Consider a counter with a single clerk that serves customers arriving according to a Poisson process with rate c = 8 hr1 following a FCFS protocol. The serving of any given customer by the clerk involves the processing of some paperwork and the required time for this paperwork is normally distributed with mean tc = 5 min and st. deviation c = 3 min. However, while serving a customer, the clerk might need to make some clarifying phone calls, and past observations have shown that these phone calls occur according to a Poisson process with rate p = 5 hr1 and their duration is exponentially distributed with mean tp = 3 min.

i. Show that the counter will serve the arriving customers in a stable manner.

ii. What is the throughput with which customers are serviced at this counter?

iii. Also, provide a Mean Value Analysis (MVA) of this counter with respect to the serviced customers; in particular, compute: (i) E[W ], the expected waiting time by any customer before she is picked up for service by the clerk; (ii) E[S], the expected total time spent by a customer at this counter; (iii) E[Xq], the expected number of customers waiting for service; and (iv) E[X], the expected number of customers present at the counter when considering also the potential customer in service.