2. (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: 1=20/ hour, 2=16/ hour, and 3=13/ 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 i of the customers is directed to the ith teller: where i=13i=1.0. Assuming that customers arrive at an average rate of 35/ hour, determine the split-scheduling parameters {i}i=1,2,3 for the three tellers with the service-rates {i} given above. [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), is the mean arrival rate of transactions, and D is the mean transaction delay incurred in the system.] Quality of customer service enforcement at a service center: say, bank Customer transaction arrival rate and Teller service rate x : waiting customer are expressed as "number of transactions per hour" Figure 1: Illustration of split-scheduling of customers in a service-center: say, bank