Download W8-3a Answer 1

Software Architecture in Practice
Theoretical Exercise in Performance
Engineering
Exercise 1a: Response Time
Calculation
Web Browser
Web Browser
(per user)
150 users
12 txn per min
•
•
– Network latency (transmission time
overhead) is 500ms
– User transaction arrival rate is fixed
and exponentially distributed across
the user community
– Ignore processing time of browser
100 KB
Internet
20 KB
Amount of
data sent
over network
1 Mbps
per user
Web Server
0.03 s service time
uni-processor
system
What is the end-user response time?
Assume:
•
Hints:
– Network: Use the utilization law
– Server: Use graphs of service time
under increasing load for server
response time OR calculate using
formula for response time
Exercise 1a: Answer
• The solution to this problem is to break down the
response time into manageable pieces.
• User response time (RU) consists of:
– Request network time (RRQ)
– Web server response time (RS)
– Response network time (RRS)
• RU = RRQ + RS + RRS
• First, consider the Request Network Time
• Each user sends 20KB of network data/1Mbps
– Transmission:
• S = 20*1024*8 bits on a 1024*1024 bits/sec line = 163840 bits
/ 1048576 bits/sec = 0,15625 sec
– R = S + W,
W is given as 0,5 sec
– Request Network Time = 0,156 + 0,500 = 0,656 sec
• Next, consider the Response Network Time
• Each user receives 100 KB of network data
– Transmission
• 100*1024*8 bits on a 1024*1024 bits/sec line = 819200 bits /
1048576 bits/sec = 0,78125 sec
– Response Network Time = 0,78 + 0,500 = 1,281 sec
• Finally, consider the response time of the web
server
– Transaction arrival rate (lambda) = Throughput (X) =
150 users * 12 txn / min = 150 * 0,2 txn/sec = 30 tps
– Utilization Law: U = X * S = 30 * 0,03 = 0,90 = 90%
Alternative 1: use the graph
Response Time
0.7
0.6
Effect of service time on expected response time
for c=1
0.5
0.03
0.4
0.02
0.01
0.3
0.005
0.2
Service
Time (s)
0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
Utilization
0.7
0.8
0.9
0.95
Alternative 2: Calculate Response
Time
• Response Time = Service Time + Wait Time
• RS = S / (1 – U)
• RS = 0,03 / (1 – 0,90)
• RS = 0,03 / 0,1 = 0,30 sec
Exercise 1a: The Result
• RU = RRQ + RS + RRS
• RU = 0,656 + 0,300 + 1,281 = 2,237 sec
Exercise 1b: Answer