This exercise examines the basic principles and concepts of discrete event simulation. Let's start with a single-channel queue. Assume a small grocery store has only one checkout counter. Customers arrive at this checkout counter at random intervals from 1 to 8 minutes apart with each possible value of integer interarrival time having the same probability of occurrence. That is, customer arrival times are uniformly distributed over the eight integer values 1 through 8. Assume that customer service times vary from 1 to 6 minutes with the following probabilities: Service time: Probability: 1 .10 2 3 20 .30 4 5 6 .25 .10 .05 The essence of manual simulation is a simulation table. The table construction is designed for the problem at hand and structured to answer any posed questions. For this simple queue we may want to analyze and answer the following questions: 1) What is the average customer waiting time? 2) What is the probability a customer had to wait? 3) What proportion of the time is the server idle? 4) What is the average service time? 5) What is the average time between arrivals? 6) What is the average waiting time for those customers that had to wait? 7) What is the average time a customer spends in the system? With these questions a simulation table may have the following column headings: (you may adjust this table if needed) Customer Time Arrival since time Service Service time Time begins in Service end last arrival queue Time in system time Server idle Problem 1. (35 points) Analyze system performance by simulating the arrival and service for 200 customers. Complete the simulation table for the 20 customers and develop the system performance estimators outlined above (answer the 7 questions above). Any time you use a random variate, you need to create your own formula and include the random variate formula in your problem summary. Problem 2. (25 points) Now let the arrival distribution be uniformly distributed between 1 and 10 minutes and repeat the 200-customer analysis. What is the effect of changing the arrival time distribution? Problem 3. (25 points) Let the service distribution be changed to the following: Service time: Probability: 1 2 3 4 5 .05 .10 .20 .30 .25 6 .10 Assume that the customer arrival times are again uniformly distributed over the eight integer values 1 through 8. Repeat the 200-customer analysis. Again, include your random variate generator in your summary. What is the effect of changing the service time distribution?