PERFORMANCE MEASURES FOR INTERNET SERVER BY USING M/M/m QUEUEING MODEL

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1 IJRET: International Journal of Research in Engineering and Technology ISSN: PERFORMANCE MEASURES FOR INTERNET SERVER BY USING M/M/ QUEUEING MODEL Raghunath Y. T. N. V, A. S. Sravani 2 Assistant professor, Dept.of ECE, DVR & Dr. HS MIC College of Technology, Andhra Pradesh, India, 2 P.G. Scholar, Dept. of ECE, St. Ann s College of Engg &Tech, Andhra Pradesh, India, bobby_ytnv@yahoo.co, sravani.ayachitula@gail.co Abstract This paper deals with the perforance easureent of single queue ultiple server odel. This gives the perforance easure for internet server for highly dynaic traffic conditions. Our previous work is related to perforance easureent of single queue single server odel. This is achieved by analyzing the perforance easures and capacity planning of internet server using different queuing odels by coparing the paraeters like queuing length, response tie, waiting tie for different links. Keywords- Internet server, waiting tie, response tie, queue length, queuing odels ***** INTRODUCTION above syste is odeled in queueing network by using the above queuing odels. Figure.: Layout of Internet Server-Data Arrival/ Data departure []. In Figure., the client requests for accessing the web page through different links those are link and link 2. These links ay be either satellite link or optical link in real tie. The net block is echange servers, in the above diagra there are echange servers in link and n echange servers in links []. These echange servers are connected to internet server. In this syste, the client requests for the web page by typing the doain nae of particular web page. Then the echanges servers those are used to apping that particular doain nae with particular IP address. After that the web server will process the IP address and generates the client requested web page. Like this the echange servers and internet servers are used process the client requests [2]. The objective of the paper is getting the perforance easures and capacity estiation of the above syste by using different queueing odels i.e., M/M/, M/G/, M/D/ and M/Ek/.The Analyzing a Queue Syste: A full queuing situation involves arrivals and service[3], so we need soe ore Greek letters: : labda is the average custoer arrival rate per unit tie μ : u is the average custoer service rate (when custoers are waiting) =/(average service tie) ρ : rho is the server utilization factor It uses the Poisson and eponential distributions to odel both arrival ties and service ties. As entioned, the Poisson and eponential distributions are atheatically related. If the nuber of service copletions per unit of tie, when there is a backlog of custoers waiting, has the Poisson distribution, then service tie has the eponential distribution. It's conventional to think of service in ters of the length of service tie. The standard siple queuing odel assues that [4]:. Arrivals have the Poisson distribution 2. Service ties have the eponential distribution 3. Arrivals and service ties are all independent. (Independence eans, for eaple, that: arrivals don't coe in groups, and the server does not work faster when the line is longer.) The perforance easures those can be done by using queuing odels are utilization, queue length, waiting tie and response tie [8]. Volue: 0 Issue: 04 Dec-202, 69

2 IJRET: International Journal of Research in Engineering and Technology ISSN: Utilization factor :- The utilization gives the fraction of tie Queue length :- It defines the aiu capacity of the queue or nuber of custoers in the queue. Waiting tie :- It is defined as the ratio of average queue length to arrival rate or it defines the aount of tie the custoer has to be waited in the queue. Response tie :- It defines the su of waiting tie and service tie for a particular custoer [8]. 2. LITERATURE REVIEW In [], this paper deals with an iproved schee for autonoous perforance of gateway servers under highly dynaic traffic loads. The ost wide spread conteplation is perforance, because gateway servers offer cost-effective and high perforance odeling and predictions. This paper describes possible queuing odels that can be applied in capacity planning analysis. This is achieved by utilizing the internal queue length easureents. Etensive siulation study shows that the new schee can provide sooth perforance control and better tracking ability in web server systes. In [2], this paper presents a workload characterization study for Internet Web Servers. Si different data sets are used in the study: three fro acadeic environents, two fro scientific research organizations, and one fro a coercial internet provider. These data sets represent three different orders of agnitude in server activity, and two different order of agnitude in tie duration, ranging fro one week of activity to one year of activity. In [3], this paper provides inforation about High perforance web site design techniques. Perforance and high availability are critical at web sites that receive large nubers of requests. This paper presents several techniques including redundant hardware, load balancing. Web server acceleration, and efficient anageent of dynaic data that can be used at popular sites to iprove perforance and availability. It describes how several techniques are deployed at the official web site. 3. SINGLE QUEUE SINGLE SERVER MODELS 3. Queuing network odel for Internet Server using/m/ odel: The M/M/-Queue has interarrival ties [6], which are eponentially distributed with paraeter and also service ties with eponential distribution with paraeter. The syste has only a single server and uses the FIFO service discipline. The waiting line is of infinite size. Fig 3. Block diagra for queuing network odel for Internet server using M/M/. Different Queueing odels [6]:. M/M/ 2. M/D/ 3. M/G/ 4. M/Ek/ Previous work is related to the coparison of server perforance with different queueing odels. This paper deals with the perforance of single queue ultiple server odel. 4. SINGLE QUEUE MULTIPLE SERVER MODEL 4. M/M/ queueing odel: In this M/M/ queueing odel, the st M indicates the interarrival tie distribution arrivals follows Poisson distribution with paraeter, and 2nd M indicates service tie distribution [5]. Here, it is eponential distribution with paraeter μ and 3rd indicates nuber of servers available those are in parallel. The syste has ultiple server and uses the FIFO service discipline. The waiting line is of infinite size. In the case M/M/ queueing odel, there is only one single server. It eans that the syste can process a single request at a tie. But in this M/M/ queueing odel, there are nuber of servers that are connected in parallel [5]. That eans, this odel can process requests at a tie. So copared with the M/M/ queueing odel, this odel gives better perforance easures. In figure 3., the M/M/ queueing odel coprises internet servers. In this syste, the client requests for accessing the web page is by using doain nae of that particular web page. then the request arrives at one of the echange servers. These echange servers are used to ap the client request doain nae with the corresponding IP address and that result is arrived at any one of the internet servers, Volue: 0 Issue: 04 Dec-202, 620

3 IJRET: International Journal of Research in Engineering and Technology ISSN: because this syste uses ultiple servers that are connected in parallel. Based on that arrived IP address, these internet servers that generate the web page which is displayed in the client s onitor. The perforance easures those can be done by using this queueing odel are ulilization, queue length, waiting tie and response tie [5]. Utilization factor :- The utilization gives the fraction of tie Queue length :- It defines the aiu capacity of the queue or nuber of custoers in the queue. Waiting tie :- It is defined as the ratio of average queue length to arrival rate or it defines the aount of tie the custoer has to be waited in the queue. Response tie :- It defines the su of waiting tie and service tie for a particular custoer Queueing network odel for Internet Server using M/M/ odel: in link and n echange servers in link 2. These echanges are used for apping the doain nae with the corresponding IP address. Later, it arrives at any one of the k parallel internet servers that are used to process the IP address and generate the web page Perforance easures for M/M/ odel: The perforance easure for single queue ultiple server syste can be obtained by finding the utilization factor, queue length, waiting tie, response tie. Utilization factor: - The utilization gives the fraction of tie According to figure 4., the utilization factor can be epressed as follows: ρ = μ + s κμ s, (for link ) (4.) ρ = nμ + s κμ s. (for link 2) (4.2) Queue length: - It defines the aiu capacity of the queue or nuber of custoers in the queue. According to figure 4., the total queue length can be epressed as follows: E [N tot ] = E [N] + E [N s ], (for link ) (4.3) E [N tot ] = E [N ] + E [N s ]. (for link 2) (4.4) E [N] = ( μ ) + ( μ )( μ )! μ μ!! (for link ) (4.5) μ ( μ )2, Fig 4.. Block diagra for queueing network odel for Internet server using M/M/. The analysis of queueing network for internet server is described as follows: In figure 4., there are two links which are connected to the internet server to provides services to the users. In figure 4., S o, S are two source indicators that are used to request the web pages. Let A, A 2,, A be the parallel echange servers in link and let A, A 2,, A n be the n parallel echange servers and A s, A s2,, A sk be the k parallel internet servers. Let be the arrival at link and be the arrival rate at link 2. After the request arrives fro the source, it arrives into the queue which is connected to the echange servers E [N ] = n ( nμ ) + ( μ )n nμ )( n! n n μ μ! n! ( n μ )2 n μ (for link 2).(4.6) E [N s ] = k ( s ) + ( s ) ( k! k s s k μ s μ s! k! (for internet server) (4.7) s,. ( s )2 Waiting tie: - It is defined as the ratio of average queue length to arrival rate or it defines the aount of tie the custoer has to be waited in the queue. Volue: 0 Issue: 04 Dec-202, 62

4 IJRET: International Journal of Research in Engineering and Technology ISSN: According to figure 4., the total waiting tie can be epressed as follows: 5. Nuerical Results E [W tot ] = E [W] + E [W s ] (for link ) E [W tot ] = E [W ] + E [W s ] (for link 2) E [W] = ( μ ) + ( μ )( μ )! (for link ) (4.8) μ μ!! μ ( μ )2, E [W ] = n ( nμ ) + ( (for link 2) (4.9) μ )n nμ )( n! E [W s ] = k ( ) + ( ) ( k! (for internet server) (4.0) n n μ μ! n! k s s k μ s μ s! k! ( n μ )2 n μ s, ( s )2 Fig 4.2: Plot for finding the Utilization factor for internet server using M/M/ queuing odel. Figure 4.2 shows the curves for utilization versus arrival rate with different values. Here, represents the nuber of utilization factor because, if the nuber of servers increases, the incoing arrivals will be shared for service with different servers. Then, the utilization factor for each internet server Response tie: - It defines the su of waiting tie and service tie for a particular custoer. According to figure 4., the total response tie can be epressed as follows: E [R tot ] = E [R] + E [R s ] (for link ) E [R tot ] = E [R ] + E [R s ] (for link 2) E [R] = ( μ ) + (, (for link ) (4.) E [R ] = n ( nμ ) + (, (for link 2) (4.2) μ )( μ )! μ )n nμ )( n! μ μ!! n n μ μ! n! μ n μ + μ ( μ )2 ( n μ )2 + μ Fig 4.3: Plot for finding the queue length for internet server using M/M/ queuing odel. Figure 4.3 shows the curves for queue length versus arrival rate with different values. Here, represents the nuber of queue length, if the nuber of servers increases, the incoing arrivals will be waited in the queue, they will be shared for service with different servers. Then, the queue length E [R s ] = k ( k μ s ) + ( s k s k μ s μ =0 + s! k! (4.3) s k μ s ) ( k μ s k! + ( s k μ s )2 μ s. (for internet server) Volue: 0 Issue: 04 Dec-202, 622

5 IJRET: International Journal of Research in Engineering and Technology ISSN: Fig 4.4: Plot for finding the waiting tie for internet server using M/M/ queuing odel. Figure 4.4 shows the curves for waiting tie versus arrival rate with different values. Here, represents the nuber of waiting tie, if the nuber of servers increases, the incoing arrivals will be waited in the queue, they will be shared for service with different servers. Then, the waiting tie Fig 4.5: Plot for finding the response tie for internet server using M/M/ queuing odel. Figure 4.5 shows the curves for response tie versus arrival rate with different values. Here, represents the nuber of response tie, if the nuber of servers increases, the incoing arrivals will be waited in the queue, they will be shared for service with different servers. Then, the response tie REFERENCES [] Dr. L.K. Singh, Riktesh Srivastava, Estiation of Buffer Size of Internet Gateway Server via G/M/ Queuing Model, International Journal of Applied Science, Engineering and Technology, Volue 4, No., pp , January [2] M. Arlitt and C. Williason, "Internet Web Servers: Workload Characterization And Perforance Iplications", IEEE/ACMTransactions on Networking, Vol. 5, No. 5, pp , Oct [3] A. Iyengar, et al., "High-Perforance Web Site Design Techniques", IEEE Internet Coputing, Vol. 4, No. 2, pp. 7-26, [4]. Kishor S.Trivedi, Probability & Statistics with Reliability, Queuing, andcoputer Science Applications. Prentice- Hall of India Private Liited. New Delhi [5] J.P.Buzzen, A Queueing network odel of MVS, ACM Coputing surveys, Sept 978, Vol. 0, No 3, pp [6] Anderson, Darrell et. al.( 999), A Case for Buffer Servers, pp , IEEE Seventh Workshop on Hot Topics in Operating Systes. [7] Diitri Bertsekas, Robert Gallager, Data Networks, Second Edition, Prentice Hall of India Private Liited, 997. [8] A. Iyengar, et al., "High-Perforance Web Site Design Techniques", IEEE Internet Coputing, Vol. 4, No. 2, pp. 7-26, [9] D. Dias, et al., "A Scalable And Highly Available Web Server", in COMPCON '96. Technologies for the Inforation Superhighway Digest of Papers., San Jose, CA., pp , 996. BIOGRAPHIES: Raghunath Y. T. N. V, Assistant Professor, ECE dept. in DVR & Dr. HS MIC College of Technology, Vijayawada, Andhra Pradesh, India. A.S.Sravani, P.G Scholor, ECE Dept. in St. Anns College of Engineering and Technology, Chirala, Andhra Pradesh, India CONCLUSIONS In this paper, perforance easures for Internet server such as average queue length, average response ties and average waiting ties are derived and plotted by using M/M/ queuing odel. Volue: 0 Issue: 04 Dec-202, 623