An Analytical Model of Web Server Load Distribution by Applying a Minimum Entropy Strategy

Transcription

1 Internatonal Journal of Coputer and Councaton Engneerng, Vol. 2, No. 4, July 203 An Analytcal odel of Web Server Load Dstrbuton by Applyng a nu Entropy Strategy Teeranan Nandhakwang, Settapong alsuwan, Jesada Svaraks, and Navneet adan Abstract Ths paper presents an analytcal odel and the way of sulaton for dstrbutng workload on a dstrbuted web server syste. The ncrease n the Internet traffc has also necesstated the conventonal Doan Nang Servce (DNS) to operate at a uch lower effcency. Aong a nuber of probles assocated wth the DNS, a key proble has to do wth the authortatve DNS not beng able to process coplete knowledge of the proxty. Ths akes the authortatve DNS less effectve n ontorng server avalablty and routng ncong requests around faled servers. The workload dstrbuton strategy on the other hand, keeps track of the state and health of the web server. Ths avods connecton delay due to, for exaple, a faled server, whch can be teporarly by passed by workload dstrbuton. Fro a odelng standpont, the conventonal DNS assues equal queue sze for each web server n a round-robn settng. Under load balancng, the queue sze for each web server dffers based on the probablty of accessng that server. Ths probablty s based on such factors as the geography, server health, server response, server threshold, sesson capactes, and the round trp te. In ths paper, both conventonal and global workload dstrbuton strateges are developed and copared based on a fnte set of practcal traffc scenaros. Index Ters Doan nae server, entropy, workload dstrbuton strategy, round-robn settng. I. INTRODUCTION Increasngly copanes are turnng to World-Wde-Web (WWW) as an opton channel for software dstrbuton, onlne custoer servce, and busness transactons. In the odern day, the role perfored of web server s vtal to busnesses. Successful copanes need the capacty to cater to llons of transactons on ts server. Intally, several copanes reported that they who could not support the colossal volue of transactons specfcally on days when stock arkets experenced a crash []. The phenoenal growth n popularty of the Internet has necesstated nternet traffc to be ontored and controlled. Ths growth has posed the need for research delberated to decrease the volue of nternet traffc orgnated web users and servers, by usng Doan Nae Server (DNS). Ths paper consders a global workload dstrbuton strategy on a dstrbuted web server syste []-[3]. The ost coon conventon dstrbuted web server anuscrpt receved February 4, 203; revsed Aprl 7, 203. Teeranan Nandhakwang s wth the Securty and ltary Analyst n Thaland (e-al: jesada.s@nbtc.go.th). Settapong alsuwan s wth the Vce Charan of Natonal Broadcastng and Telecouncatons, Bangkok, Thaland. Jesada Svaraks and Navneet adan are wth the Natonal Broadcastng and Telecouncatons Cosson. syste s based on round-robn doan nae resoluton (RR-DNS), whch assgns HTL docuent requests to web server [3]. The round-robn technque s useful specfcally n the case that HTTP requests access HTL docuent of a standard sze and the load and servce rate of web servers are farly coparable [4]. Nevertheless, the web servers are heterogeneous systes hence processng nodes are expected to have dsslar processng speeds. They can leave and jont the syste resource pool at any te [4]. Therefore dynac strateges are desrable to balance workload aong the web servers [5]. The drawback of the round-robn DNS s that address-cachng echans perts DNS control on a relatvely sall porton of the requests. An uneven dstrbuton of clents requests fro dverse nuber of doans causes balance so when any clents fro one sngle doan are assgned to the sae sngle server these results n overload of the web server [3]. II. SYSTE ODEL The syste s odeled by open queung network, whch s ade of nuerous nterconnected queued servers. An excessve nuber of requests are entered nto the syste ndependently. Therefore ths research consders a dstrbuted web server syste archtecture that uses DNS as a typcal centralzed scheduler, apples soe schedulng strategy n routng the requests to the ost sutable web server []. A well defned and transparent archtecture s obtaned fro a sngle vrtual nterface to the outsde world, at the least at URL level [4], as shown n Fg.. Fg.. Syste odel and network flow. Network s fault free and strongly connected. However, the traffc of the network s varous. It depends on the request fro web clent. Also, web servers can leave and jon the syste resource pool at any te [8]. They are no councaton between web servers. DOI: /IJCCE.203.V

2 Internatonal Journal of Coputer and Councaton Engneerng, Vol. 2, No. 4, July 203 Ths research denotes the average page response te ER [ ] by. Ths ay wrte ER [ ] as the su of the average total watng te, the average councaton delay, and the average DNS synchronzaton; that s, R]= W]+ D]+ S ] () where EW [ ] denotes the average watng te, EDdenotes [ ] the average councaton delay, and ES [ ] denotes the average DNS synchronzaton. To understand workload behavor on the dstrbuted web server syste (physcal or logcal connecton), the research adds two fcttous statons to the network: request and receve. The request staton generates all external arrval and the receve staton receves all custoers leavng the web server cluster. Ths s shown n Fg. 2. Ths paper uses q e ( q e ) [5], [6], and [7] to denote the probablty that an external arrval s drected to web server. Slarly, ths paper uses to denote the probablty of the task that fnshes t servces at web server and leaves the web cluster. Fro [5], [8], [9], [0], [], and [2], the traffc equaton for the network s gven by: j q j. Where denotes the average arrval rate at web server, denotes the external arrval nto web server fro a Posson strea ( qe ). Then. qo The average councaton delay and the average DNS synchronzaton te are the average te that packet spent watng for usng channel. They are gven by [8] and []: T] xk ( ) where ET [ ] s the average essage delay, x s the average length of a data packet, and K s the capacty channel at channel. Usng (4), then and D] x ( DKD ) N S] xsks ( ) where x D denotes the average length of a data packet that send and receve between web server and web clent, K D denotes the capacty channel at channel between web server and web clent, x S denotes the average length of a data packet that send and receve between DNS and web server, K denotes the capacty channel at channel between S DNS and web server, and N denotes nuber of DNS n DNS cluster. Ths research assues the capacty channel between DNS to web server and web clent to web server are equal, also the average length of a data packet fro web server to web clent and web server to DNS are equal. Usng (), (3), (5), and (6), therefore: (4) (5) (6) R] xdk D ( ) 2 ( ) xd K D ( )( ) j xs K j Sj j ) N ( (7) Fg. 2. Represent of an open web server queung network. Ths paper uses qj to denote the routng probablty that on leavng web server to web server j. However, ths odel, the web servers do not councate to each other. Therefore, q 0 and. It follows [7], [0], and [4] that the j average watng te n the network s gven by: where W s the servce rate, and (2) ( ) The utlzaton of web server s gven by s the traffc ntensty. U. In ths odel, the servce rates of the web server are load-dependent [] and [5]. Then C (n), where s called the basc rate servce rate. Ths research uses C (n) to denote the capacty functon where n denotes populaton vector, and by defnton C ( ). Usng (2) therefore: W ] ( ) (3) Therefore (7) s The average page response te corresponds to nterval elapsed between the subsson of the web clent request for gven page and the arrval at the clent of all objects correspondng to the page request. It ncludes Transsson Control Protocol (TCP) establsh connecton te, delays at web server, network transsson te [5]. III. A INIU ENTROPY STRATEGY FOR WEB SERVER LOAD DISTRIBUTION The uncertanty equaton s derved for ths group of objects whch s an equaton fro Shannon. The nforaton theoretc heurstc s analyzed at each decson level thus, decreasng the lower bound for the sub proble. In 948, a easure of uncertanty of a dscrete stochastc syste known as entropy was ntroduced [8], [9], and [4]. For a probablty dstrbuton p defne on a fnte set [ n ],...,n the Shannon entropy of p s defned by wth the conventon that 0log 0 0. H ( p) s k P( )log P( ) Entropy s now an essental concept n decson akng. (8) 404

3 Internatonal Journal of Coputer and Councaton Engneerng, Vol. 2, No. 4, July 203 Addtonally, entropy s a constructve nforaton theory whch s generally adopted n the nforaton theory s used as a easure for the uncertanty of a dscrete probablty densty functon. Snce ths defnton s slar to the one used n statstcal echancs, ths easure of uncertanty s labeled entropy. When all probabltes are equal, the entropy reaches ts axu or nu. Entropy s adopted n the case that the decson atrx for a set of optons contans a certan aount of nforaton. Therefore, entropy s adopted as a tool n certanty level evaluaton. Entropy s ost practcal n nvestgate the dfferences aong data sets. Although entropy has ncreasngly adopted n these past years for a varety of cases n nforaton theory, t has great potental as a decson-akng tool untl now ths has not been fully exploted. Ths study underlnes the functonal capablty of entropy whch ncludes the dervaton of probablty dstrbutons. Ths research proposes a strategy that as at provng the perforance of dstrbuted load to web servers that s lkely to perfor poorly schedulng algorth RR-DNS. The proposed schedulng strategy uses nforaton fro each web server to ake the decson n the appng of URL naes to IP-address of web servers, as llustrated n Fg. 3. Ths decson proble s solved wth a greedy technque, whch s used the entropy functon as weghted lnear functon to decde the best web server. The entropy functon s an uncertanty easure at the web server for the decson n each request. Therefore H ( X j,..., X n ) P( x )log P( x ) () k jk jk j k OPT ( H ) n ( H ( X,..., X )) (2) j n j where OPT H ) s the web server that has nu entropy. ( j It follows [6], the entropy functon s nu, n fact equal to zero, when ts values s certan, an observaton can yeld a good condton on the web server. Slarly, the entropy functon axu when the rando varable s unforly dstrbuted; the outcoe of the web server has axu uncertanty. Ths research easures entropy level by server atrces fro each web server to calculate the desred relatve workload dstrbuton workload between the dstrbuted web servers. Fg. 4 shows an exaple of certanty level n each web server. The workload wll be assgned to the web servers are depended on the entropy. The web server wth saller entropy wll be assgned workload ore than the web server wth hgher entropy. j k Fg. 4. Web server entropy easureent. Fg. 3. DNS-Based web server load balancng wth nu entropy polcy. Let H be entropy of a web server wth server atrces j, j and let x jk be a set of utually exclusve events of web server wth server atrces j. The entropy functon of web server wth server atrces j, H X ), s defned as j k k jk j ( k H ( X ) P ( x )log P( x ) (9) In ths paper, the server atrces (e.g., TTL, health condton, sesson capacty threshold, round-trp te, and geographcal regon) are utually exclusve events, then [8] and [4] H j ( k j j 2 j k X,..., X jk ) H ( X ) H ( X )... H ( X ) (0) jk IV. PARAETER AND EXPERIENTS DESIGN Ths secton presents the experent wth ther base value and dstrbutons that characterze the entre syste and the DNS wth nu entropy polcy. Table I suarzes the syste and workload paraeters that copare the perforance of the nu entropy load balancng strategy wth the tradtonal RR-DNS, the RR- DNS [3] and [0]. HTL docuent response te s a ajor ndex to easure the perforance of the load balancng strategy. In partcular, lookng at the nu average page response te, ths can deduce whether the load balance or not. Hence, the perforance of several schedulng polces s evaluated by focusng on the nu page response te observed durng the sulaton runs. Ths experent dvdes global DNS cluster nto sall regons. When a clent requests the HTL docuent fro web server, t sends the query to nteredate nae server. Both Interedate nae server and clent s the sae regon, and assue that the nuber of hop to reach web server fro DNS and clent are slar. Entre syste operates wth no cache. Each DNS, the nu entropy load balancng polcy, sends the queres to each web server and other DNS for updatng ther nforaton. Server etrcs on each DNS 405

4 Internatonal Journal of Coputer and Councaton Engneerng, Vol. 2, No. 4, July 203 contans wth web server round trp te, TTL to reach the web server, and response te. TABLE I: PARAETERS OF THE SYSTE Category Paraeter Value(default) DNS Nuber of DNS 3 Web Server Nuber of Web 5 Server Basc Servce Rate packet/second Workload Nuber of HTTP 000 Requests Docuents Sze 0 00 packets Server atrces Round Trp Te s. Response Te 0 s. TTL DNS wth round-robn strategy. Ths fgure shows that both polces guarantee that the axu HTL docuent response te s below 550 s. The 90-percentle of the nu entropy polcy s less than 225 s and the 50-percentle s below 25 s. The RR polcy has slghtly worse perforance wth the 90- percentle s less than 450 s., and the 50-percentle s less than 275 s. The propose ethod can prove the average response te uch further by tunng the web server atrces to the workload level. To archve ths goal, the experent needs to ontor the server atrces, choosng nu entropy web server to assgn the heavly load and choosng axu entropy web server to assgn lght load. Fg HTL docuents average response te. Ths research uses load dstrbuton and cuulatve dstrbuton of the HTL docuent response te as the perforance crteron, because n a hghly varable syste t s ore sgnfcant than average values [4] and [5]. For the perforance evaluaton of proposed polcy, ths research carred out a large nuber of experents. The gold s to easure how effectvely the nu entropy load balancng that controls only a very sall percentage of address resoluton requests can nze the workload of the dstrbuted web server. Fg. 5 shows the HTL docuent average response te of each strategy n 000 HTTP docuent requests. The average of the HTL docuent response te of the nu entropy strategy s less than the RR-DNS. Fg. 6. A nu entropy load dstrbuton strategy and Round-Robn strategy. Fg. 7. Cuulatve dstrbuton of HTL docuent average response te. TABLE II: THE EXPERIENT STATISTICAL VALUES Polcy Average nu axu Varance Std.Dev nu Entropy 2 4 Round-Ro bn 2 3 Fg. 6 shows load dstrbuton of 000 HTL docuent request on nu entropy and round-robn strategy. In the nu entropy polcy, 40-percent of the requests are between s., 4-percent of the request are between s., and 46-percent are greater than 50 s. In the other hand, round-robn polcy, 2-percent are between s. and s., 4-percent of the requests are between s., -percent are greater than 500 s. and the rest are spread fro 50 s. to 450 s. Fg. 7 copares the cuulatve dstrbuton for the DNS proxty usng nu entropy strategy and tradtonal V. CONCLUSION In ths paper, the experent odfed the tradtonal schedulng strategy to the Doan Nae Server (DNS), proposed new polcy, and studed the pact for a dverse range of scenaros. The new approach proposed s based on the entropy functon of the web server atrces (e.g., health condton, sesson capacty threshold, round-trp te, and geographcal regon). The tradton round-robn DNS (RR-DNS) polcy s not applcable to network wth dynac traffc scenaros. The experents of new polcy showed that they are able to provdng sutable web server n each request to the web clent. The entropy strategy can be useful for analyzng and odfyng an exstng syste, and assessng other newly proposed strateges. In the near future, the experent wll proved the technque to dstrbutng workload on the dstrbuted web server syste whether local 406

5 Internatonal Journal of Coputer and Councaton Engneerng, Vol. 2, No. 4, July 203 or global connecton. The research s also gong on buldng a sulaton envronent to have ore valdaton for the obtaned results. REFERENCES []. Colajann, P. S. Yu, and D.. Das, Analyss of task assgnent polces n scalable dstrbuted web-server systes, n Proc. IEEE Transactons on Parallel and Dstrbuted Systes, vol. 9, no. 6, pp , 998. [2] V. Cardelln,. Colajann, and P. S. Yu, Geographc load balancng for scalable dstrbuted web systes, n Proc. The 8th Internatonal Syposu on odelng, Analyss and Sulaton of Coputer and Telecouncaton Systes, [3] V. Cardelln, Dynac load balancng on web-server systes, n Proc. IEEE Internet Coputng, vol. 3, no. 3, pp , 999. [4] D. Andresen, T. Yang and O. Ibarra, Toward a scalable dstrbuted WWW server on workstaton clusters, Journal of Parallel and Dstrbuted Coputng, 997. [5] P. S. 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Patel, Perforance odelng of councaton networks and coputer archtectures, Internatonal Coputer Seres, Addson Wesley Longan, Inc., 992. [] K. Kant and.. Srnvasan, Introducton to Coputer Syste Perforance Evaluaton, cgraw-hll Hgher Educaton, 992. [2] L. Klenrock, Queung systes: Theory, vol. I, Wley, John and Sons, Incorporated, 975. [3] L.Klenrock, Queung systes: Theory, vol. II, Wley, John and Sons, Incorporated, 976. [4] T. G. Robertazz, Coputer Networks and Systes: Queung Theory and Perforance Evaluaton, Sprnger-Verlag New York, Incorporated, [5] R. Jan, The art of coputer systes perforance analyss: Technques for experental desgn, easureent, sulaton, and odelng, Wley, John and Sons, Incorporated, 990. [6]. L and P. Vtany, An Introducton to Kologorov Coplexty and Its Applcatons, Sprnger-Verlag New York, Incorporated, 997. [7] H. Kaeda, J. L, C. K, and Y. Zhang, Optal Load Balancng n Dstrbuted Coputer Systes, Sprnger-Verlag New York, Incorporated, 997. Teeranan Nandhakwang was born n Thaland. He receved hs PhD n Optzng Web Server Load Dstrbuton wth Evolutonary Coputaton fro Florda Insttute of Technology, USA n He receved hs S. In Engneerng anageent fro Florda Insttute of Technology, USA and copleted hs BSc fro Kng ongkut's Insttute of Technology Ladkrabang, Thaland n 998. He currently works as a Securty and ltary Analyst n Thaland. Hs prevous appontents were as a counter-terrorst assault tea leader, Syste Analyst Offcer, Coand and Control Syste s Network Engneer, Instructor at Peace Operatons Center, and Research Fellow at Strategc Studes Center. He joned the Natonal Defense College, Royal Tha Ared Forces Head Quarters n 200, and s the Deputy Drector of Poltcal and ltary Affars Dvson. Settapong alsuwan was born on 24 th arch 966 n Bangkok, Thaland. He receved hs PhD n electrcal engneerng (telecouncatons), specalzng n oble councaton systes fro Florda Atlantc Unversty (State Unversty Syste of Florda), Boca Raton n He receved an Sc n electrcal engneerng n oble councatons syste, fro George Washngton Unversty n 996, an Sc n electrcal engneerng n telecouncaton engneerng fro Georga Insttute of Technology n 992 and a BSc n electrcal engneerng fro the Chulachoklao Royal ltary Acadey, Nakhon-Nayok, Thaland n 990. He served n the Royal Tha Ared Forces for ore than 25 years and s currently the Vce Charan of Natonal Broadcastng and Telecouncatons, Bangkok, Thaland. Hs research nterests are n effcent spectru anageent and Telecouncatons polcy and anageent n Thaland. Col. Dr. Settapong alsuwan Settapong alsuwan s currently the Elected Vce Charan and Board eber n the Natonal Broadcastng and Telecouncatons Cosson, Thaland Jesada Svaraks was born on 2 th ay 970 n Bangkok, Thaland. He receved hs SEE degree fro Oklahoa State Unversty n 996 and BEng fro Kng ongkut''s Insttute of Technology, Thaland. He copleted hs PhD n electrcal engneerng at Florda Atlantc Unversty, Boca Raton, FL n 200. Snce 20, he has been workng n Natonal Broadcastng and Telecouncatons Cosson as the Secretary to the Vce Charan. Hs PhD work s on the syste aspects of Bluetooth, WLAN and oble IP/CDPD. Hs current research nterests are n telecouncaton plannng and related syste analyss and effcent spectru anageent. He s a eber of Tau Beta P, Florda Epslon and was an Honorary Advsory s Charan of Scence & Technology cottee of Parlaent n Navneet K. adan was born n Bangkok, Thaland on 22 nd Aprl, 987. She receved her Bachelor of Busness Adnstraton n nternatonal busness anageent fro ahdol Unversty n 2008, and receved aster of Scence degree n strategc anageent and arketng, ddlesex unversty, London, Unted Kngdo. She has been workng as an Assstant to Vce Charan n Natonal Broadcastng and Telecouncatons, Bangkok, Thaland snce January 202. Her research nterests are n Spectru anageent Strategc Flexblty, arket Orentaton and Envronental Uncertanty n Fast Clockspeed Industres 407