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Arrival and service time for a shop is randomly distributed.

Arrival and service time for a shop is randomly distributed. Simulate the system to help the shopkeeper in making a decision of taking helpers in his shop. - | Arrival time | Probability | Service time | Probability | |--------------|-------------|--------------|-------------| | 0 | 0.06 | 4 | 0.04 | | 3 | 0.09 | 6 | 0.10 | | 6 | 6 | 8 | 0.18 | | 9 | 0.37 | 10 | 0.44 | | 12 | 0.16 | 12 | 0.24 | | 15 | 0.07 |   |   |

Random numbers: 5887, 4739, 2328, 6997, 3569, 5587, 6952, 9052, 8615, 7485 - $1^{st}$ 2 digits represent – random no. of arrival - Last 2 digits represent – random no. of service -

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Arrival time Probability Cumulative Probability Random Numbers Assigned
0 0.06 0.06 0-5
3 0.09 0.15 6-14
6 0.25 0.40 15-39
9 0.37 0.77 40-76
12 0.16 0.93 77-92
15 0.07 1.00 93-99
Service time Probability Cumulative Probability Random Numbers Assigned
4 0.04 0.04 0-3
6 0.10 0.14 4-13
8 0.18 0.32 14-31
10 0.44 0.76 32-75
12 0.24 1.00 76-99
No. Random,No. Arrival Random No. Arrival Time Service Random,No. Service Time Service Starts Service Ends Server Idle Time Custo-mer wait time
1 5887 58 0+9=9 87 12 9 21 9 -
2 4739 47 9+9=18 39 10 21 31 - 3
3 2328 23 18+6=24 28 8 31 39 - 7
4 6997 69 24+9=33 97 12 39 41 - 6
5 3569 35 33+6=39 69 10 41 51 - 2
6 5587 55 39+9=48 87 12 51 63 - 3
7 6952 69 48+9=57 52 10 63 73 - 6
8 9052 90 57+12=69 52 10 73 83 - 4
9 8615 86 69+12=81 15 8 83 91 - 2
10 7485 74 81+9=90 85 12 91 103 - 1

Besides the first customer, all the customers who arrive have to wait for some time. The average waiting time is 3.4. So it is advisable for the shopkeeper to take help.

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