A bank has one drive-in teller and room for one additional customer to wait. Cus

Question

A bank has one drive-in teller and room for one additional customer to wait. Customers arriving when the queue is full park and go inside the bank to transact business. The times between arrivals and the service-time distribution follow: Simulate the operation of the drive-in teller for 10 new customers. The first of the 10 new customers arrives at a me determined at random. Start the simula on with customer being served, leaving at me 3, and on in the queue. How many customers went into the bank to transact business?

Explanation / Answer

First, let us determine the random number ranges for the Probablilty Distribution for time between arrivals.

Second, we deduce similar ranges for the service time (minutes).

Below, we calculate the customers who end up going to the bank depending on the random range # of arrival and service time.

For example, in the table below, customer 3 has Inter-Arrival time 2 (corresponding to 0.50 in inter-arrival time range 0.26-0.52) and Service Time 4 (corresponding to 0.90 in service time range 0.88-0.99). Since his/her no. in queue is 0, the customer does not go to the bank and service starts immediately after customer 2 i.e. at 6 min and ends at 10 min (service time of 4 min). Similarly, for other customers, the above process is followed to determine whether the customer goes to the bank or not.

Hence, to sum up, by the above values taken, 2 customers went to the bank to transact business.

P.S. - A typo in the question, should have been "...leaving at time 3" instead of "...leaving at me 3". The above tables are self-explanatory, please do let me know if you have any further clarification.

Time between arrivals (minutes) Probability Cumulative Probability Range 0 0.09 0.09 0.00-0.08 1 0.17 0.26 0.09-0.25 2 0.27 0.53 0.26-0.52 3 0.20 0.73 0.53-0.72 4 0.15 0.88 0.73-0.87 5 0.12 1.00 0.88-0.99

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