Question

The Royal Bank is trying to decide how many drive-in teller windows to open on a busy Saturday. Director of Operations Ted Eschenbach estimates that customers arrive at a rate of about λ=18 per hour and that each teller can service about μ=20 customers per hour. Use Table D.5 to compute Lᵩand Wᵩ for each of the situations of the three situations where the number of windows is either M=1,M=2, or M=3 We assume now that the number of customers arriving on a Thursday afternoon at the Royal Bank is 15 per hour and the service rate is still 20 customers per hour. How many people are in the queue if there are 1,2 , or 3 servers?

Answer 1

On average, about 3.33 minutes elapse between two successive arrivals at the bank with an arrival rate of 18 customers per hour. For three customers to arrive, it would take approximately 10 minutes on average.

Step-by-step explanation:

Arrival Time and Probability Calculations

To answer your question, we first need to calculate the average time between customer arrivals, which is also known as the inter-arrival time. Given the arrival rate (λ) is 18 customers per hour, we can use the following formula to find the average inter-arrival time:

Average inter-arrival time = 1/λ = 1/18 hour/customer

Since there are 60 minutes in an hour, we convert this to minutes:

Average inter-arrival time = (1/18) * 60 minutes/customer ≈ 3.33 minutes/customer

On average, about 3.33 minutes elapse between two successive arrivals.

For the store to receive three customers, since customers arrive on average every 3.33 minutes, we simply multiply:

Time for three customers to arrive = 3 * 3.33 minutes ≈ 10 minutes

On average, it takes about 10 minutes for three customers to arrive.