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Given the input parameters, simulation variable, output statistics for the queueing system.

Calculate the output statistics for the queueing system whose inter-arrival and service times for ten arrivals are given below:

Inter-arrival time - 8 6 1 8 3 8 7 2 3
Service time 4 1 4 3 2 4 5 4 5 3

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Solution:

Customer IAT AT ST Time
Service
Begin
Time
Cust
waits
in queue
Time
Service
ends
Time
Cust
spends
in s/m
Idle
time
server
1 - 0 4 0 0 4 4 0
2 8 8 1 8 0 9 1 4
3 6 14 4 14 0 18 4 5
4 1 15 3 18 3 21 6 0
5 8 23 2 23 0 25 2 2
6 3 26 4 26 0 30 4 1
7 8 34 5 34 0 39 5 4
8 7 41 4 41 0 45 4 2
9 2 43 5 45 2 50 7 0
10 3 46 3 50 4 53 7 0
- $\sum$ 46 - $\sum$ 35 - $\sum$ 9 - $\sum$ 44 $\sum$ 18

AT: Arrival time

IAT: Interarrival time

ST: Service Time

o/p statistics

1. Avg waiting time for a customer = $\frac{9}{10} = 0.9$

2. Probability of Idle server = $\frac{18}{53} = 0.34$

3. Probability customer has to wait = $\frac{3}{10} = 0.3$

4. Avg service time = $\frac{35}{10} = 3.5$

5. Avg time between arrival = $\frac{46}{9} = 5.11$

6. Avg waiting time for customer who waits = $\frac{9}{3} = 3$

7. Avg time customer spent in the system = $\frac{44}{10} = 4.4$

8. Max queue length = 1