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F irst National Bank of Chicago is considering opening a drive-through window for customer service. Management estimates that customers will arrive at the rate of 15 per hour ( arrival rate = λ). The teller who will staff the window can serve customers at the rate of one every three minutes (service rate = µ). Note: These symbols that are required can be found in MS Word – Insert – Symbols to answer the following questions:
1. Average number of customers in service (for single phase, this is equivalent to utilization of the teller and should be expressed as a percent).
2. Average number in line (queue).
3. Averaage number in system.
4. Average waiting time in line (queue).
5. Average waiting time in system.
Your answers and help and ALL questions will be appreciated. Thanks.
Expert Answer
Arrival rate() = 15 per hour
Service rate() = 1 per 3 minutes = (60/3) per hour = 20 per hour
1) Average number of customer in service or average utilization of the teller = /
= 15/20 = 0.75 = 75%
2) Average number in line(Lq) = Square of / [
(
–
)]
= Square of 15 / [20(20-15)]
= 225 / 100
= 2.25 customers
3)Average number in the system (Ls) = /(
–
) = 15 / (20-15)= 15/5 = 3 customers
4) Average waiting time in the queue = Lq / = 2.25 / 15 = 0.15 hours or 9 minutes
5) Average waiting time in the system = Ls/ = 3/15 = 0.2 hours or 12 minutes
