4. A supermarket has two exponential checkout counters, each operating at rate u. Arrivals are Poisson at rate λ. The counters operate in the following way: 1) One queue feeds both counters. 2) One customer is operated by a permanent checker; and the other by a stock clerk who instantaneously begins checking whenever there are two or more customers in the system. The clerk returns to stocking whenever he completes a service, and there are less than two customers in the system. a. Let Pn solve. = proportion of time there are n in the system. Set up equations for Pn and b. At what rate does the number in the system go from 0 to 1? From 2 to 1? c. What proportion of time is stock clerk checking? d. Hint: Be a little careful when there is one in the system. atomer left