Hand simulation is required; provide the handwritten solution. Dont use excel or other software.

The interarrival times and service times of 10 customers (in mins) for Single Queue, Single Server System Simulation. Performance measures are 1) average number of customers in queue, 2) average delay, and 3) server utilization. The system starts its operation at 9am.

Arrival Times: 1, 6, 9, 15, 19, 21, 30, 34, 39, 50

Service Times: 4, 20, 5, 10, 5, 9, 2, 8, 4, 5

That is, customer 1 arrives at 9:01am and will require 4 minutes for his/her service to be completed once he/she enters the service. At the beginning of the simulation, theres no customer in the system and the server is idle. Theres no limit on the queue size. The simulation will terminate when the 10th delay is observed.

(a) What are the system state(s) that need(s) to be introduced to calculate the three performance measures?

(b) What are the events?

(c) Draw the event timeline diagram.

(d) Draw the system state(s) graph(s) (i.e., a graph with a system state (y axis) vs simulation time (x axis))

(e) Find departure times of 10 customers.

(f) Calculate the three performance measures. Show the steps in detail.

To do the part (c)(f), create a table that shows simulation clock, next arrival time, next departure time, customer delay, number of delays, number of customers in queue, and server status.