Assocton for Informton Systems AIS Electronc Lbrry (AISeL) AMCIS 2009 Proceedngs Amercs Conference on Informton Systems (AMCIS) 2009 On The Study of Estblshng Responsve Infrstructure for Mssvely Multplyer On-Lne Gme Robert Abooln Clforn Stte Unversty Sn Mrcos, rbool@csusm.edu Y Sun Clforn Stte Unversty Sn Mrcos, ysun@csusm.edu Jck Leu Clforn Stte Unversty Sn Mrcos, leu@csusm.edu Follow ths nd ddtonl works t: http://sel.snet.org/mcs2009 Recommended Ctton Abooln, Robert; Sun, Y; nd Leu, Jck, "On The Study of Estblshng Responsve Infrstructure for Mssvely Multplyer On- Lne Gme" (2009). AMCIS 2009 Proceedngs. 762. http://sel.snet.org/mcs2009/762 Ths mterl s brought to you by the Amercs Conference on Informton Systems (AMCIS) t AIS Electronc Lbrry (AISeL). It hs been ccepted for ncluson n AMCIS 2009 Proceedngs by n uthorzed dmnstrtor of AIS Electronc Lbrry (AISeL). For more nformton, plese contct elbrry@snet.org.
On The Study of Estblshng Responsve Infrstructure for Mssvely Multplyer On-Lne Gme Robert Abooln, Y Sun, nd Jck Leu Deprtment of Deprtment of Informton Systems & Opertons Mngement, Clforn Stte Unversty Sn Mrcos, Sn Mrcos, CA 92096-0001, USA {rbool@csusm.edu, ysun@csusm.edu, Leu@csusm.edu} A mssvely multplyer onlne gme (MMOG) often requres gme publsher to deploy dozens or hundreds of n-tered servers to support mllons of concurrent plyers round the world. Plnnng such mssve network nfrstructure, prtculrly n n envronment where uncertn demnd nd lmted server cpcty could cuse congestons n host ste nd the network, poses gret chllenge. A slow response tme stemmng from n ll-desgned nfrstructure could render n otherwse technclly superor MMOG noncompettve n the mrketplce. In ths study, we focus on three crtcl ssues relted to estblshng n MMOG server nfrstructure: selectng host fcltes on brodbnd provder s bckbone network nodes, ssgnng clent clusters represented by the Pont of Presences (PoPs) to these MMOG fcltes, nd determnng the requred cpcty for ech host ste. The problem s frst formulted s non-lner nteger progrm bsed on n M/M/1 queung system n ech host fclty. We then develop n exct soluton pproch obtned from solvng mnmum cost set-coverng problem. The effcency of the soluton pproch s lso reported. Key words: Onlne Gme, Congested fclty locton models, Non-lner nteger progrm, Set-coverng problem. 1
1. Introducton Mssvely multplyer onlne gmes (MMOGs) hve become one of the most vbrnt sectors n the vdeo gme ndustry becuse of ther ppel to the younger generton. MMOGs refer to genres of onlne role-ply vdeogmes n whch gmers cn freely crete or ssume chrcter n persstent nd dynmc vrtul communty. The globl mrket for these gmes ws estmted to be $2.7 bllon n revenue n 2006 (Stehln, 2003), nd successful gme often serves lrge group of plyers wth mor economc stke. For exmple, t ws estmted tht World of Wrcrft, one of the most populr MMOGs, hd 5.5 mllon users nd revenue of $300 mllon n 2005 (Helm, 2006). In order to support mllons of plyers round the world, n MMOG publsher needs to crete mssve clentserver nfrstructure wth dozens to hundreds of copes of the pplcton deployed globlly. In ddton to gme contents, the success of n MMOG lso hnges on ts plyblty, often mesured by server throughput nd network response tme. Throughput s lrgely dctted by the cpcty of gme servers. MMOGs typclly employ n n-tered server rchtecture, wth the front-ter mngng securty nd lod blnce, the md-ter hndlng gme smultons, nd the dtbse ter keepng trck of nformton bout gme obects nd mneuvers (Dolber, 2007 2007b, 2007c; Vn der Steen, 1997). To determne the server cpcty for ech ter, gme dstrbutor must be ble to estmte the number of concurrent plyers per geogrphy (Dolber, 2007). Ths mples tht the servce zone of server must be ether known pror or determned concurrently wth server cpctes. Network response tme, on the other hnd, lrgely depends on the dstnce between plyer nd the server (Johnsson, 2000). Whle t s dffcult to boost the propgton speed of network sgnls, n MMOG publsher cn strtegclly locte gme servers wth dequte servce cpcty on network to mntn certn level of servce qulty. To llevte the lst-mle bndwdth constrnt, t s hghly recommended tht n MMOG server be hosted wthn brodbnd provder s fclty or n the close proxmty (Megler, 2004). Thus, one of MMOG key reserch questons s how to strtegclly locte gme servers wth pproprte cpctes on brodbnd network nodes so tht the gme dstrbutor s cost cn be mnmzed whle meetng the servce qulty requrement. In ths pper, the problem s frst formulted s non-lner nteger progrm bsed on n M/M/1 queung system n ech host fclty. We then develop n exct soluton pproch obtned from solvng mnmum cost set-coverng problem. We beleve tht we re mong the frst to study the optml servce desgn for MMOGs. Although the model nd the lgorthm re 2
developed specfclly for MMOGs servce desgn problem, we expect them to be pplcble, wth modfctons, to mny pplctons wth smlr structures. The pln for the pper s s follows. A lterture revew s provded n the next secton. In Secton 3, we ntroduce notton nd formultons for the MMOG deployment problem. In Secton 4, we develop n exct soluton pproch, whch nvolves solvng mnmum cost set-coverng problem. Results for computtonl experments nd senstvty nlyses re presented n Sectons 5 nd 6, respectvely. Fnlly, the strengths, the lmttons, nd future extensons of ths study re dscussed n the Secton 7. 2. Lterture Revew Deployng n MMOG nvolves sgnfcnt economc trdeoffs n terms of costs ssocted wth openng nd opertng server fcltes nd mntnng certn level of servce qulty. For n cton-pcked MMOG, gme ccess tme, defned s the tme from clent mchne sends out gme request tll t receves response from the server, s regrded s the foremost mportnt qulty mesure s t correltes strongly wth user stsfctons (Armtge, 2001; Dck, Wellntz, & Wolf, 2005; Henderson 2001; Henderson & Bhtt, 2002; Henderson, 2002). Gme ccess tme hs two mor components, network response tme nd server response tme, whch hve been t the center of MMOG deployment consderton (Dolber, 2007, 2007b, 2007c). In fct, the study of network response tme dted bck to the reserch n dstrbuted dtbse systems. Johnsson (2000) exmned the mkeup of network response tme nd concluded tht only network ltency, defned s the tme needed to propgte sgnl between the sendng nd recevng nodes once the sgnl hs been sent onto the network, would become the lmtng fctor. On the contrry, other fctors such s the tme needed to lod nformton to the medum nd the dely due to network ccess contentons were of mmterl n hgh-speed networkng envronment. Hs study further showed tht gnorng network ltency could underestmte the response tme by more thn 80 percent n some cse. In ths study, we follow ths reserch result nd use network ltency to mesure network response tme. The conventonl wsdom beleves tht network ltency depends not only on the dstnce between the sendng nd recevng nodes but lso on the protocols nd topologes. However, physcl dstnce hs been shown to be the most relevnt mesurement for ltency n recent studes. For exmple, Huffker et l. (2002) exmned the correlton between 3
ltency nd four populr Internet dstnce metrcs: IP pth length, utonomous system pth length, gret crcle geogrphc dstnce, nd round trp tme. They concluded tht metrcs bsed on physcl (geogrphc) chrcterstcs correlted better wth ltency thn those bsed on logcl topologes. Ths fndng ws lso supported by the reserch on the geogrphc dstrbuton of onlne gme servers nd plyers (Dck, Wellntz, & Wolf, 2005; Feng & Feng, 2003). Bsed on these results, ths study uses dstnce to pproxmte network ltency nd server loctons to control the mount of network nduced gme ltency. The second component of gme ccess tme s server response tme, whch ncludes the tme wtng for ccessng servers (queung tme) nd beng served by server (processng tme). Queung tme hs been ncorported nto mny servce system desgn problems employng queung models to determne the pproprte server cpcty so s to keep wtng tme or servce qulty t n cceptble level (Bermn & Drezner, 2002; Mrnov & Serr, 1998; Wng, Btt, & Rump, 2002). However, we submt tht usng queung tme s surrogte mesurement for servce qulty s too lmtng nd does not reflect the entre dely experenced by n MMOG plyer. Therefore, ths study suggests the more encompssng gme ccess tme, whch s defned s the sum of network ltency nd server response tme, be used to mesure the servce qulty. There re two populr types of MMOG rchtecture: the zoned rchtecture, n whch server mnges the gme stte for the plyers n ts dedcted zone, nd the semless rchtecture, n whch ll servers collborte such tht ech server mnges only smll pece of the gme world (Vn der Steen, 1997). In ths study, we consder only the zoned MMOG, n whch server cnnot llevte congestons by redrectng servce requests to proxy server becuse the nformton bout user s gme stte s cptve to the zone. Therefore, the problem for ths study s to determne the locton nd the cpcty of ech gme server s well s to ssgn clents to the servers, so s to blnce the cost of openng nd opertng gme fcltes whle keepng the servce qulty (mesured by gme ccess tme) t certn level. We cll ths the MMOG deployment problem herefter. Whle not much reserch hs been devoted to the MMOG deployment problem, there s rch body of Opertons Reserch lterture dedcted to the desgn of mmoble servce fcltes. For exmple, Abooln et l (2008), Bermn & Drezner (2007), nd Wng et l. (2002) took customer s perspectve nd focused on mnmzng the totl trvel nd wtng cost; Wng et l. (2002) nd Mrnov nd Serr (1998) ddressed the need of servce provders wth n emphss on mnmzng the totl fclty cost whle holdng certn level of servce qulty; nd Abooln et l. (2008b, Amr,1997, Cstllo et l. (2002), nd Elhedhl 4
(2006) held more blnced perspectve known s the Soclly Optml Servce System Desgn nd tckled the cost of servce cpcty nd the qulty of servces smultneously. In ths pper, we lso pproch the MMOG deployment problem from provder s perspectve. These problems re commonly modeled s nonlner MIP problem. However, we re ble to reduce the MMOG nonlner MIP problem to trctble set-coverng IP problem due to the unque defnton of servce qulty. 3. Model Formulton Let M = {1, 2,..., m} be the set of m cnddte host fclty loctons. We ssume tht the demnd for servce s concentrted t n Pont of Presences (PoPs) or demnd nodes N = {1, 2,..., n}, wth node genertng n ndependent Posson strem of servce requests t men rrvl rte for servce request of λ per unt of tme. Posson rrvls re commonly used n modelng the performnce of trdtonl Web pplctons nd onlne gmes (Ye & Cheng, 2006). We wll use S M to denote the set of fcltes selected s the host stes. We ssume tht ech MMOG fclty hosts sngle server wth sclble cpcty. Whle server wth hgher cpcty my llow severl physcl Ethernet nterfces, these nterfces re typclly ggregted nto one vrtul nterfce through process known s Chnnel Bondng. Therefore, wthout the loss of generosty, scled-up server could be consdered s sngle server wth n mproved servce rte. Defneµ to be the servce cpcty t fclty M. In other words, fclty M s ssumed to serve the requests t men rteµ > 0. Note thtµ here s decson vrble, whch cn lso be regrded s the men servce rte wth whch servce request s fulflled. Also note tht 1/ µ s the verge processng tme for servce request t fclty. Defne γ to be the men rrvl rte of servce requests for the fclty locted t M. Also, defne H to be the set of ll customer nodes served by the fclty locted t ste. Then, γ = λ. Assumng n exponentl probblty dstrbuton for the servce H tme, n MMOG host fclty t M cn be modeled s n M / M /1 queung system wth servce rte µ nd rrvl rte γ. Defne w ( γ, µ ) to be the verge response tme, defned s the tme from dt pcket rrvng t fclty tll return pcket redy to be sent, whch ncludes queung dely nd processng tme. In other words, w ( γ, µ ) 5
represents how quckly server cn respond to gme request nd cn be clculted s follows: 1 w ( γ, µ ) = S. µ γ Let t be the network ltency from n MMOG host fclty locted t S to clents locted t N nd defne the verge ccess tme to be the verge tme clent mchne tkes to receve gme response from the server. Gven the bove defntons, t + w ( γ, µ ) for S becomes the verge gme ccess tme for clents locted t H. To mntn certn servce stsfcton level, we ssume tht ech host fclty needs to ensure tht the verge gme ccess tme does not exceed certn mount, denoted s ϕ ; therefore, t + w ( γ, µ ) ϕ S, H. (2) (1) As mentoned before, µ s decson vrble representng the server cpcty n fclty locted t M. Let x be bnry decson vrble, whch wll tke vlue of one f the decson s to open n MMOG host fclty t cnddte ste M nd zero otherwse. Defne f to be the nstllton cost (e.g., nfrstructure cost) for openng host fclty t M, nd c to be the cost for ech unt of server cpcty. We ssume tht the gme publsher dopts type of shred-memory MIMD (Multple Instructon strem, Multple Dt strem) mchnes, whch llows more CPUs to be dded s needed. We further ssume tht these ndependent CPUs re connected through bus network; therefore, the cost for ech dded CPU unt cn be consdered dentcl (Vn der Steen, 1997). In ths pper, ech customer s ssumed to be served by sngle fclty. Let y be bnry decson vrble tht tkes the vlue of one f customers t N re to be served by the fclty locted t M nd zero otherwse. Then, γ, the rrvl rte for the server t M, cn be obtned by γ = λ y M. (3) N Wth the defntons nd the dscussons provded thus fr, the MMOG nfrstructure problem cn be formulted s the followng optmzton model: S. t. f x + c µ (4) Problem P 1 mn M M 6
y x N, M, (5-1) y = 1 N, (5-2) M µ λk yk + ε x M, (5-3) k N ( γ µ ) t + w (, ) y ϕ N, M, (5-4) x w ( γ, µ ) = M, µ λ y + 1 x N (5-5) µ 0 M, x {0,1} M, y {0,1} N, M. Equton (4), the obectve functon, mnmzes the totl fxed fclty nd vrble cpcty cost. Constrnts (5-1) ssure tht f fclty t gven locton s not opened ( x = 0) then no customer s llocted to t ( y = 0 ). Constrnts (5-2) gurntee tht ech clent on the network wll be served by one nd only one MMOG host fclty. Constrnts (5-6 3) prevent n unlmted response tme (here ε = 10 clents per unt of tme). Constrnts (5-4) ffrm tht the verge gme ccess tme n ech fclty wll not exceed certn threshold. Constrnts (5-5) mke sure tht the verge tme to servce completon n ech host fclty wll equl to 1 µ γ f the host fclty s opened ( x = 1) nd wll equl to zero otherwse (note tht when x = 0, µ = λ y = 0 s well becuse of the obectve functon N nd the constrnts n (5-1). Ths s nonlner nteger progrm, whch generlly s hrd to solve. In the next secton, we develop soluton pproch to solve Problem P1 optmlly. 4. Soluton Approch for Problem P1 Before we present the exct soluton methodology for Problem P1, consder the followng result. Lemm 1: For S, defne $ t = mx{ t} to be the mxmum network ltency from H fclty S to clent nodes n H. Also, denote be the totl rrvl rte on the network. Then e = ϕ 1 t$ nd defne N Λ = λ to 7
) The server response tme (short for the response tme herefter) t fclty S, w ( γ, µ ) = ϕ t $, nd e cn be defned to be the men rte for servce completon (ncludng dely nd processng tmes) t fclty S nd cn be expressed s 1 e = w ( γ, µ ) ; nd b) The totl fxed fclty nd vrble cpcty cost f S + c µ S cn be S. S rewrtten s f + c e c + Λ Proof: () From (2), for S, we hve w ( γ, µ ) ϕ t H. Therefore, w ( γ, µ ) = mn{ } = mx{ } H ϕ t ϕ t ϕ t H = $. Thus, 1 1 e= ϕ t$ = w ( γ, µ ). (b) From (1) nd the result of prt (), we conclude e = µ γ or µ = γ + e for S. Then µ = γ + e = λ + e =Λ+ e. S S S S H S S S = S S S Therefore, f + c µ the proof. f + c e + c Λ, whch concludes Lemm 1 shows tht the totl cost cn be rewrtten s the functon of fxed fclty nd vrble response tme (nsted of cpcty) costs nd tht mnmzng ths functon wll utomtclly mnmze the totl fxed fclty nd vrble cpcty cost. Ths lso mens tht once the response tmes n ll fcltes re decded, how the clents re ssgned wll not ffect the obectve functon provded tht the ssgnment scheme does not volte the estblshed response tme t ech fclty. Gven the bove rgument, we wll provde new formulton for selectng fclty loctons nd estblshng the response tme for ech of those selected fcltes. Then, wth the optml soluton to ths new problem, we wll fnd fesble clent ssgnment nd determne the server cpcty for ech fclty ccordngly. Defne N = { t < ϕ} to be ll the clent nodes wth network ltency to fclty S lower thn ϕ. Defne z N to be bnry decson vrble, whch tkes vlue of one f the mxmum response tme t MMOG host fclty M equls ϕ t, nd vlue of zero otherwse. For the smplcty of presentton nd the correctness of the defnton of z, we ssume tht no two clent nodes wll hve the sme network ltency for 8
ccessng fclty M. Ths ssumpton s relstc gven tht ltency s mesured by network dstnce whose representton ccurcy cn lwys be ncresed for the dscrmntng purpose. Snce equls one f fclty s locted t M nd equls zero otherwse, we hve: z N 1. (6) z N Gven Lemm 1, the totl fxed fclty nd vrble cpcty cost cn be rewrtten s 1 f z M N c ϕ t z c + M + Λ N. If we denote 1 = f + c ϕ t, the obectve functon cn be expressed s + Λ. (7) z c M N Now, consder the followng defnton nd results regrdng the coverge condtons for clent node. Defnton 1 (Cover): the MMOG host fclty locted t ste S s sd to cover (cn provde servces to) clents locted t N f t + w ( γ, µ ) ϕ. (8) Lemm 2: For M nd N, defne K = { k t tk, k N } to be ll the clent nodes wth network ltency to fclty S lower thn ϕ but hgher thn or equl to tht of node. Then, ) If = 1, then fclty covers clents t node ; nd z k K k. b) The coverge condton for clents t node N s 1 z M k N K k Proof: () Snce = 1, then z k K k k K such tht z = 1. Now, by the defnton of k zk nd K, we hve w ( γ, µ ) = ϕ t ϕ t or t + w ( γ, µ ) ϕ. k Therefore, we cn conclude, by Defnton 1, tht fclty covers clents t node. (b) Follows drectly from the result n prt (). Wth the bove defntons nd results, the new problem cn be formulted s the followng optmzton model: mn + Λ (9) Problem P 2 S. t. z c M N 9
zk 1 N, (10-1) M k K z 1 M, (10-2) N z {0,1} M, N. (10-3) It s esy to verfy tht obectve functon (9) nd constrnt (10-1) ensure tht (10-2) wll lwys hold; therefore, (10-2) becomes redundnt. To prove ths for ny M, ssume tht two dstnct clent nodes p, q N such tht z p = z q = 1 ( > 1) nd z N t p > t. Then, we cn conclude tht q K p K, whch mens tht clent node tht s q supposed to be covered by z p = z q = 1 t cost of p + q cn be covered by z p = 1 t lower cost of p. Also, cλ n (9) hs no effect on the soluton of problem P2. Thus, problem P2 cn be wrtten s the followng mnmum cost set coverng problem: mn Problem P 2 M z N S. t. (10-1) nd (10-3). Although set coverng problems re NP hrd, there re plenty of effcent soluton pproches vlble n the OR lterture. After fndng the optml MMOG host fclty loctons nd the response tme n ech fclty through solvng problem P2, we need to fnd fesble llocton scheme to ssgn clents to these fcltes wthout voltng ther respectve response tmes. Defne to be the * * z to be the optml soluton to problem P2, S = { z = 1 N } optml set of stes to host MMOG fcltes obtned from problem P2, nd { * 1 k K k } S = z = the set of optml fcltes coverng clent node. Plese note tht constrnts (10-1) ensure S { } for ll N. To fnd fesble clent llocton, we cn rbtrrly ssgn clent node to one of the fcltes n S. Next, we show tht ths clent llocton scheme would not volte the optml response tme t fclty S. Gven the defnton of S, K, nd t$, f S, then t t $. Therefore, 1 1 ϕ t ϕ t = w ( γ, µ ) $, whch mens tht lloctng clent node N to ny fclty t S would not ncrese the response tme of tht fclty. In order to hve 10
dstnct llocton scheme, we propose tht clent node be ssgned to the closest fclty n S for ll N. Defne H to be ll the clent nodes llocted to fclty S ; therefore, H = { t t k S, N }. k After obtnng the fesble clent llocton, we cn determne the cpcty requred t ech fclty. More specfclly, the requred cpcty t fclty S cn be expressed s 1 $ t H. (11) H µ = λ + ϕ For convenence, we defne C = { µ S } to be the set of requred cpctes for ll fcltes n S. Note tht we my hve dfferent fesble clent lloctons to Problem P2, whch n turn my result n dfferent cpcty cost n some fcltes, but, gven Lemm 1, the overll cpcty cost for ny fesble lloctons would lwys equl to 1 ϕ $ + Λ. S c t c To summrze the bove rguments on how to fnd soluton for the orgnl problem, we present the followng lgorthm: Algorthm 1 Step 0: For M, N, set f c t Step 1: Solve set-coverng problem P 2 nd fnd 1 = + ϕ nd K { k t tk, k N } z M, N. * Step 2: Fnd S = { z = 1 N }, nd S * { 1 = z k = } k K *. =. Step 3: For S, fnd H = { t tk k S, N }. Step 4: Fnd Step 5: Set Step 6: Stop. C, the requred cpctes for fcltes n 1 P1= f + c ϕ t$ c S + S N Z λ. S, C, H, nd P1 S, usng (11). Z re the solutons to Algorthm 1. Next, we prove tht the soluton for Algorthm 1 s n optml soluton for the orgnl problem P1. The exctness of the Algorthm 1 s bsed on the followng result. Theorem 1: Defne * Z P1 to be the optml obectve functon vlue of problem P 1. Also, defne Z to be the obectve vlue obtned by Algorthm 1. Then P1 Z = Z. * P1 P1 * Proof: Defne S, nd H to be n optml set of fclty loctons nd n optml * set of clent lloctons for the orgnl problem, respectvely. Also defne 11
= rg mx{ t } nd H *, * for S, * H we hve z k K * 1 f k=, nd S =. By defnton, for every 0 otherwse nd z = 1. Therefore, (10-1) n problem P2 holds k K k * H. In other words, the optml soluton for problem P1 s fesble soluton for problem P2. Accordng to Lemm 1, we hve 1 * P1= * f + c * ϕ $ t + c S S N Z λ. Now, by the defnton of Z P1 n Algorthm 1 nd the optmlty condtons n problem P2, we hve f c ϕ t $ * * S S 1 + proof s complete. f c ϕ t 1 + $ S. Thus, S Z = Z nd the * P1 P1 In the next two sectons, we conducted seres of experments to evlute the effcency of the exct soluton pproch presented here nd exmne ts behvor wth respect to chnges n prmeters. 5. Experment nd Results We conducted computtonl experment to ssess the effcency of the proposed soluton pproch (Algorthm 1). The lgorthm ws coded n C++, wth the excepton of Step 1, n whch the CPLEX IP Solver Verson 10.0 ws nvoked to solve Problem P 2. The progrm ws run on n Intel 2.0 GHz computer wth 2 GB RAM usng set of smulted cses generted ccordng to the settngs of the followng three mn fctors: I. The number of cnddte host fclty loctons (M) s set t four levels: M=25, 50, 75, nd 100. II. The number of demnd nodes (N) s set t four levels: N=100, 150, 200, nd 250. III. The mxmum gme ccess tme, ϕ, s set t three levels: low (15), medum (30), nd hgh (45). A plot study ws conducted frst to help determne the levels of the frst two fctors so tht the optml solutons could be obtned wthn resonble mount of tme. The three levels of the mxmum gme ccess tme were chosen bsed on the result of some studes showng tht even dely of 50 ms 75 ms could become notceble (Begbeder, Coughln, Lusher, Plunkett, Agu, & Clypool, 2004, Dck, Wellntz, & Wolf, 2005). 12
We lso set other prmeters n the followng fshon nd deferred the nvestgton of ther mpct to the next secton devoted to senstvty nlyses. Network ltency, t, ws rndomly generted from unform dstrbuton on (0, 600). The upper bound of the ntervl ws rough estmte of the ltency hlfwy cross the globe on frme rely bsed network durng the pek usge perod. Servce request rrvl rte λ N ws rndomly generted from unform dstrbuton on [1,000, 10,000]. We ssumed tht server could support up to 600 concurrent users (Dolber, 2007, 2007b, 2007c; Smed, Kukornt, & Hkonen. 2001) nd tht t ws desrble to keep the mxmum gme ccess tme t 60 ms. Hence, we set the upper bound to 10,000 servce requests per second. Unt server cost ws set to $1.00 per request nnully. We estmted tht server costs rnge from $5,000 to $10,000 per yer. Wth mxmum of 10,000 servce requests per second, the nnulzed unt server cost for one request per second would be between $.50 nd $1.00. We, however, fxed the unt server cost t $1 for ths experment nd then nvestgted the mpct of ts vrtons lter becuse the cost of server should be ble to be estmted rther ccurtely. Fclty fxed cost on [25,000, 100,000]. f M ws rndomly generted from unform dstrbuton The ntervl of fclty fxed cost ws chosen to suggest dverse rnge of fclty costs mong cnddte fclty loctons. Ths experment represented 4*4 *3 fctorl desgn. Ech experment combnton ws replcted 10 tmes for totl 480 test cses. Our obectve n ths experment ws to mesure how the three mn fctors ffect the computtonl speed of Algorthm 1, the number of selected fclty loctons, the overll cost, nd the clent s expected ltency. An nlyss of vrnce (ANOVA) ws crred out for ech performnce mesurement to dentfy sgnfcnt mn nd ntercton effects. Tble 2 showed the verge CPU tmes for ech combnton of ten test cses. The verge CPU tmes requred rnged from frcton of second for smller test cses to nerly hlf n hour for the lrgest cse. It s esy to understnd the rse n computtonl tmes wth respect to the ncrese n the number of cnddte fclty loctons (M) nd the number of demnd nodes (N). However, the mpct of mxmum gme ccess tme,ϕ, s much more profound nd wrrnts further nvestgton. The ANOVA result n Tble 3 showed tht ll mn nd ntercton effects were sttstclly sgnfcnt. It lso reveled tht, mong ll sgnfcnt effects, ϕ hd the 13
strongest explntory power (hd the lrgest men squre errors nd F-vlue) n ccountng for the vrtons n CPU tmes. As shown n Tbles 3b-3d, smlr concluson bout the effect of ϕ could be ppled to the other three performnce mesures. In Fgure 1, we further explored how dfferent levels of mxmum gme ccess tme ffect Algorthm 1 s computtonl speed. More specfclly, we devsed sttstc clled the CPU rto defned s CPU rto = CPU fctor level / CPU bse cse fctor level, where ϕ = 30 s the bse cse for every M nd N combnton. Fgure 1 reveled tht when ϕ ws set t 15 ms, the gn n computton speed ws less thn 30%. However, the computtonl tme for ϕ t 45 ms skyrocketed to n verge of 155 tmes hgher thn tht for ϕ t the bse level. The exponentl ncrese n computtonl tme could be lrgely ttrbuted to the rpd ncrese n the number of bnry vrbles requred to solve the set-coverng problem n Step 1. In ddton to the computtonl speed, ϕ lso ffected mny spects of the MMOG deployment. To llustrte ths, we used sttstcs smlr to tht used n Fgure 1 n tht the performnce mesure t ϕ = 30 ws used s bse level for performnce comprsons. Fgure 2, whch showed the reltonshp between the dfferent levels of ϕ nd the number of loctons selected, reveled tht ncresng the mxmum gme ccess tme would result n fewer server loctons. Ths ws becuse hgher level of ϕ would llow servers to hve slower servce rtes nd/or permt gme request to trvel longer dstnce to rech ts desgnted server. In ether cse, ϕ would hve n mpct on the degree of network congestons. In ddton, gven the ssumpton of constnt server cost per request n ths experment, chnges n the number of loctons would ffect the totl fxed fclty cost, nd, therefore, the overll cost s shown n Fgure 3. As depcted n Fgure 4, nother consequence of vryng ϕ ws tht longer mxmum gme ccess tme would result n longer expected ltency for the clents, thus lower servce qulty. These experment results suggested n mportnt mngerl mplcton. Tht s, the proposed pproch llows the mngement to strke blnce between the nfrstructure cost nd the qulty of servce through dustng the mxmum gme ccess tme. 6. Senstvty Studes nd Results The proposed model n (9) through (10-3) hs few prmeters tht mght be crtcl to ts performnce. In the lst experment, we nvestgted the effects of prmeters tht mnly chnge the number of constrnts nd the number of vrbles of the set-coverng 14
problem. In ths secton, we conducted three senstvty nlyses, ech of whch focused on the effect of one of the prmeters n the obectve functon: servce request rrvl rte ( λ ), fxed fclty cost ( f ), nd nnulzed unt server cost (c). Our obectve ws twofold: (1) to vldte the fndngs n Experment I nd (2) to offer ddtonl nsghts nto the pros nd the cons of the proposed model. Unlke n Experment I where λ nd f were ssumed to be unformly dstrbuted nd c ws fxed t $1, n the senstvty studes, they were set to followng three levels: λ = 1,000, 5,000, nd 9,000; f = 25,000, 50000, nd 75, 000; c = $.5, $1.0, nd $1.5. Snce the effects of M, N, nd ϕ were known through the prevous experment, we generted only subset of test cses used n Experment I bsed on the followng settngs: M = 75 nd 100; N = 100, 150, 200, nd 250; ϕ = 30; Therefore, ech senstvty study ws 2*4*1*3 fctorl desgn. We lso replcted ech experment combnton 10 tmes for totl of 240 experment runs per nlyss. Other prmeter settngs unless forementoned were kept the sme s those n Experment I. However, performnce evlutons were only bsed on the rtos of computtonl speed, the number of loctons selected, expected ltency, nd overll cost to cncel out effects due to confoundng fctors so tht ny performnce dfferences could be ttrbuted solely to the ntended prmeter chnges. The results were shown n Fgures 5-8 where prmeter settng level 2 ws lwys used s bse level for clcultng the rtos, nd the followng conclusons could be mde: We could nfer from Fgure 5 tht the dfferences n computton speed due to chnges n λ, f, nd c were ether nl or not sttstclly sgnfcnt. Ths s becuse the totl rrvl rte ws only constnt n the obectve functon nd chnges n f nd c ffected only the serch pth not the soluton spce. In the bsence of budget nd cpcty constrnts, the number of selected fclty loctons ws not t ll ffected by the chnges n the obectve prmeters. Insted, ny chnges n these prmeters were only reflected n the overll cost. Ths could be 15
verfed by exmnng Fgures 6 nd 7. Not ncludng these ddtonl constrnts, however, s not wekness of the proposed model. Frst, these constrnts would drstclly ncrese the complexty of the set-coverng problem nd would possbly render t ntrctble even for md-szed MMOG deployment problem. Second, nother dffculty for ncludng budget nd cpcty constrnts n ddton to the qulty constrnts n (5-4) s tht ll of them mght hve to be delt wth explctly s these constrnts mke the converson to the set-coverng problem dffcult, f not mpossble. Rther, the proposed model ffords mnger to blnce cost nd qulty of servce v the mxmum ccess tme prmeter s dscussed n Experment I. In effect, the proposed model llows ths complex problem to be decomposed nto severl set-coverng problems wth dfferent mxmum ccess tmes. As shown n Fgure 8, the effect of chnges n the obectve prmeters on clent s expected ltency ws neglgble. Becuse these prmeters dd not ffect the locton selectons nd the proposed lgorthm lwys ssgned clent to hs/her nerest server, the neglgble ltency dfference ws due to the exstence of lterntve solutons n locton selectons. Ths reveled n mportnt trt of the proposed model -- less ccurte cost nd demnd estmtes would not pprectvely ffect the decson of server loctons. In ll, the senstvty studes not only ffrmed the vldty of the fndngs n Experment I, but lso reveled few nherted dvntges n the proposed model. In ddton, these experments showed tht the proposed lgorthm ws cpble of obtnng n optml soluton to decent szed MMOG deployment problem nd the soluton should be ble to wthstnd the test of emprcl dt becuse the model depended only on the ssumpton of exponentl dstrbuton of servce tme nd Posson strem for servce request rrvl rte. 7. Concludng Remrks nd Future Reserch The MMOG ndustry hs become one of most vbrnt e-commerce segments due to ts ppel to the younger generton globlly. As the competton ntensfes, gme publsher must mtgte the dverse effect of network ltency. In ths study, we proposed non-lner mthemtcl model for deployng n MMOG system on the Internet. The proposed model ws subsequently converted to set-coverng problem, nd n exct lgorthm ws developed. We lso proved tht the lgorthm ws ble to obtn the optml soluton to the 16
orgnl problem. An experment ws then crred out to evlute the effectveness of the lgorthm bsed on four performnce mesurements. Importnt conclusons from the experment ncluded: (1) the lgorthm ws cpble of solvng good szed problem wthn resonble mount tme; nd (2) mxmum ccess tme, whch could drectly ffect the degree of network congestons, could be used for mnger to blnce the nfrstructure cost nd the qulty of servce. The fndngs of the experment were vldted v three senstvty nlyses, whch lso shed lghts on some nterestng propertes of the proposed model. Whle we presented novel pproch to the MMOG deployment problem, mny ssues hve yet to be ddressed. Frst, ths study dd not consder deployng gme n compettve envronment, n whch the mportnce of prcng, ltency, nd server cpblty would be heghtened nd good model must hve the provson for mnger to use them s compettve wepon. Second, whle the proposed lgorthm ws shown to be effectve for md-szed problem, heurstc lgorthm must be developed n order to del wth lrgeszed problem. Thrd, to mntn ts trctblty, the proposed model dd not nclude constrnts for budget, cpcty, nd so forth. The trdeoffs for the ncluson of such constrnts should be exmned. It lso only consdered the mnmzton of the cost. The trdeoffs for other obectve functons nd the ncluson of budgetry nd cpctted constrnts should be exmned. Fourth, whle our experments showed tht mnger could explore the settng of mxmum ccess tme to strke blnce between nfrstructure cost nd qulty of servce, t s possble to develop proft mxmzton model for obtnng the optml mxmum ccess tme n leu of the brutl force pproch suggested n ths study. Ffth, ths study focused only on the zoned MMOGs. An nvestgton nto the deployment problem concernng the semless MMOGs would enhnce the contrbuton to the onlne gme ndustry. Sxth, to study the effccy of the heurstcs nd the chrcterstcs of the model, we used smulted dt. Despte our best effort to generte resonble nd representtve dt, we cknowledge tht the study mght beneft from usng emprcl dt. Lstly, the proposed model nd lgorthm form generl optmzton methodology. We wll explore ther pplcblty to the desgn of other servce systems. 17
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Tble 1: Summry of Notton Sets M set of cnddte fclty loctons M = {1, 2,..., m}, N set of demnd ponts N = {1, 2,..., n}, S set of fcltes selected s the host stes, H set of ll customer nodes served by the fclty locted t ste, N set of the clent nodes wth ltency to fclty S lower thn mxmum gme ccess tme, S set of stes to host MMOG fcltes obtned from Algorthm 1, S set of optml fcltes coverng clent node N, obtned from Algorthm 1. Prmeters λ men rrvl rte of servce request per unt of tme t demnd pont N, γ men rrvl rte of servce requests for the fclty locted t M, t network ltency from the MMOG host fclty S to demnd node N, t$ mxmum ltency from fclty S to clent nodes n H, ϕ mxmum ccess tme requred for ech host fclty. f fxed nstllton cost for openng host fclty t ste M, coeffcents of z n the obectve functon n Problem P2, = f + c ϕ t c cost for ech unt of server cpcty. Decson Vrble x bnry vrble to ndcte whether new fclty t M s opened, µ servce cpcty t fclty M, z bnry vrble to ndcte whether the mxmum response tme t fclty M equls ϕ, t y bnry vrble to ndcte whether customers t N re served by the fclty t M. Computed Vlues Z optml obectve functon vlue of problem P 1, * P1 Z P1 obectve functon vlue obtned from Algorthm 1, Λ totl rrvl rte on the network, e men rte for servce completon (ncludng dely nd processng tmes) t fclty S, µ cpcty t fclty S obtned from Algorthm 1, w ( γ, µ ) verge response tme t MMOG host fclty S. 1, 21
Tble 2: Soluton Speeds of Algorthm 1 M N ϕ Averge CPU Tme (n seconds) M N ϕ Averge CPU Tme (n seconds) 25 100 15 0.0295 75 100 15 0.0438 25 100 30 0.0295 75 100 30 0.0674 25 100 45 0.0295 75 100 45 0.2988 25 150 15 0.0431 75 150 15 0.0610 25 150 30 0.0325 75 150 30 0.0781 25 150 45 0.0386 75 150 45 0.6038 25 200 15 0.0436 75 200 15 0.0780 25 200 30 0.0451 75 200 30 0.3457 25 200 45 0.0468 75 200 45 2.5235 25 250 15 0.0470 75 250 15 0.1015 25 250 30 0.0486 75 250 30 0.1189 25 250 45 0.0563 75 250 45 25.8682 50 100 15 0.0386 100 100 15 0.0534 50 100 30 0.0373 100 100 30 0.1705 50 100 45 0.0436 100 100 45 2.4085 50 150 15 0.0470 100 150 15 0.0716 50 150 30 0.0518 100 150 30 0.4797 50 150 45 0.0642 100 150 45 13.3569 50 200 15 0.0630 100 200 15 0.1000 50 200 30 0.0626 100 200 30 0.8130 50 200 45 0.0938 100 200 45 368.7879 50 250 15 0.0780 100 250 15 0.1334 50 250 30 0.0828 100 250 30 1.0198 50 250 45 0.0970 100 250 45 1775.1040 22
Tble 3: ANOVA for Soluton Speed Type III Sum of Source Squres df Men Squre F Sg. Corrected Model 31875985.750() 47 678212.463 18.011.000 Intercept 1002184.527 1 1002184.527 26.614.000 Cnddte Locton (CL) 2894722.282 3 964907.427 25.624.000 Clent Node (CN) 1819471.843 3 606490.614 16.106.000 Mxmum Access Tme (MAT) 1998648.728 2 999324.364 26.538.000 CL * CN 5253896.367 9 583766.263 15.503.000 CL * MAT 5776647.070 6 962774.512 25.568.000 CN * MAT 3665836.184 6 610972.697 16.225.000 CL * CN * MAT 10529056.157 18 584947.564 15.534.000 Error 16267399.353 432 37656.017 Totl 49145992.198 480 Corrected Totl 48143385.104 479 R Squred =.662 (Adusted R Squred =.625) 23
Tble 3b: ANOVA for Overll Cost (n Thousnds) Type III Sum of Source Squres df Men Squre F Sg. Corrected Model 196378108.217() 47 4178257.622 497.276.000 Intercept 2292052282.903 1 2292052282.903 272789.165.000 Cnddte Locton (CL) 17399837.214 3 5799945.738 690.282.000 Clent Node (CN) 87637875.528 3 29212625.176 3476.748.000 Mxmum Access Tme (MAT) 60974206.678 2 30487103.339 3628.430.000 CL * CN 3321852.301 9 369094.700 43.928.000 CL * MAT 25059246.935 6 4176541.156 497.072.000 CN * MAT 700380.383 6 116730.064 13.893.000 CL * CN * MAT 1466230.612 18 81457.256 9.695.000 Error 3629787.084 432 8402.285 Totl 2493068080.597 480 Corrected Totl 200007895.301 479 R Squred =.982 (Adusted R Squred =.980) 24
Tble 3c: ANOVA for the Number of Selected Fclty Loctons Type III Sum of Source Squres df Men Squre F Sg. Corrected Model 68701.955() 47 1461.744 558.511.000 Intercept 524228.793 1 524228.793 200300.332.000 Cnddte Locton (CL) 11981.087 3 3993.696 1525.934.000 Clent Node (CN) 6698.308 3 2232.769 853.109.000 Mxmum Access Tme (MAT) 33997.962 2 16998.981 6495.068.000 CL * CN 1791.732 9 199.081 76.066.000 CL * MAT 13214.501 6 2202.417 841.512.000 CN * MAT 402.104 6 67.017 25.606.000 CL * CN * MAT 738.823 18 41.046 15.683.000 Error 1130.636 432 2.617 Totl 594270.000 480 Corrected Totl 69832.592 479 R Squred =.984 (Adusted R Squred =.982) 25
Tble 3d: ANOVA for Expected Ltency Type III Sum of Source Squres df Men Squre F Sg. Corrected Model 8967.304() 47 190.794 450.123.000 Intercept 77317.351 1 77317.351 182408.178.000 Cnddte Locton (CL) 300.459 3 100.153 236.282.000 Clent Node (CN) 87.731 3 29.244 68.992.000 Mxmum Access Tme (MAT) 8485.903 2 4242.951 10010.030.000 CL * CN 13.779 9 1.531 3.612.000 CL * MAT 45.549 6 7.591 17.910.000 CN * MAT 23.173 6 3.862 9.112.000 CL * CN * MAT 6.002 18.333.787.717 Error 183.112 432.424 Totl 86589.488 480 Corrected Totl 9150.415 479 R Squred =.980 (Adusted R Squred =.978) 26
Fgure 1: The Impct of Mxmum Ltency on the Soluton Speed Fgure 2: The Impct of Mxmum Ltency on the Number of Selected Fclty Loctons 27
Fgure 3: The Impct of Mxmum Ltency on the Overll Cost. Fgure 4: The Impct of Mxmum Ltency on the Expected Ltency 28
Fgure 5: The Impct of Chnges n Unt Server Cost, Fxed Fclty Cost, nd Servce Request Arrvl Rte on the Soluton Speed Fgure 6: The Impct of Chnges n Unt Server Cost, Fxed Fclty Cost, nd Servce Request Arrvl Rte on the Number of Selected Fclty Loctons 29
Fgure 7: The Impct of Chnges n Unt Server Cost, Fxed Fclty Cost, nd Servce Request Arrvl Rte on the Overll Cost Fgure 8: The Impct of Chnges n Unt Server Cost, Fxed Fclty Cost, nd Servce Request Arrvl Rte on the Expected Ltency 30