Web Capacity Planning
Final Questions

Guidelines:

For this assignment you may not share information. You are to work out the answers to these questions on your own, using the text, the reference text, other assigned readings, and the CD materials for the class. Turn in all your work with your answers. This assignment is due on or before the start of class on Thursday, July 29.

1. (30 points)

Write a mean value analysis program for a single class closed queueing network. The program should take as input the number of devices, the total demand at each device, and the multiprogramming level. The program should output the average queue length at each device, the average utilization at each device, the average residence time at each device, the total system response time and the system throughput.

Use your MVA program to give performance metrics for questions a), b), and c) posed in Example 9.4 in the text, for 10, and 20 concurrent requests in the system. Also, use a graphing tool to graph the system response time for each number of possible multiprogramming levels from 1 up to 30 for a), b), and c). (You may wish to run a modified version of the program that prints the response time values only for MPL 1 up to 30.)

Hand in a printout of your source code and your program output from this problem.

2. (25 points)

Solve the following two-class system using exact MVA. Show the steps of your MVA on paper, or, you may use a spreadsheet or program that you write yourself.

         CPU       Network       Disk
         +-+         +-+          +-+
      +--| |<>-------| |<>--------| |<>----+
      |  +-+         +-+          +-+      |
      |                                    v
      +------------------<-----------------+

The CPU and disk are scheduled round robin. The network is lightly-loaded, so it can be considered a delay server (i.e., no queueing). There are two classes, each with two customers in it. The following table contains the demands (in seconds) placed on each device by each of the classes.

Class	CPU	Network	Disk
1	2	10	3
2	4	5	9

3. (20 points)

Consider the following historical data:

Month	Throughput
January	25
February	20
March	28
April	30
May	32
June	31
July	35

Forecast the throughput value for August using:

(a)

moving average (with n that minimizes the MSE on the given data)

(b)

exponential smoothing where alpha is 0.25

(c)

exponential smoothing where alpha is 0.5

4. (25 points)

The throughput of a Web server varies with the number of concurrent requests as shown in the following table. Assume that the average arrival rate of requests is 30 requests/sec. The server refuses a connection when the number of requests in the systems is equal to 10. What is the server average response time, average throughput, and the fraction of requests rejected?

Number of requests	Throughput (req/sec)
1	4
2	8
3	11
4	15
5	18
6	20
7	20
8	20