A drug store has two windows available for serving customers, who arrive at the Poisson rate of 40/hr. Service time is exponentially distributed with the mean of 2 min. Only one window is open as long as there are three or less customers in shop. Identical server opens second window when there are four or more customers in shop. Manager of shop helps two attendants when there are six or more customers in shop. When manager is helping, mean service time for each of two servers is reduced to 1.5 min. Shop can’t legally hold more than 20 customers. Make use of general birth-death process to find out:
i) expected number of customers in shop
ii) probability that manager will be helping serve customers and,
iii) probability that store is full.