1. 1 Web Performance Modeling Chapter 10

2. 2 New Phenomena in the Internet and WWW Self-similarity - a self-similar process looks bursty across several time scales. Heavy-tailed distributions in workload characteristics, that means a very large variability in the values of the workload parameters.

3. 3 WWW Traffic Burst 10 6 10 7 Bytes Chronological time (slots of 1000 sec)

4. 4 Incorporating New Phenomena in the Workload Characterization Burstiness Modeling burstiness in a given period can be represented by a pair of parameters (a,b) –a is the ratio between the maximum observed request rate and the average request rate during the period. –b is the fraction of time during which the instantaneous arrival rate exceeds the average arrival rate.

5. 5 Burstiness Modeling Consider an HTTP LOG composed of L requests to a Web server.  : time interval during which the requests arrive : average arrival rate, = L /  The time interval  is divided into n equal subintervals of duration  / n called epochs Arr(k) number of HTTP requests that arrive in epoch k k arrival rate during epoch k

6. 6 Burstiness Modeling Arr + total number of HTTP requests that arrive in epochs in which k > b = (number of epochs for which k > ) / n above-average arrival rate, + = Arr + / (b*  ) a = + / = Arr + / (b*L)

7. 7 Burstiness Modeling: an example Example: Consider that 19 requests are logged at a Web server at instants: 1 3 3.5 3.8 6 6.3 6.8 7.0 10 12 12.2 12.3 12.5 12.8 15 20 30 30.2 30.7 What are the burstiness parameters?

8. 8 Burstiness Modeling: an example Let us consider the number of epochs n=21 Each epoch has a duration of  / n = 31 /21 = 1.48 The average arrival rate = 19/31 = 0.613 req./sec The number of arrivals in each of the 21 epochs are: 1, 0, 3, 0, 4, 0, 1, 0, 4, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 4 Thus, 1 = 1/1.48 = 0.676, that exceeds the avg. = 0.613 In 8 of the 21 epochs, k exceeds b = 8 / 21 = 0.381 a = Arr + / (b*L) = 19 / (0.381 * 19) = 2.625

9. 9 The Impact of Burstiness As shown in some studies, the maximum throughput of a Web server decreases as the burstiness factors increase. How can we represent in performance models the effects of burstiness? We know that the maximum throughput is equal to the inverse of the maximum service demand or the service demand of the bottleneck resource.

10. 10 The Impact of Burstiness To account for the burstiness effect, we write the service demand of the bottleneck resource as: –D = D f +   b –D f is the portion of the service demand that does not depend on burstiness –  is a factor used to inflate the service demand according to burstiness factor b. It is given by: –  = (U 1 /X 1 0 - U 2 /X 2 0 )/(b 1 -b 2 ) –The measurement interval is divided into 2 subintervals  1 and  2 to obtain U i, X i 0, and b i

11. 11 The Impact of Burstiness: an example Consider the HTTP LOG of the previous slides. During 31 sec in which the 19 requests arrived, the CPU was found to be the bottleneck. What is the burstiness adjustment that should be applied to the CPU service demand to account for the burstiness effect on the performance of the Web server? The number of requests during each 15.5 sec subinterval is 14 and 5, respectively. The measured CPU utilization in each interval was 0.18 and 0.06

12. 12 The Impact of Burstiness: an example (2) The throughput in each interval is: –X 1 0 = 14/15.5 = 0.903 –X 2 0 = 5/15.5 = 0.323 Using the previous algorithm: –b 1 = 0.273, b 2 = 0.182 –  = (0.18/0.903 - 0.06/0.323)/(0.273-0.182) = 0.149 –the adjustment factor is:  × b = 0.149 × 0.381 = 0.057 Assuming Df = 0.02 sec, we are able to calculate the maximum server throughput as a function of the burstiness factor (b).

13. 13 The Impact of Burstiness: an example (2) 0.30.10.00.2

14. 14 Incorporating New Phenomena in the Workload Characterization Accounting for Heavy Tails in the Model Due to the large variability of the size of documents, average results for the whole population would have very little statistical meaning. Categorizing the requests into a number of classes, defined by ranges of document sizes, improves the accuracy and significance of performance metrics. Multiclass queuing network models, with classes associated with requests for docs of different size.

15. 15 Accounting for Heavy Tails: an example (1) The HTTP LOG of a Web server was analyzed during 1 hour. A total of 21,600 requests were successfully processed during the interval. Let us use a multiclass model to represent the server. There are 5 classes in the model, each corresponding to the 5 file size ranges.

16. 16 Accounting for Heavy Tails: an example (2) File Size Distributions.

17. 17 Accounting for Heavy Tails: an example (3) The arrival rate for each class r is a fraction of the overall arrival rate = 21,600/3,600 = 6 requests/sec. 1 = 6  0.25 = 1.5 req./sec 2 = 6  0.40 = 2.4 req./sec 3 = 6  0.20 = 1.2 req./sec 4 = 6  0.10 = 0.6 req./sec 5 = 6  0.05 = 0.3 req./sec

18. 18 Client Side Models Questions to answer for clients capacity –Bandwidth of the link to ISP –Bandwidth of the LAN –No Cache proxy server –Cache proxy server

19. 19 Client Side Models No cache proxy server case Internet Router Client 1Client M Webserver LAN

20. 20 Client Side Models No cache proxy server case 1 2 3 4 5 6 Incoming link Internet web server Outgoing link Router LAN Clients

21. 21 Client Side Models No cache proxy server case Dcl = 1/Browser Rate 8 x [m + Overhead (m)] Network Time (m) = 10 x LANBandwidth Overhead (m) = TCP Ovhd + Ndatagrams (m) x (IPOvhd + FrameOvhd) = 20 + NDatagrams (m) x (20 + FrameOvhd) 6

22. 22 Client Side Models No cache proxy server case  m + TCPOvhd  datagrams (m) = MaxPDU - IPOvhd D LAN = NetworkTime (AVGSizeHTTP request) + NetworkTime (1,024 x DocmentSize) D router = [Ndatagrams (1,024 x DocumentSize + 7] x RouterLatency X 10 D int = 1.5 x InternetDelayRTT/1,000 + DocumentSize/InternetDataRate 

23. 23 Client Side Models No cache proxy server case 8x [AvgSizeHTTPRequest + 5 x (20 +20)] D OutL = 1,024 x LinkBandwidth 8 x (1,0224 x DocumentSize + LinkOvhd D inL = 1,024 LinkBandwidth 1,024 x DocumentSize LinkOvhd = X (TCPOvhd + IPOvhd) 65,535 1,024 x DocumentSize = x 40 65,535

24. 24 Client Side Models No cache proxy server case Example 10.4

25. 25 Client Side Models Cache proxy server case Internet Router Client 1Client M Webserver Proxy Cache server LAN

26. 26 Client Side Models Cache proxy server case Request from clients go first to cache proxy server Cache Hit if document found in cache Cache Miss Document not found in cache –Proxy server acts as client, connects to web server, requests the document, stores it into its cache, the returns it to client. –Proxy overhead for cache misses caused slow down of document retrieval by a factor of two

27. 27 Client Side Models Cache proxy server case 1 2 3 4 5 6 Incoming link Internet web server Outgoing link Router LAN Clients 7 8 CPU Disk Proxy cache server

28. 28 Client Side Models Cache proxy server case Additional parameter for proxy model –P hit Fraction of requests that can be served from proxy server cache –HitCPUTime - CPU time in seconds needed to process the request at the proxy server –MissCPUTime - CPU time in seconds to process a request at proxy, request from originating server, store it into the cache, send the docoment to client. –DiskTime - disk time per kb at the cache proxy in milliseconds

29. 29 Client Side Models Cache proxy server case D lan = P hit x D lan + (1- P hit ) x 2 x D lan = (2 - P hit ) x D lan D router = (1 - P hit ) x D router D OutL = (1 - P hit ) x D OutL D int = (1 - P h it ) x D int D InL = (1 - P h it ) x D InL p p p p p

30. 30 Client Side Models Cache proxy server case D cpu = P hit x HitCPUTime + (1 - P hit ) x MissCPUTime D disk = DiskTime x DocumentSize / 1,000 p pp

31. 31 Client Side Models Cache proxy server case Examples 10.5 and 10.6

32. 32 Server Side Models Questions to be answered for Servers –Bandwidth of the link from web server to internet –Mirror sites? How many? –Redundant Array of Inexpensive Computers (RAIC) or single powerful server –Assessment of relocating documents within the web server

33. 33 Server Side Models(cont.) Questions –Replication popular documents strategies –File placement on disk –Compression –CGI scripts or Java applets? –Compiled or interpreted CGI scripts –etc. etc.

34. 34 Server Side Models(cont.) Single Web Server Mirrored Web Servers

35. 35 Single Web Server Web server Internet Client LAN Router

36. 36 Single Web Server The Performance Model Open QN model Multiclass - Number of classes R – r =  x PercentSize r for r = 1,…,R –  is the overall arrival rate

37. 37 Single Web Server The Performance Model 1 2 3 6 4 cpu 5 Incoming linkRouter LAN Web Server Outgoing link disk

38. 38 Single Web Server The Performance Model Additional Parameters –CPUTimePerHTTPRequest r Total CPU time, in seconds, to process one HTTP request of class r –DiskTime Disk time per kb transferred, in milliseconds

39. 39 Single Web Server The Performance Model Text book pages 239 to 243 Examples 10.7 and 10.8

40. 40 Mirrored Web Servers with a shared file system Web server n Internet Client LAN Router Web server 1 File server

41. 41 Mirrored Web Servers with Shared file system 1 2 3 6 4 cpu 6 Incoming linkRouter LAN Web Server 1 Outgoing link Disk farm 5 cpu Web server n

42. 42 Mirrored Web Servers with Shared file system Text book pages 243 - 246 Examples 10.9 and 10.10

43. 43 Summary Chapter 10 How to account for burstiness of web traffic Multiclass models for heavy-tailed Client-side model analyzed with closed QN Server-side models with open multicalss