(20 pts) Let be the service capacity of a bank teller serving customers measured as the maximum number of customers who can be serviced by the teller per unit time. Consider three tellers with the service capacities: = 20/hour, = 15/hour, and = 12/hour. The bank wishes to ensure that the average time spent by a customer in the bank is no more or less the same. So, the bank employs a scheduler that splits the customer flows across the different tellers in a suitable way. See Figure 1 for illustration. Mathematically, a fraction a; of the customers is directed to the ith teller: 3 where where ; = 1.0. Assuming that customers arrive at an average rate of 30/hour, determine the split-scheduling parameters {a}i=1,2,3 for the three tellers with the service-rates {i} given above. i=1 [Hint: Use Little's law in Queuing Theory, namely: N = D , where N is the mean number of transactions in the system (i.e., the queue and service facility together), A is the mean arrival rate of transactions, and D is the mean transaction delay incurred in the system.]