Performance analysis of hybrid (M/M/1 and M/M/m) client server model using Queuing theory

Transcription

1 International Journal of Electronic and Couter cience Engineering vailable Online at wwwijeceorg IN erforance analyi of hybrid M/M/ and M/M/ client erver odel uing ueuing theory atarhi Guta, Dr Rajan John, Tannia Rubavathy Deartent of Electronic and Counication Engineering Deartent of Couter cience & Engineering ll Nation Univerity, Koforidua, Ghana, et frica Eail- btract- Internet ue acet witching and it i called delay yte hen any requet coe fro client ide, erver ay erve that requet iediately or it goe into queue for oe tie client i the couter, which requet the reource ail, audio, video etc, equied with a uer interface uually a web brower for reentation uroe DN Doain nae erver will a the web addre to it correonding Internet rotocol addre ll counication tae lace uing tranfer of acet acet arrive according to a oion roce with rate Router will route the requet to that articular Internet rotocol I of the alication erver The alication erver ta i to rovide the requeted reource ail, audio, video, authentication, but by calling on another erver Data erver, which rovide the alication erver with the data it require Thi aer deal with ingle erver and ultile erver queue Thi aer intend to find out the erforance average queue length, average reone tie, average waiting tie analyi of hybrid M/M/, M/M/ client erver odel uing queuing theory Keyword ueuing theory, Client erver odel, ingle erver queue, Multile erver queue I INTRODUCTION In -tier architecture, there i an interediary level, eaning the architecture i generally lit u between: a client, ie the couter, which requet the reource, equied with a uer interface uually a web brower for reentation uroe b The alication erver alo called iddleware, whoe ta it i to rovide the requeted reource, but by calling on another erver c The data erver, which rovide the alication erver with the data it require Figure Three-tier architecture of client erver odel ] IN 77-9/VN--0

2 IJECE,Volue,Nuber atarhi Guta et al In -tier architecture, each erver tier and erfor a ecialized ta a ervice erver can therefore ue ervice fro other erver in order to rovide own ervice a reult, -tier architecture i otentially an n-tiered architecture ] However, eb traffic i highly dynaic and volatile The data arrive and deart fro different node randoly Thu, we can enviage that, nuber of channel for arrival and nuber of channel for dearting ut be identical The incoing data can be tochatically treated a a roce and o will be the cae of dearting fro the eory of eb erver Thee ituation ae the woring of Meory of eb erver - a tyical cae of - ueuing roce ] It ha been ilicated that eory ae through divere ituation of ueue Model, ie, M/M/, M/M/ M/M/ odel i ot dicilined and can be analyzed analytically to etiate the queuing araeter ] The tandard queuing notation, /B/C, rereent the arrival ditribution, B the ervice ditribution, and C the nuber of erver For M/M/, odel nuber of erver i and for M/M/ odel denote ultile erver M ean eory le, which in thi context ilie oion ditribution for arrival rate and exonential ditribution for ervice tie ] II HYBRID UEUING RCHITECTURE FOR CLIENT ERVER MODEL Figure Hybrid queuing M/M/, M/M/ odel architecture client erver odel There are -inut in the queuing networ conidered in Figure with the arrival at the -inut being and The ervice rate are and The arrival rate at ource 0 i The robabilitie of arrival at ource inut 0 are, reectively Let be the arrival rate at firt queue, be the arrival at econd queue at the client brower Let the ervice rate of the erver and be and reectively Client brower will a the web addre to it correonding Internet rotocol addre fter getting erviced by erver and, the job arrive at queue Router Let be the arrival rate of the job at Router, o the arrival rate at i The ervice rate of the erver i Here, router chec the IN 77-9/VN--0

3 erforance analyi of hybrid M/M/ and M/M/ client erver odel uing ueuing theory I addre Internet rotocol addre of the articular alication erver which i aed by the DN Doain nae erver and the router forward that requet to that articular alication erver Uon getting erviced by erver, the job arrive at queue lication erver or lication erver Thi tranaction totally deend on the I addre of lication erver which ha been aed by the DN Doain nae erver Now, the job arrive at the queue, with robabilitie and, where o, the arrival rate at i, and that at i If the job arrive at with robability with the arrival rate then the arrival rate of will be becaue and are in erial connection The ervice rate of lication erver, and i and that of Databae erver 9, 0, i The ervice rate of lication erver, and are equal becaue they are M/M/ queue, Liewie the ervice rate of Databae erver 9, 0 and are equal becaue they are M/M/ queue a well Finally, job after ervice coletion at erver and arrive at the in databae, the databae erver, which rovide the alication erver with the data it require Here, lication erver act lie a web erver which erve age for viewing in a eb brower with the arrival rate then the arrival rate of will be If the job arrive at with robability becaue and are in erial connection The ervice rate of the lication erver, 7 and 8 i and the ervice rate of Databae erver,, i The ervice rate of lication erver, 7 and 8 are equal becaue they are M/M/ queue, liewie the ervice rate of Databae erver, and are equal becaue they are M/M/ queue a well Here i the nuber of erver Finally, job after ervice coletion at erver and arrive at in databae, the databae erver, which rovide the alication erver with the data it require Here, lication erver act lie a web erver which erve age for viewing in a eb brower erforance eaure for hybrid queuing client erver odel The erforance of the ingle and ultile erver i eaured by the average queue length, average waiting tie, average reone tie and the average no of job in the yte ] The queue in the odel are aued to be M/M/ and M/M/ Hybrid Here client brower and router are M/M/ tye lication erver and and databae erver and are M/M/ tye erforance eaure uch a a average queue length, b average reone tie, c average waiting tie are derived in thi ection verage queue length The average queue length in and client brower are E N ], E N ] iilarly, the average queue length in router i E N ] IN 77-9/VN--0

4 IJECE,Volue,Nuber atarhi Guta et al IN 77-9/VN--0 The average queue length in alication erver and databae erver,,, i EN ], where, robability that an arriving cutoer ha to wait in queue cutoer or ore in the yte i!- 0, and in the M/M/ cae, the robability of n cutoer in the yte i 0!! 0 ccording to Figure the alication erver and conit of ub erver each o here for each and fter ilification the average queue length for alication erver i EN ] here, robability that an arriving cutoer ha to wait in queue i 0, and in the M/M/ cae, the robability of n cutoer in the yte i 0 fter ilification the average queue length for alication erver i EN ] here, 0 and 0 ccording to Figure databae erver and conit of ub erver each o here for each and fter ilification the average queue length for databae erver i EN ] here, 0 and 0 fter ilification the average queue length for databae erver i EN ] here, 0 and 0 verage reone tie The average reone tie in and are ] R E ] E, ] R E ] E

5 erforance analyi of hybrid M/M/ and M/M/ client erver odel uing ueuing theory IN 77-9/VN--0 iilarly, the average reone tie in router i ] R E ] E The average reone tie in alication erver and databae erver,,, be ER], where, robability that an arriving cutoer ha to wait in queue cutoer or ore in the yte i!- 0, and in M/M/ cae robability of n cutoer in the yte i 0!! 0 ccording to Figure alication erver and conit of ub erver each o here for each and fter ilification the average reone tie for alication erver i ER ] 7 here, 0 and 0 fter ilification the average reone tie for alication erver i ER ] 8 here, 0 and 0 ccording to Figure the databae erver and conit of ub erver each o here for each and fter ilification the reone tie for databae erver i ER ] 9 here, 0 and 0 fter ilification the average reone tie for databae erver i ER ] 0 here, 0 and 0 verage waiting tie: The average waiting tie in and client brower are ] E ] N E, ] E ] N E

6 IJECE,Volue,Nuber atarhi Guta et al IN 77-9/VN--0 iilarly, the average waiting tie in router i ] E N E ] The average waiting tie in alication erver and databae erver,,, be E], where, robability that an arriving cutoer ha to wait in queue cutoer or ore in the yte i!- 0 and in M/M/ cae robability of n cutoer in the yte i 0!! 0 ccording to Figure the alication erver and conit of ub erver each o here for each and fter ilification the average waiting tie for alication erver i E ] here, 0 and 0 fter ilification the average waiting tie for alication erver i E ] here, 0 and 0 ccording to Figure the databae erver and conit of ub erver each o here for each and fter ilification the average waiting tie for databae erver i E ] here, 0 and 0 fter ilification the average waiting tie for databae erver i E ] here, 0 and 0 Total nuber of job, reone tie and waiting tie for different ath: For ath,,,, the total nuber of job fro t brower to data bae erver i E Nx] ] N E ] N E EN ] EN ] For ath,,,, the total reone tie fro t brower to data bae erver i

7 7 erforance analyi of hybrid M/M/ and M/M/ client erver odel uing ueuing theory IN 77-9/VN--0 E Rx] ] R E ] R E ER ] E R ] 7 For ath,,,, the total waiting tie fro t brower to data bae erver i E x] ] E ] E E ] E ] 8 For ath,,,, the total nuber of job fro nd brower to data bae erver i E Ny] ] N E ] N E EN ] E N ] 9 For ath,,,, the total reone tie fro nd brower to data bae erver i E Rx] ] R E ] R E ER ] E R ] 0 For ath,,,, the total waiting tie fro nd brower to data bae erver i E x] ] E ] E E ] E ] Nuerical reult for Hybrid queuing client erver odel ueue length v rrival rate for lin to and lin to

8 IJECE,Volue,Nuber atarhi Guta et al 8 Figure ueue length v rrival rate for lin to and lin to Let be the total nuber of arrival in the -inut queuing networ In the exale conidered in thi ection, the arrival rate,,,, 0 The other ecification include robability of arrival at queue and are 0 and 0 The ervice rate ecification of different erver in the networ are 78, 7, 7, 70,, 800, 07 robability of arrival at queue ', ' and ' and ', 7' and 8' are 0 and 0 For each value of, the average queue length in all node of the -inut queuing client erver networ i couted The average queue length in ath to and to are couted fro to The total queue length in ath to and to are couted in and 9 reectively The total queue length of lin to and lin to v different arrival rate are lotted in Figure Fro Figure it i found that a the arrival rate increae, the queue length of the lin to increae ore than the queue length of the lin to Becaue the ervice rate for erver and are ore than the ervice rate of and Reone tie v rrival rate for lin to and lin to IN 77-9/VN--0

9 erforance analyi of hybrid M/M/ and M/M/ client erver odel uing ueuing theory 9 Figure Reone tie v rrival rate for lin to and lin to For each value of, the utilization, average reone tie in all node of the -inut queuing client erver networ i couted The average reone tie in ath to and to are couted fro to 0 The total reone tie in ath to and to are couted in 7 and 0 The total reone tie of lin to and lin to v different arrival rate are lotted in Figure Fro Figure it i found that a the arrival rate increae, the reone tie of the lin to increae ore than the reone tie of the lin to Becaue the ervice rate for erver and are ore than the ervice rate of and, aiting tie v rrival rate for lin to and lin to Figure aiting tie v rrival rate for lin to and lin to IN 77-9/VN--0

10 IJECE,Volue,Nuber atarhi Guta et al 0 For each value of, the utilization, average waiting tie in all node of the -inut queuing client erver networ are couted The average waiting tie in ath to and to are couted fro to The total waiting tie in ath to and to are couted in 8 and The total waiting tie of lin to and lin to v different arrival rate are lotted in Figure Fro Figure it i found that a the arrival rate increae, the waiting tie of the lin to increae ore than the waiting tie of the lin to Becaue the ervice rate for erver and are ore than the ervice rate of and, IIICONCLUION In thi aer, erforance eaure for client erver odel uch a average queue length, average reone tie and average waiting tie are derived for M/M/ and M/M/ Hybrid tye odel and the reult how that reone tie i le Becaue of thi le reone tie robability of acet lo reduce and yte becoe fater The ervice rate of the equivalent erver i alo derived and couted nuerically ueue length v rrival rate, Reone tie v rrival rate, waiting tie v rrival rate are lotted uing MTLB 70 oftware Deciion for routing i ade at the lat node in each tage of the networ a to which ath to chooe for obtaining the leat reone tie IV REFERENCE ] htt://enioeanet/content/c/ctierh#qecurityinclient%ferverodel&cur&url%f ] Diitri Bertea, Robert Gallager, Data Networ, econd Edition, rentice Hall of India rivate Liited, 997 ] ingh, and rivatava, Meory Etiation of Internet erver Uing ueuing Theory: Coarative tudy between M/G/, G/M/ & G/G/ ueuing Model, orld cadey of cience, Engineering and Technology, ] Vidhyacharan Bhaar & atric Lalleent, ctivity routing in a ditributed uly chain: erforance evaluation with two inut Journal of Networ and Couter lication, cience Direct, IN 77-9/VN--0