Reference no: EM133637752

Question: Consider a bank with one teller. The average time between customer arrivals to the bank is 10 minutes. The teller can serve customers in 7.5 minutes, on average. Assume that the coefficient of variation of the inter-arrival times and service times is 1.

What is the average time a customer spends in the system (i.e., W)?

What is the average number of customers waiting in the system (i.e., Lq)?

Suppose that the bank reduces the coefficient of variation for inter-arrival times to zero (i.e. CVIAT = 0) by implementing an appointment system. What is now the average time a customer spends in the system (i.e., W) after the implementation of the appointment system?

For questions 4-6 use the following scenario: A gas station currently has two gas pumps serving its customers. On average, 18 vehicles arrive to the gas station every hour. The coefficient of variation of inter-arrival times equals 1. Each vehicle requires an average of 6 minutes at the pump. The coefficient of variation of service times equals 0.5. The traffic in the gas station is organized such that a single waiting line is formed for both pumps.

What is the average utilization (i.e., u) of the gas station?

How much time (both waiting and pumping gas) do vehicles spend in the gas station, on average (i.e., what is W)?

The manager of the gas station realizes that she is losing customers due to long waiting lines. As a result, she decides to add a third pump (that would be identical to the existing pumps) that would serve the customers in 6 minutes on average with a service time coefficient of variation of 0.5. What is the average number of vehicles waiting in line (i.e., Lq) in this new layout in which customers form a single line for all three pumps?

When there is variability in service times and/or inter-arrival times, the effect of an increase in utilization on waiting time is greater when utilization is high.