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Please answer the question acurately. Thank you very much. ( 2 0 p t s ) Let be the service capacity of a bank teller

Please answer the question acurately. Thank you very much. (20pts) 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: ?bar(N)?b=ar(D)bar(), where ?bar(N) is the mean number of
transactions in the system (i.e., the queue and service facility together),?bar() is the mean arrival rate of
transactions, and ?bar(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
are expressed as "number of transactions per hour"
Figure 1: Illustration of split-scheduling of customers in a service-center: say, bank
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