Question: 1. [20 points] A small grocery store has one checkout counter. Customers arrive at the checkout counter at random times that range from 1 to

1. [20 points] A small grocery store has one checkout counter. Customers arrive at the checkout counter at random times that range from 1 to 7 minutes apart. We assume that interarrival times are integer-valued with each of the 7 values having equal probability, this is a discrete uniform distribution. The service times vary from 1 to 5 minutes (also integer-valued). Our objective is to analyze the system by simulating the arrival and service of 10 customers and to compute a variety of typical measures of performance for queueing models. The following table shows the simulation table for the single-server queue. We assume that the first customer arrives at time 0 with service beginning immediately. i At W Si D Elapsed Time in System Idle Time of Server 1 N 2 2 ano 5 7 AN 3 AN 4 12 6 3 5 4 6 1 2 4 7 4 8 5 7 1 9 9 3 3 5 10 5 (a) [15 points] Complete the spreadsheet table. (b) (1.5 points) What is the average waiting time of 10 customers? (c) (1.5 points) What is the average time that a customer spends in the system? (d) [2 points] What is the probability that a single server is idle for running the simulation? (Hint: Total simulation run time = 45 minutes) 1 1. [20 points] A small grocery store has one checkout counter. Customers arrive at the checkout counter at random times that range from 1 to 7 minutes apart. We assume that interarrival times are integer-valued with each of the 7 values having equal probability, this is a discrete uniform distribution. The service times vary from 1 to 5 minutes (also integer-valued). Our objective is to analyze the system by simulating the arrival and service of 10 customers and to compute a variety of typical measures of performance for queueing models. The following table shows the simulation table for the single-server queue. We assume that the first customer arrives at time 0 with service beginning immediately. i At W Si D Elapsed Time in System Idle Time of Server 1 N 2 2 ano 5 7 AN 3 AN 4 12 6 3 5 4 6 1 2 4 7 4 8 5 7 1 9 9 3 3 5 10 5 (a) [15 points] Complete the spreadsheet table. (b) (1.5 points) What is the average waiting time of 10 customers? (c) (1.5 points) What is the average time that a customer spends in the system? (d) [2 points] What is the probability that a single server is idle for running the simulation? (Hint: Total simulation run time = 45 minutes) 1

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