      In the second exa mp le, we co mpa re the profit of the above five scenarios unde r the given server speed. The results are given in Fig. 13. The figure shows the trend of profit when the server speed is increasing fro m 0.1 to 2.9. From the figure, we can see that the curves increase firstly and reach the peak at certain speed, and then decrease along with the incre asing speed on the whole. The figure verifies

      0

      D [ ]

      = (1 Pq )u(t) + m µ m e (1 )mµ t

      0

      ardt

      that our proposed scheme can obtain more profit than the SQU re ntin g scheme. Notic ed that the changing t rends o f the curves of the SQU rent ing scheme with 100%, 99%,

      = (1 Pq

      )ar + m µm ar

      1

      e(1 )mµD

      (1 )mµ

      92%, and 85% qualit y-gua rant eed ratio are interesting. They show an incre asing t rend at the beginning and then decrease

      = ar(1 Pq e (1 )mµD ). du ring a small range of speed re peat ed ly. The reason is

      TABLE 1: Co mpa rison of the two methods for fin ding the optima l size

      	Given Spee d	0.2	0.4	0.6	0.8	1.0	1.2	1.4	1.6	1.8	2.0
      Idea l So lution	Optimal Size	29.1996	14.6300	9.7599	7.3222	5.8587	4.8827	4.1854	3.6624	3.2555	2.9300
      	Maximal Profit	11.5546	45.5262	54.6278	57.5070	57.8645	56.9842	55.3996	53.3498	51.0143	48.4578
      Actual So lution	Optimal Size	29	15	10	7	6	5	4	4	3	3
      	Maximal Profit	11.5268	45.4824	54.6014	57.3751	57.8503	56.9727	55.3259	53.0521	50.8526	48.4513
      Relative Difference		0.2411%	0.0964%	0.0483%	0.2299%	0.0246%	0.0202%	0.1332%	0.5612%	0.3180%	0.01325%

      TABLE 2: Co mpa rison of the two methods for fin ding the opt ima l spe ed

      	Given Size	5	7	9	11	13	15	17	19	21	23
      Idea l So lution	Optimal Spee d	1.1051	0.8528	0.6840	0.5705	0.4895	0.4288	0.3817	0.3440	0.3132	0.2875
      	Maximal Profit	57.3742	57.7613	56.0783	53.3337	49.9896	46.2754	42.3167	38.1881	33.9366	29.5933
      Actual So lution	Optimal Spee d	1.0	0.8	0.8	0.6	0.6	0.4	0.4	0.4	0.4	0.4
      Maximal Profit	57.0479	57.3751	54.7031	53.1753	48.4939	45.4824	42.2165	37.4785	32.6795	27.8795
      Relative Difference		0.5721%	0.6732%	2.5140%	0.2979%	3.0843%	1.7435%	0.2373%	1.8934%	3.8470%	6.1474%

      TABLE 3: Co mpa rison of the two methods for fin ding the optima l size and the optima l spe ed

      		r	0.50	0.75	1.00	1.25	1.50	1.75	2.00
      Idea l So lution = 4.99		Optimal Size	2.5763	3.8680	5.1608	6.4542	7.7480	9.0420	10.3362
      		Optimal Spee d	0.9432	0.9422	0.9413	0.9406	0.9399	0.9394	0.9388
      		Maximal Profit	24.0605	36.0947	48.1539	60.1926	72.2317	84.3121	96.3528
      	Actual So lution	Optimal Size	3	4	5	6	7	9	10
      		Optimal Spee d	1.0	1.0	1.0	1.0	1.0	1.0	1.0
      		Maximal Profit	23.8770	35.7921	48.0850	60.1452	72.0928	83.9968	96.2230
      	Relative Difference		0.7695%	0.8454%	0.14355%	0.0789%	0.1927%	0.3754%	0.1349%
      Idea l So lution = 5.99		Optimal Size	3.1166	4.6787	6.2418	7.8056	9.3600	10.9346	12.4995
      		Optimal Spee d	0.9401	0.9393	0.9386	0.9380	0.9375	0.9370	0.9366
      		Maximal Profit	28.9587	43.4364	57.9339	72.4121	86.9180	101.3958	115.9086
      	Actual So lution	Optimal Size	3	4	6	7	9	10	12
      		Optimal Spee d	1.0	1.0	1.0	1.0	1.0	1.0	1.0
      		Maximal Profit	28.9158	43.1208	57.8503	72.2208	86.7961	101.2557	115.7505
      	Relative Difference		0.1484%	0.7317%	0.1445%	0.2649%	0.1405%	0.1384%	0.1365%

      70

      D Q G 60

      60 S QU 1 0 0 %

      S QU 9 9 %

      50 S QU 8 5 %

      Profit

      40

      S QU 9 2 %

      50

      4

      Profit

      0

      30 30

      20 20

      10 10

      0 0

      D Q G

      S QU 1 0 0 %

      S QU 9 9 %

      S QU 92%

      S QU 8 5 %

      1 2 3 4 5 6 7 8 9 10 11 1 2 13 14 1 51 6 17 18 1 9 20 21 2 2 23 24 25

      The n um b er of serv ers

      Fig. 12: Profit ve rsus m and diffe re nt qu a lity -gua ra nteed rat ios.

      ana ly zed as follows. When the server speed is changing with in a small speed range, in order to satisfy the requ ired dead line -g ua rante ed ratio, the nu mbe r of serve rs rented by a service prov id er keeps unchanged . At the beginning, the added reven ue is more than the add ed cost, so the profit is inc reas ing. Ho weve r, wh en the speed becomes greate r, the energy consu mpt ion increases, lead ing to the total incre ased cost surpassing the incre ased revenue , hence, the profit decreases.

      In the third e xa mp le, we explore the changing t rend o f the profit with diffe rent D, and the results are sho wn as

      0.1 0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 2.5 2.7 2 . 9

      The S p ee d

      Fig. 13: Profit ve rsus s and diffe rent qua lity -gu a rante ed rat ios.

      Fig. 14. Fig. 14(a) gives the nume ric al results wh en the server speed is fixed at 0.7, and Fig. 14(b) shows the nume ric al results when the nu mb e r of serve rs is fixed at 5. We analy ze the results as follows.

      From Fig. 14(a), we can see that the profit obta ined using the SQU rent ing scheme increases slightly with the inc re ment of D. That is because the service charge keeps constant but the extra cost is reduc ed when D is greater. As a consequence, the profit increases. The second pheno menon from the figure is that the curves of SQU 92% and SQU 85% have sharp d rop at some points and then ascend gradua lly

      6 0

      ratio. Hence, the revenu e as well as the profit drops.

      55

      Profit

      50

      45

      40 D Q G

      S QU 9 9 %

      S QU 9 2 %

      S QU 8 5 %

      18 19 20 21 22 23 24 2

      S QU 1 0 0 %

      35

      30

      5 6 7 8 9 10 11 12 13 14 15 16 17 5

      De a dl in e D

      1. Fixed server spee d s = 0.7.

         65

         60

         55

         Profit

         50

         45

         40 D Q G

         S QU 1 0 0 %

         S QU 9 9 %

         35 S QU 9 2 %

         S QU 8 5 %

         30

         De a dl in e D

      2. Fixed server size m = 5.

      Fig. 14: Profit ve rsus D and d iffe rent qu alit y-gua rant eed rat ios.

      and smoothly. The reasons are exp la in ed as follows. When the server speed is fixed, enough serve rs are neede d to satisfy the given quality -gu arante ed ratio. By calculating, we know that the nu mb er of requ ired serv ers is the same for all D va lu es in a certain interva l. For e xa mp le, [5,7] and [8,25] are two inte rva ls of D for the curve of SQU 92%, and the required serve rs are 10 and 9, respectively. For a ll D with in the same inte rva l, their costs are the same with each other. Whereas, their actual quality -gua ra nteed rat ios are different which get greater with the increasing D. Hence, du ring the same interv a l, the reven ue gets greater as we ll as the profit. Ho weve r, if the deadline inc reases and enters a different inte rva l, the quality -gua ra nteed ratio sharply dro ps due to the reduced serve rs, and the lost revenue surpasses the reduced cost, hence, the profit sharp ly drops as well. Moreover, we can also see that the profit of SQU 100% is much less than the other scenarios. That is because when the quality -gu arante ed ratio is great enough, a dd ing a small re venue leads to a much high cost.

      From Fig. 14(b), we can see that the curves of SQU 92% and SQU 85% descend and ascend repeated ly. The reasons are same as that of Fig. 14(a). The deadlines with in the same inte rva l share the same min ima l speed, hence, the cost keeps constant. At the same time, the revnue inc reases due to the increas ing qua lity-gu arant eed ratio. As a consequence, the profit increases. At each break point, the min i ma l speed satisfying the requ ired q ua lity -gua ra nteed ratio gets sma ller, which leads to a sharp d rop of the actual quality -gu a rante ed

   3. Com parison of Optimal Profi t

      In order to fu rthe r verify the superio rity of our proposed scheme in terms of profit, we conduct the follo wing co m-

      rent ing scheme and that of the SQU rent ing scheme in [2]. In this group of c o mpa risons, is set as 6.99, D is 5, r is vary ing from 0.75 to 2.00 in step of 0.25, and the other para me te rs are the same as Section 5. In Fig. 15, the opt ima l p rofit and the correspond ing con figuration of two renting sche mes are presented. From Fig. 15(a) we can see that the optimal profit obtain ed using our scheme is always greate r than that using the SQU rent ing scheme. According to the calculation, our scheme can obtain 4.17 percent more profit on the averag e than the SQU rent ing scheme. This shows that our scheme outperfo rms the SQU renting scheme in terms of both of quality of service and profit. Figs. 15(b) and 15(c)

      figures show that using our renting scheme the capacity pro v ide d by the long-t erm rented se rve rs is much less than the capacity using the SQU renting scheme. That is because a lot of requests are assigned to the te mpo ra ry se rve rs using our scheme, and less servers and slower server speed are configured to reduce the waste of resources in idle period. In conclusion, our scheme can not only guarant ee the service quality of all requ ests, but also achieve more profit than the co mpa red one.

   1. CO NC LU S IO NS

   In order to guara ntee the quality of service req uests and ma xi mize the profit of service prov ide rs, this pape r h as propose d a novel Double -Qua lity -Gua rante ed (DQG) rent- ing scheme for service provide rs. This scheme comb ines short-te rm rent ing with long-t erm rent ing , which can reduce the resource waste greatly and adap t to the dynamica l de ma nd of co mputing capac ity. An M/M/ m+ D qu eue ing model is build for our mu lt iserve r system with vary ing system size. And then, an optima l con figurat ion p roble m of profit ma ximi zat ion is formu lated in which many factors are taken into considerat ions, such as the ma rket d e ma nd, the workload of requests, the server-lev e l ag ree me nt , the rental cost of servers, the cost of energy consu mpt ion , and so forth. The optima l solut ions are solved for two different situations, which are the ideal optima l so lutions and the actual opt ima l solut ions. In add it ion , a series of calcula- tions are conducted to co mp are the profit obtained by the DQG rent ing scheme with the Sing le -Qua lity -Ungua ranteed (SQU) rent ing scheme. The results show that our scheme outpe rfo rms the SQU scheme in terms of both of service quality and profit.

   In this paper, we only consider the profit ma xi mizat ion prob le m in a ho mog eneous cloud environ ment , b ecause the analysis of a hete rogen ous env iron me nt is much more co m- plic ated than that of a homog enous env iron me nt. Ho weve r, we will e xt end our study to a heterogenous env iron ment in the future.

   140 1

   D

   DQG DQG

   Q

   G

   Optimal Profit

   Optimal Speed

   120 SQU 20 SQU 0.98

   S

   Q

   100 15 0.96

   Optimal Size

   80 10 0.94 U

   60 5 0.92

   r

   75

   .5 1.

   1 1.25 1

   75

   .5 1.

   1 1.25 1

   40 0 0.9

   Average

   Average

   0.75

   2 0.75

   2 0.75 1 1.25 1.5 1.75 2

   r

   Average r

   1. Comparison of Profit. (b) Comparison of Server Size. (c) Comparison of Server Speed.

      AC K N O W L ED G M EN TS

      Fig. 15: Co mp arison bet ween our scheme with that in [2].

      1. A. Odlyzko, Should flat-rate int ernet pricing continue,

         The authors tha n k the anony mous re vie we rs for their valu- able comme nts and suggestions. The research was partia lly fun ded by the Key Prog ra m of Nationa l Natu ra l Sc ience Found ation of China (Grant Nos. 61133005, 61432005), the Nat iona l Natu ra l Science Foundat ion of China (Grant Nos. 61370095, 61472124, 61173013, 61202109, and 61472126).

         REF ER EN C ES

         1. K. H w ang, J. D ongarra, and G. C. Fox, Distributed and Cloud Computing. Els evier/M organ K aufmann, 2012.

         2. J. Cao, K. H w ang, K. Li, and A. Y. Z omay a, Optimal

            multis erver configuration for profit maximiz ation in cloud comp uting, IEEE Trans. Pa r all el Distrib. Syst., vol. 24, no. 6, pp. 10871096, 2013.

         3. A. Fox, R. Griffith, A. Joseph, R. Katz, A. Konwinski,

            G. Lee, D. P atterson, A. Rabkin, and I. Stoica, A bove the clouds: A berkeley view of cloud computing, D ept. El ectri cal Eng. and Comput. Sciences, vol. 28, 2009.

         4. R. Buyya, C. S. Yeo, S. Venugopal, J. Broberg, and

            1. Brandic, Cloud comp ut ing and emerging it platforms : Vision, hype, and reality for delivering comp uting as the 5th utility, Future Gener. Comp. Sy., vol. 25, no. 6, pp. 599 616, 2009.

         5. P. M ell and T. Grance, The NIST definition of cloud com- puting. nat ional instit ute of st andards and technology, Information Technology L ab o ra to r y, vol. 15, p. 2009, 2009.

         6. J. Chen, C. Wang, B. B. Zhou, L. Sun, Y. C. Lee, and

            A. Y. Zomay a, Tradeoffs bet w een profit and customer satis faction for service provis ioning in the cloud, in Proc. 20th Intl Symp. High Performance Distributed Computing. ACM , 2011, pp. 229238.

         7. J. M ei, K. Li, J. Hu, S. Yin, and E. H.-M . Sha, Energy-

            aw are preemptive s cheduling algorit hm for sporadic t as ks on dvs platform, MICRO PRO CESS MICRO S Y., vol. 37, no. 1, pp. 99112, 2013.

         8. P. de Langen and B. J uurlink, Leakage-aw are mult ip ro- cessor scheduling, J. Signal Pr o cess . Sys., vol. 57, no. 1, pp. 7388, 2009.

         9. G. P. Cachon and P. F eldman, Dy namic versus static pricing in the pres ence of strategic cons umers, Tech. Rep., 2010.

         10. Y. C. Lee, C. Wang, A. Y. Zomay a, and B. B. Zhou, Profit- driven scheduling for cloud services with data access awarenes s, J. Parallel Distr. Com., vol. 72, no. 4, pp. 591 602, 2012.

         11. M . Ghamkhari and H. M ohsenian- Rad, Energy and p er- formance management of green data centers: a profit max- imiz ation app roach, IEEE Trans. Smart Grid, vol. 4, no. 2, pp. 10171025, 2013.

         IT Pr of essi o n al , vol. 2, no. 5, pp. 4851, 2000.

      2. G. Kesidis, A. Das, and G. de Veciana, On flat-rate and us age-bas ed pricing for t iered commodity int ernet services, in 42nd Annual Conf. Information Sciences and Systems. IEEE, 2008, pp. 304308.

      3. S. Shakkottai, R. Srikant, A. Oz daglar, and D. A cemoglu,

         The price of simplicity, IEEE J. Selected Areas in Commu- nications, vol. 26, no. 7, pp. 12691276, 2008.

      4. H. Xu and B. Li, Dynamic cloud pricing for revenue maximiz ation, IEEE Trans. Cloud Computing, vol. 1, no. 2, pp. 158171, July 2013.

      5. M . M ac´as and J. G uit art, A genetic model for pricing in cloud comput ing markets, in Proc. 2011 ACM Sym p. Applied Computing, 2011, pp. 113118.

      6. A maz on EC2, http ://aw s.am az on.co m, 2014.

      7. A maz on EC2 spot instances, http://aws.amazon.com/ ec2/spot- instances , 2014.

      8. R. L. Hall and C. J. Hitch, Price theory and business behaviour, Oxford eco no mi c p a p er s , no. 2, pp. 1245, 1939.

      9. D. Kahneman, J. L. Knetsch, and R. Thaler, Fairness as a constraint on profit seeking: Ent itlements in the market,

         The American eco n o mi c r eview, pp. 728741, 1986.

      10. D. E. Irwin, L. E. Grit, and J. S. Chase, Balancing risk and rew ard in a market -bas ed task service in 13th IEEE Intl Symp. High performance Distributed Computing, 2004, pp. 160169.

      11. J. Heo, D. H enriks son, X. Liu, and T. A bdelzaher, In-

          tegrating adaptive comp onents : An emerging challenge in performance-adaptive systems and a server farm cas e- study, in RTSS 2007, Dec 2007, pp. 227238.

      12. E. P inheiro, R. Bianchini, E. V. Carrera, and T. H eat h,

          Dynamic cluster reconfiguration for pow er and p erfor- mance, in Compilers and operating systems for low power. Springer, 2003, pp. 7593.

      13. X. Fan, W.-D. Weber, and L. A. Barroso, P ow er provis ion- ing for a w arehouse-s iz ed comp ut er, in ACM SIGARCH Computer Architecture News, vol. 35, no. 2. ACM , 2007, pp. 1323.

      14. J. S. Chase, D. C. A nderson, P. N. T hakar, A. M. Vahdat, and R. P. Doyle, M anaging energy and server res ources in hosting cent ers , in ACM SIGOPS Operating Systems Review, vol. 35, no. 5. ACM , 2001, pp. 103116.

      15. M . M azzucco and D. Dy achuk, Optimiz ing cloud providers revenues via energy efficient server allocat ion, Sustainable Computing: Informatics and Systems, vol. 2, no. 1, pp. 112, 2012.

      16. Y.-J. Chiang and Y.-C. O uyang, Profit optimiz at ion in sla- aw are cloud services with a finite cap acity queuing model, Math. Probl. Eng., 2014.

      17. B. Rochw erger, D. Breit gand, E. Levy, A. Galis, K. Na- gin, I. M. Llorent e, R. M ont ero, Y. Wolfsthal, E. Elmroth,