BU275 Assignment 2 Equations Question 1 A Station 1: Prep Inter-arrival time is the time between consecutive arrivals of the customers. Because the inter-arrival times are exponentially distributed, customers arrive at random times. The mean is 100 customers/ hours. This indicates that a customer arrives every 0.6 minutes. Time of arrival for this station is the time that the customer arrives at the store. The time of arrival of the first customer is given as the first customer’s inter-arrival time. With each subsequent customer, the time of arrival is equal to the previous customer’s arrival time + the inter-arrival time for the current customer. Service begin time at this station is when the service for the customer begins. This …show more content…
The service time for this store is normally distributed. This number was found by taking the maximum between 0 and the normally distributed service times. A zero-service time is used to for premade sandwiches, where the customer does not have to wait because the sandwich is ready for them when they arrive. End service time is the sum of service begin time and service time. Time in line is the time the customer spends waiting in line to be served, which is calculated by finding the difference between the time they arrived and when their service began. Station 2: Toast Time of arrival at this station is the time that the service ends at station 1, as this is the time the customer is finished at station 1 and the customer arrives at station …show more content…
The formula is the utilization rate found is 93%, which represents the percentage of time that the toaster is in use. This was calculated by taking the inter arrival time average . Then, the average of the service time of the toaster was calculated, and lambda was calculated by the following equation,. Finally the value was the used to find utilization factor . The siumlation was ran 1000 times and in the long run the utilization rate will be very close to 70% (69.44%) as 70% of the customers prefer to toast. Question 2 A To make sure the 7th customer is not served right away, the maximum or the arrival time of the 7th customer, end of service time of the 6th customer at station 1 and the end of service time of the first customer at station 3. The max of the first customer was used to ensure the queueing discipline is first come first serve, and the first customer who enters will be served before any proceeding customers. Also, to ensure there are always 6 customers in the store. The max between. The max between the arrival time and end of service time at station 1 is used to ensure the 7th customer is served after the 6th is