Exhibit 12.5
The following questions use the information below.
The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem.
-An arrival process is memoryless if the time until the next arrival occurs is inversely proportional to the time elapsed since the last arrival.

Question

Exhibit 12.5
The following questions use the information below.
The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem.  
-An arrival process is memoryless if the time until the next arrival occurs is inversely proportional to the time elapsed since the last arrival.

Quizplus · Accepted Answer

The statement describes the property of a Poisson process, not necessarily all memoryless arrival processes. A memoryless arrival process only requires that the probability distribution of the time until the next arrival does not depend on how much time has elapsed since the last arrival.

Exhibit 12.5 The Following Questions Use the Information Below