Análise e Modelagem de Desempenho de Sistemas de Computação: Component Level Performance Models of Computer Systems

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1 Análise e Modelagem de Desempenho de Sistemas de Computação: Component Level Performance Models of Computer Systems Virgilio ili A. F. Almeida 1 o Semestre de 2009 Introdução: Semana 5 Computer Science Department Federal University of Minas Gerais Brazil

4 Component-level Models The internal components of a server (e.g., processors, disks) as well as network links are modeled explicitly. Changes in server architecture, component upgrades (e.g., use of a faster CPU or faster network connections) can be evaluated with component-level l models. 4

5 Component-level models server incoming link outgoing link server 5

6 Component-level models server cpu incoming link disk 1 outgoing link disk 2 server 6

7 Component-level models server cpu incoming link disk 1 outgoing link disk 2 server 7

8 Component-level Models Each component is represented by a resource (e.g. CPU, disk, communication link) and a queue of requests waiting for the resource. resource queue 8

10 Computing Service Demands cpu incoming link disk 1 disk 2 outgoing link server The average size of a file retrieved per request is 20KBytes. The average disk service time per KByte accessed is 10 msec. 40% of the files are on disk 1 and 60% on disk 2. The speed of the link connecting the server to the Internet is 1.5 Mbps (a T1 link). The CPU processing time per request is 2 msec msec per KByte accessed. The average size of an HTTP request is 200 bytes. 10

11 Disk Service Demand incoming link cpu disk 1 disk 2 outgoing link server The average size of a file retrieved per request is 20KBytes. The average disk service time per KByte accessed is 10 msec. 40% of the files are on disk 1 and 60% on disk 2. D disk1 = 0.4*10 msec/kbyte * 20KBytes = 80 msec = sec D disk2 = 0.6*10 msec/kbyte * 20KBytes = 120 msec = sec 11

12 CPU Service Demand cpu incoming link disk 1 disk 2 outgoing link server The average size of a file retrieved per request is 20KBytes. The CPU processing time per request is 2 msec msec per KByte accessed. D cpu = 2 msec msec/kbyte * 20 Kbyte = 3 msec = sec 12

13 Incoming Link Service Demand cpu incoming link disk 1 disk 2 outgoing link server The speed of the link connecting the server to the Internet is 1.5 Mbps (a T1 link). The average size of an HTTP request is 200 bytes. D IncLink = 200 * 8 bits / 1,500,000 bps = sec 13

14 Outgoing Link Service Demand cpu incoming link disk 1 disk 2 outgoing g link server The average size of a file retrieved per request is 20KBytes. The speed of the link connecting the server to the Internet t is 1.5 Mbps (a T1 link). D OutLink = 20 * 1024 * 8 bits / 1,500, bps = sec 14

15 Computing Service Demands sec cpu sec sec incoming link 0.08 sec disk 1 outgoing link 0.12 sec disk 2 server Service demands do not include any queuing time! It is just service time. 15

16 Computing Waiting Times sec cpu sec sec incoming link 0.08 sec disk 1 outgoing link 0.12 sec disk 2 server Waiting times depend on the load (arrival rate of requests) and on the service demands. 16

18 Computing Residence Times n transactions seen, on the avg, by arriving request J. Each E hof fthe n requests found dby J need dd sec of ftotal t service. So, J has to wait for n * D seconds before being served. If we add J s Js total service time D we get J s Js residence time R at the resource: J R = D + n*d n R D From Little s Law: n = R * λ So, R = D + R * λ * D R = D / (1 - λ *D) 18

19 Computing Residence Times D i Service demand at resource i R i R i D = i 1 λ Di Utilization of resource i (U i ) 19

20 Residence Time at Incoming Link sec cpu sec sec incoming link 0.08 sec disk 1 outgoing g link λ = 5 req/sec 0.12 sec disk 2 Web server R IncLink D 1 λ D IncLink = IncLink = sec =

21 Residence Time at Outgoing Link sec cpu0.003 sec sec incoming link 008sec 0.08 disk 1 outgoing link λ = 5 req/sec R OutLink D 1 λ D 012secdisk = OutLink = 0.239sec OutLink Web server =

22 Residence Time at the CPU sec cpu0.003 sec sec incoming link 008sec 0.08 disk 1 outgoing link λ = 5 req/sec 012sec 0.12 disk 2 Web server R CPU = D cpu 1 λ D cpu = = sec 22

23 Residence Time at Disk sec cpu0.003 sec sec incoming link 008sec 0.08 disk 1 outgoing link λ = 5 req/sec R D 012sec 0.12 disk 2 disk1 disk 1 = = 1 λ Ddisk1 = sec Web server 23

24 Residence Time at Disk sec cpu0.003 sec sec incoming link 008sec 0.08 disk 1 outgoing link λ = 5 req/sec 012sec 0.12 disk 2 Web server R disk 2 = D disk 2 1 λ Ddisk 2 = sec =

25 Summary of Results Average Response Time 25

26 Response vs. Arrival Rate Time (sec) Avg g. Response Arrival Rate (req/sec) 26

27 Open vs. Closed QN Models The models presented so far are open QN models because there is no limit on the number of requests in the system. When the number of requests in the system is limited, it we need closed QN models. e.g., servers with limited degree of MPL. C/S systems with known number of clients. 27

28 Open Model Equations U R = λ i D i = 1 D i U i i U i < 1for all i 28

29 Multiple Classes of Requests Different HTTP requests may have different file sizes, frequency of arrival and different resource service demands. d Time per HTTP Class Avg. File Size (KB) % Requests request (sec) % % % % %

30 Equations for Open Multiple Class QN Models U i, r = λ Di, r R U = U i i r= 1 D, r R i, r i, r = 1 U K R = R r i, i= 1 r i 30

31 Multiclass Example A Web server has one CPU and two disks. It receives two types of HTTP requests: for small text files and for large images. The average arrival rates are 5 requests/sec for text and 2 requests/sec for images. What is the response times for each type of request? 31

32 Open Multiclass l Queuing Networks This wokbook comes with the book "Capacity Planning for Web Performance", by D. A. Menascé and V. A. F. Almeida, Prentice Hall, No. Queues: 3 No. of Classes: 2 Classes Arrival Rates: 5 2 Service Demand Matrix Classes Queues Type (LI/D/MPn) LI LI LI

33 Classes Queues Text Image CPU Disk Disk Total Open Multiclass Queuing Networks - Residence Times This wokbook comes with the book "Capacity Planning for Web Performance", by D. A. Menascé and V. A. F. Almeida, Prentice Hall,

34 Classes Queues 1 2 Total Open Multiclass Queuing Networks - Utilizations This wokbook comes with the book "Capacity Planning for Web Performance", by D. A. Menascé and V. A. F. Almeida, Prentice Hall,

35 A Complete Web Server Example router (50μsec/packet) Internet 6 HTTP req/sec T1 link ISP Web server 10 Mbps Ethernet 35

36 A Complete Web Server Example (cont d) incoming link router LAN outgoing link cpu disk Web server 36

37 A Complete Web Server Example (cont d) Workload CPU time per HTTP Class Avg. File Size (KB) % requests requests (sec)

38 Open Multiclass l Queuing Networks This wokbook comes with the book "Capacity Planning for Web Performance", by D. A. Menascé and V. A. F. Almeida, Prentice Hall, No. Queues: 3 No. of Classes: 2 Classes Arrival Rates: 5 2 Service Demand Matrix Classes Queues Type (LI/D/MPn) LI LI LI

39 Classes Queues Text Image CPU Disk Disk Total Open Multiclass Queuing Networks - Residence Times This wokbook comes with the book "Capacity Planning for Web Performance", by D. A. Menascé and V. A. F. Almeida, Prentice Hall,

40 Classes Queues 1 2 Total Open Multiclass Queuing Networks - Utilizations This wokbook comes with the book "Capacity Planning for Web Performance", by D. A. Menascé and V. A. F. Almeida, Prentice Hall,

41 A Web Server e Example (cont d) Server Side Model This wokbook comes with the book "Capacity Planning for Web Performance", by D. A. Menascé and V. A. F. Almeida, Prentice Hall, Parameters: Lan Bandwidth (Mbps): 10 Max. LAN PDU (bytes): 1518 LAN Frame Overhead (bytes): 18 Router Latency (microseconds/packet): 50 Internet Link Bandwidth (Kbps) 1500 Average Size of HTTP requests (bytes): 100 Number of Classes of Documents: 4 Average Document Size (Kbytes): Total Arrival Rate of HTTP requests (req/sec): 8 CPU time per HHTP request (sec): Average Disk Service Time/Kbyte (msec) 6 Number of Web Servers 1 Number of Disks at File Server 0 (use 0 if no file server is used) CPU time at the File Server Request per Kbyte (sec): Row for Document Sizes 21 Document Sizes per Class (Kbytes): Percent of Documents per Class: Class Arrival Rates:

42 A Web Server Example (cont d) Classes: Service Demands (sec): LAN Router Outgoing Link Incoming Link Web Server CPU (per web server) Web Server Disk (per web server)

43 A Web Server Example (cont d) Open Multiclass Queuing Networks This wokbook comes with the book "Capacity Planning for Web Performance", by D. A. Menascé and V. A. F. Almeida, Prentice Hall, No. Queues: 6 No. of Classes: 4 Classes Arrival Rates: Service Demand Matrix Classes Queues Type (LI/D/MPn) LAN LI Router LI Outgoing Link LI Incoming Link LI Web Server CPU (per web server) LI Web Server Disk (per web server) LI

44 A Web Server Example (cont d) Open Multiclass Queuing Networks - Utilizations This wokbook comes with the book "Capacity Planning for Web Performance", by D. A. Menascé and V. A. F. Almeida, Prentice Hall, Classes Queues Total LAN Router Outgoing Link Incoming Link Web Server CPU (per web server) Web Server Disk (per web server)

45 A Web Server Example (cont d) Open Multiclass Queuing Networks - Queue Lengths This wokbook comes with the book "Capacity Planning for Web Performance", by D. A. Menascé and V. A. F. Almeida, Prentice Hall, Classes Queues Total LAN Router Outgoing Link Incoming Link Web Server CPU (per web server) Web Server Disk (per web server)

46 A Web Server Example (cont d) Classes Queues LAN Router Outgoing Link Incoming Link WebServerCPU(perwebserver) Web Server Disk (per web server) Total Open Multiclass Queuing Networks - Residence Times This wokbook comes with the book "Capacity Planning for Web Performance", by D. A. Menascé and V. A. F. Almeida, Prentice Hall, major contribution to response time 46

48 Closed QN Model A Web server has one CPU and one disk. Assume that n requests are in execution concurrently. Each request takes 3 msec of CPU and 10 msec of disk time. What is the throughput h t and response time of the Web server? 48

49 Closed QN Model cpu Web server disk n 49

50 Closed Models Equations R ( n ) = D [ 1 + n ( n 1 )] i i i n X 0 ( n) = K i= 1 R ( n ) i n ( n) = X ( n) R ( n) i o i Initialization: n i i ( 0) = 0 for all. 50

51 Solution to the Closed QN Model n Rcpu Rdisk Ro Xo ncpu ndisk

52 Solution to the Closed QN Model Xo 0.12 t (req/sec) Throughpu Number of Requests 52

53 An Intranet Example with Proxy Clients Cache Server Proxy Server External Web Servers... router (50μsec/packet) Internet LAN (10 Mbps Ethernet) t) 53

54 An Intranet Example (cont d) clients LAN Cache Hit router outgoing link cpu disk proxy cache server ISP Internet web server incoming link 54

55 An Intranet Example (cont d) clients Cache Miss LAN router outgoing link cpu disk proxy cache server ISP Internet web server incoming link 55

56 Open Multiclass l Queuing Networks This wokbook comes with the book "Capacity Planning for Web Performance", by D. A. Menascé and V. A. F. Almeida, Prentice Hall, No. Queues: 3 No. of Classes: 2 Classes Arrival Rates: 5 2 Service Demand Matrix Classes Queues Type (LI/D/MPn) LI LI LI

57 Classes Queues Text Image CPU Disk Disk Total Open Multiclass Queuing Networks - Residence Times This wokbook comes with the book "Capacity Planning for Web Performance", by D. A. Menascé and V. A. F. Almeida, Prentice Hall,

58 Classes Queues 1 2 Total Open Multiclass Queuing Networks - Utilizations This wokbook comes with the book "Capacity Planning for Web Performance", by D. A. Menascé and V. A. F. Almeida, Prentice Hall,

59 A Web Server e Example (cont d) Server Side Model This wokbook comes with the book "Capacity Planning for Web Performance", by D. A. Menascé and V. A. F. Almeida, Prentice Hall, Parameters: Lan Bandwidth (Mbps): 10 Max. LAN PDU (bytes): 1518 LAN Frame Overhead (bytes): 18 Router Latency (microseconds/packet): 50 Internet Link Bandwidth (Kbps) 1500 Average Size of HTTP requests (bytes): 100 Number of Classes of Documents: 4 Average Document Size (Kbytes): Total Arrival Rate of HTTP requests (req/sec): 8 CPU time per HHTP request (sec): Average Disk Service Time/Kbyte (msec) 6 Number of Web Servers 1 Number of Disks at File Server 0 (use 0 if no file server is used) CPU time at the File Server Request per Kbyte (sec): Row for Document Sizes 21 Document Sizes per Class (Kbytes): Percent of Documents per Class: Class Arrival Rates:

60 A Web Server Example (cont d) Classes: Service Demands (sec): LAN Router Outgoing Link Incoming Link Web Server CPU (per web server) Web Server Disk (per web server)

61 A Web Server Example (cont d) Open Multiclass Queuing Networks This wokbook comes with the book "Capacity Planning for Web Performance", by D. A. Menascé and V. A. F. Almeida, Prentice Hall, No. Queues: 6 No. of Classes: 4 Classes Arrival Rates: Service Demand Matrix Classes Queues Type (LI/D/MPn) LAN LI Router LI Outgoing Link LI Incoming Link LI Web Server CPU (per web server) LI Web Server Disk (per web server) LI

62 A Web Server Example (cont d) Open Multiclass Queuing Networks - Utilizations This wokbook comes with the book "Capacity Planning for Web Performance", by D. A. Menascé and V. A. F. Almeida, Prentice Hall, Classes Queues Total LAN Router Outgoing Link Incoming Link Web Server CPU (per web server) Web Server Disk (per web server)

63 A Web Server Example (cont d) Open Multiclass Queuing Networks - Queue Lengths This wokbook comes with the book "Capacity Planning for Web Performance", by D. A. Menascé and V. A. F. Almeida, Prentice Hall, Classes Queues Total LAN Router Outgoing Link Incoming Link Web Server CPU (per web server) Web Server Disk (per web server)

64 A Web Server Example (cont d) Classes Queues LAN Router Outgoing Link Incoming Link WebServerCPU(perwebserver) Web Server Disk (per web server) Total Open Multiclass Queuing Networks - Residence Times This wokbook comes with the book "Capacity Planning for Web Performance", by D. A. Menascé and V. A. F. Almeida, Prentice Hall, major contribution to response time 64

65 Client Side Model - Proxy Case This wokbook comes with the book "Capacity Planning for Web Performance", by D. A. Menascé and V. A. F. Almeida, Prentice Hall, Parameters: Service Demands (sec): Lan Bandwidth (Mbps): 10 Client Max. LAN PDU (bytes): 1518 LAN LAN Frame Overhead (bytes): 18 Router Router Latency (microseconds/packet): 50 Outgoing Link Internet Link Bandwidth (Kbps) 56 Internet Internet Round Trip Time (msec): 100 Incoming Link Internet Data Transfer Rate (Kbytes/sec): 20 Proxy CPU Browser Rate (HTTPops/sec): 0.3 Proxy Disk Number of Clients: 150 Percent of Active Clients: 0.1 Average Size of HTTP requests (bytes): 100 Number of Classes of Documents: 4 Average Document Size (Kbytes): Proxy Cache Hit Ratio (0..1) 0.5 Proxy CPU Time in case of Hit (sec) Proxy CPU Time in case of Miss (sec) Average Disk Service Time/Kbyte (msec) 6 Document Sizes per Class (Kbytes): Percent of Documents per Class:

66 Closed Multiclass Queuing Networks This spreadsheet comes with the book "Capacity Planning for Web Performance", by D. A. Menascé and V. A. F. Almeida, Prentice Hall, No. Queues: 8 Tolerance: No. of Classes: 1 Classes No. Requests per Class: 15 Throughput per Class: Throughput per Class: throughput in HTTP req/sec Service Demand Matrix Classes Type Queues (LI/D/MPn) 1 Client D LAN LI Router D Outgoing Link LI Internet LI Incoming Link LI Proxy CPU LI Proxy Disk LI No. Iterationsti Error largest service demand 66

67 Closed Multiclass Queuing Networks - Residence Times This spreadsheet comes with the book "Capacity Planning for Web Performance", by D. A. Menascé and V. A. F. Almeida, Prentice Hall, Classes Queues This is think time (not pat of response time)

68 Intranet t Example Increasing the Bandwidth of the link to the ISP Link Bandwidth Throughput (HTTP Resp. Time (Kbps) req/sec) (sec) Bottleneck Link to ISP ISP+Internet+External Web Server ISP+Internet+External Web Server ISP+Internet+External Web Server 68

70 Performance Modeling of Multi-Tier Archietctures Need to consider site multi-tiered architecture. Need to consider load balancing strategy. Need to consider mapping of processes to various hardware components. Need to consider software congestion Menascé. All Rights Reserved. 70

78 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. D. A. Menascé. All Rights Reserved. 78

80 Burstiness Modeling Consider an HTTP LOG composed of L requests to a Web server. τ: time interval during which the requests arrive λ: average arrival rate, λ = L / τ The time interval τ is divided into n equal subintervals of duration τ / n called epochs Arr(k) number of HTTP requests that arrive in epoch k λ k arrival rate during epoch k D. A. Menascé. All Rights Reserved. 80

81 Burstiness Modeling Arr + total number of HTTP requests that arrive in epochs in which λ k > λ b = (number of epochs for which λ k > λ) / n above-average arrival rate, λ + = Arr + / (b*τ) a = λ + / λ = Arr + /(b*l) D. A. Menascé. All Rights Reserved. 81

83 Burstiness Modeling: an example Let us consider the number of epochs n=21 Each epoch has a duration of τ /n= 31 /21 = 1.48 The average arrival rate λ = 19/31 = 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, λ 1 = 1/1.48 = 0.676, that exceeds the avg. λ = In 8 of the 21 epochs, λ k exceeds λ b = 8 / 21 = a = Arr + / (b*l) = 19 / (0.381 * 19) = D. A. Menascé. All Rights Reserved. 83

84 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. D. A. Menascé. All Rights Reserved. 84

85 The Impact of Burstiness To account for the burstiness effect, we write the service demand of the bottleneck resource as: D = D f + α b f D f is the portion of the service demand that does not depend on burstiness α is a factor used to inflate the service demand according to burstiness factor b. It is given by: α = (U /X 0 U 2 /X 0)/(b 0 1 -b 2 ) The measurement interval is divided into 2 subintervals I 1 and I 2 to obtain U i, X i 0, and db i 85 D. A. Menascé. All Rights Reserved.

86 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 D. A. Menascé. All Rights Reserved. 86

87 The Impact of Burstiness: an example (2) The throughput in each interval is: X 1 0 = 14/15.5 = X 2 0 = 5/15.5 = Using the previous algorithm: b 1 = 0.273, b 2 = α = (0.18/ /0.323)/( ) 06/ = the adjustment factor is: α b = = Assuming Df = sec, we are able to calculate the maximum server throughput as a function of the burstiness factor (b). D. A. Menascé. All Rights Reserved. 87

89 Summary Component-level models are used to represent the various components of a networked system. Parameters for component-level models include the service demands on system resources, i.e. total time spent by a request receiving service from a resource. 89

90 Summary (cont d) Waiting times, response times, throughputs can be computed using open models (e.g., web servers) closed models (e.g., intranets) t In modeling Multi-Tier architecture, need to consider software as well as hardware contention. 90

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