Question

2. Go to a cafeteria and collect data on the distributions of interarrival and service times. The distribution of interarrival times is probably different for each of the three daily meals and might also vary during the meal—that is, the interarrival time distribution for 11:00 A.M.to 12:00 noon could be different from that for 12:00 noon to 1:00 P.M. Define service time as the time from when the customer reaches the point at which the first selection could be made until the time of exiting from the cafeteria line. (Any reasonable modification of this definition is acceptable.) The service-time distribution probably changes for each meal. Can times of the day or days of the week for either distribution be grouped to suit the homogeneity of the data? (Make sure that the management gives permission to perform this

Answer 1

In order to carry out this experiment, a Cafeteria called "Grand Hyatt" was chosen. The primary data are collected at the same during the peak lunch hour period (12:30 to 2:30), peak dinner hours period (8:30 to 10:00 pm) and peak breakfast hour periods (08:00 am to 10:00 am). The data are obtained by noting the customers arrival time and departure time and the time for which they have to wait.

The arrival rate is Poisson's distribution, and the service pattern is represented by Exponential Distribution.

And we find that the average arrival pattern for the customers is : 9 per hour

Average service pattern for the customers per hour is : 10 per hour.

hence, the utilisation factor : 9/10 = 0.9

This data has been deputed as the average of 5 days by once per week.

The average queue length can also be calculated by the data obtained and is found out to be 7.1.

Te average waiting time of customers in the queue is also obtained from the obtained data is around 5.75

Also, the waiting time of customers in the system and the length of the system can also be calculated by the obtained data, where the system is defined as the customer being served + the customers in the queue.