2.You are planning to simulate a network environment and want to generate a stream of data packet the size of which is assumed to follow the exponential distribution. Explain how to generate the random variate with usual random number generator which follows the uniform distribution.

3.Consider a four-server system where arrival rate is . The interarrival times, as well as the service time, are independent and identically distributed with an exponential distribution. Draw a state-transition diagram and develop expression for state probability p_n of n jobs in the system and E[n] in terms of p₀.

4.Derive the equation R_i = S_i /(1-U_i) using operational laws, where R_i is response time, S_i is service demand, and U_i is device utilization. Subscript i denotes that they are per-device parameters. One argues that the equation is wrong because the response time must not be dependent on utilization unless the device is busy enough but the equation tells it depends all the time. Discuss for or against the argument.

(a)services
(b)performance metrics
(c)system parameters
(d)workload parameters
(e)factors and their ranges
(f)evaluation technique
(g)workload

2. The number of disk I/O's performed by a number of programs were measured as follows. {23, 33, 14, 15, 42, 28, 33, 45, 23, 34, 39, 21, 36, 23, 34, 36, 25, 9, 11, 19, 35, 24, 31, 29, 16, 23, 34, 24, 38, 15, 13, 35, 28}

a.What is the mean number of disk I/O's per program ?
b.What is the 90% confidence interval for the mean ?
c.What is the 10-percentile and 90-percentile from the sample ?

 3. For seven programs, memory size and CPU time are measured as follows. {(70,2), (75,5), (144,7), (190,9), (210,10), (235,13), (400,20)} Analyze the data using a simple regression model to predict CPU time as a function of the memory size and present the accuracy of the model.

4.Find the duration of the transient interval for the following sample using truncation: 11, 4, 2, 6, 5, 7, 10, 9, 10, 9, 10, 9, 10, 9…Does it give the correct result ?