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Consider the following inter-arrival and service times for the first 25 customers to a single server queuing system.

Customer	Inter-Arrival	Service	Time of
Number	Time	Time	Arrival
1	22	74	22
2	89	105	111
3	21	34	132
4	26	38	158
5	80	23
6	81	26
7	78	90
8	20	26
9	32	37
10	13	88
11	28	38
12	18	73
13	29	93
14	19	25
15	20	93
16	23	5
17	78	37
18	20	51
19	109	28
20	78	85

We are given the inter-arrival times. Determine the time of arrival of each customer. Complete the event and state variable change table associated with this situation. Draw a sample path graph for the variable N(t)N(t) which represents the number of customers in the system at any time tt. Compute the average number of customers in the system over the time period from 0 to 700. Draw a sample path graph for the variable NQ(t)NQ(t) which represents the number of customers waiting for the server at any time tt. Compute the average number of customers in the queue over the time period from 0 to 700. Draw a sample path graph for the variable B(t)B(t) which represents the number of servers busy at any time t. Compute the average number of busy servers in the system over the time period from 0 to 700. Compute the average time spent in the system for the customers.

• What is the time of arrival for the 16^th customer?

• What is the departure time of the 10^th customer?

• What is the system time of the 19^th customer?

• Show your sample path graph for N(t)

• What is the average time in the system?

• What is the average number of customers in the system over the time range from 0 to 700?

• What is the average number of customers waiting in queue over the time range from 0 to 700?

• What is the average number of busy servers over the time range from 0 to 700?

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