Arrival and service time for a shop is randomly distributed.

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written 8.3 years ago by

teamques10 ★ 67k

• modified 3.9 years ago

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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written 8.3 years ago by

teamques10 ★ 67k

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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