7.20. Two tellers are now on duty in a bank from Exercise 7.11, and they work as an M/M/Z queuing system with the arrival rate of 0.4 min'1 and the mean service time of 2 min. (a) Compute the steady state probabilities 1m, ...,1rm and use them to approximate the expected number of customers in the bank as 10 E(X) a 2 1:17,. :I:=D (b) Use the Little's Law to nd the expected response time. (c) From this, derive the expected waiting time and the expected number of waiting customers. (d') Derive the exact expected number of customers E(X ) without the approximation in (a) and use it to recalculate the answers in (b) and (c). (Hint: E(X) is computed as a series; relate it to the expected number ofjobs in the M/M/I system). 7.22. Sports fans tune to a local sports talk radio station according to a Poisson process with the rate of three fans every two minutes and listen it for an Exponential amount of time with the average of 20 minutes. (a) What queuing system is the most appropriate for this situation? (b) Compute the expected number of concurrent listeners at any time. (b) Find the fraction of time when 40 or more fans are tuned to this station. 7.23. Internet users visit a certain web site according to an M/M/oo queuing system with the arrival rate of 2 min-3L and the expected time of 5 minutes spent at the site. Compute (a) the expected number of visitors of the web site at any time; (b) the fraction of time when nobody is browsing this web site