Problem #2 - Assume that a web server can be modeled as an M/M/1 queue. Determine the probability that an arriving request "sees" i requests in the system for i = 0, 1, 2, ..., 5. Assume that the arrival rate is 8 requests per second and the service rate is 10 requests per second. This problem can be solved analytically, but you are to solve the problem using simulation (extra credit of 10 points if you also solve the problem analytically and thus validate your simulation results). To solve this problem with simulation you can start with mm1.c (the M/M/1 simulation model that we covered in class). Problem #2 - Assume that a web server can be modeled as an M/M/1 queue. Determine the probability that an arriving request "sees" i requests in the system for i = 0, 1, 2, ..., 5. Assume that the arrival rate is 8 requests per second and the service rate is 10 requests per second. This problem can be solved analytically, but you are to solve the problem using simulation (extra credit if you also solve the problem analytically and thus validate your simulation results). To solve this problem with simulation you can start with mm1.c (the M/M/1 simulation model that we discussed in class).

Problem #3 - Reproduce problem #2 for an M/M/1/5 queue. Compare your results to the M/M/1 results from problem #2. Again, extra credit (10 pts) for analytically validating your simulation results.

Problem #4 - Is an M/M/1/n a good model for a web server? How could you actually determine if an M/M/1/n is a good model for a web server? Carefully explain.

Problem #5 - Assume that you have five compute servers in a compute server cluster connected to the Internet. Each server can execute only one job at a time. If a job arrives when all five compute servers are busy, then the job is lost. Assume that the mean time to execute a job on a compute server is 1 second. What is the maximum possible arrival rate of jobs (assume Poisson arrivals) so that job loss is less than 1%? Hint: Think about the Erlang equations.