Communication network analysis and design1

Create the histograms for the questions. 3 G/G/1 Queueing Systems: waits and queue sizes (a) Using the analytic formulas for an M/M/1 what is average queue wait, average total time in the system and average queue size if the average inter-arrival time (not rate) is 2.7uS and the average service time (not rate) is 1.8uS? (b) If a Weibull distribution has a shape parameter of 0.65, what would be the equivalent Weibull scale parameter to produce an average inter-arrival time (not rate0 of 2.7uS? (c) Modify the program [login to view URL] have exponential inter-arrival times. What is a reasonable amount of simulation time to get good agreement between simulation results and your computation from part (a)? (d) Modify the program [login to view URL] have Weibull inter-arrival times with shape of 0.65 and the scale parameter 4 G/G/1 Queueing Systems: Queue size distributions Using the amount of simulation time you came up with in problem 3, modify the queue_monitor() function in the [login to view URL] to keep track the queue size at each sample time (use a global python list). (a) Plot a histogram of a M/M/1 queue with parameters from problem 3(a). (b) Plot a histogram of a Weibull/M/1 queue with parameters from problem 3(b). 5 G/G/k/k Queueing Systems: Service Blocking Loss Assume that due to a complicated business arrangement that your specialty video on demand start up can only simultaneously stream 25 copies of the new hit video "Smart Dogs, and Dumb People". Assume that this video has a playing time of 1.3 hours. Assume that requests arrive at an average rate of 17 per hour. Hint you may want to use the files [login to view URL] and [login to view URL] help you answer the following. (a) Based on an M/M/25/25 queue system what is the probability of a customer not being able to view this wonderful video? (Hint use Erlang loss formula) (b) Modify the program [login to view URL] to simulate the situation above. How long in simulation time do you need for good agreement between theory and simulation? (c) Why might exponential service times be a bad model for the above situation? (d) Using the same parameters simulate a M/D/25/25 queue, where D stands for deterministic, i.e., fixed service time (in video case 1.3 hours). How does the blocking probability compare with the M/M/25/25 case?