The management of a busy petrol station is concerned that customers are being lost because of long waiting times sometimes required at their petrol pump. Over a two weeks period a careful study has been taken of the arrival of cars and the length of time taken to serve customers at the petrol station. The tables below show the arrival rates and the service time distribution: Inter arrival time (minutes) Inter arrival time Midpoint Percentage of customers Cumulative frequency Random number 0 - <2 1 60 60 00 - 59 2 - <4 3 25 85 60 - 84 4 - <6 5 10 95 85 - 94 6 - <8 7 5 100 95 - 99 Service time (minutes) Inter arrival time Midpoint Percentage of customers Cumulative frequency Random number 0 - <4 2 20 20 00 – 19 4 - <6 5 30 50 20 – 49 6 - <8 7 20 70 50 - 69 8 - <10 9 15 85 70 – 84 10 - <12 11 15 100 85 – 99 Assuming that the petrol station has only one pump and only one member of staff attend the customers, simulate the arrival of the first 10 customers and calculate the following: (a) Average inter-arrival time. Average service time. Average waiting time. Average queue length. Use the random numbers given below for the simulation. 89,34,07,65,37,11,29,80,28,34,08,14,75,92,01,48,21,83,63,91.
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Question
The management of a busy petrol station is concerned that customers are being lost because of long waiting times sometimes required at their petrol pump. Over a two weeks period a careful study has been taken of the arrival of cars and the length of time taken to serve customers at the petrol station. The tables below show the arrival rates and the service time distribution:
|
Inter arrival time (minutes) |
Inter arrival time Midpoint |
Percentage of customers |
Cumulative frequency |
Random number |
|
0 - <2 |
1 |
60 |
60 |
00 - 59 |
|
2 - <4 |
3 |
25 |
85 |
60 - 84 |
|
4 - <6 |
5 |
10 |
95 |
85 - 94 |
|
6 - <8 |
7 |
5 |
100 |
95 - 99 |
|
|
|
|
|
|
|
Service time (minutes) |
Inter arrival time Midpoint |
Percentage of customers |
Cumulative frequency |
Random number |
|
0 - <4 |
2 |
20 |
20 |
00 – 19 |
|
4 - <6 |
5 |
30 |
50 |
20 – 49 |
|
6 - <8 |
7 |
20 |
70 |
50 - 69 |
|
8 - <10 |
9 |
15 |
85 |
70 – 84 |
|
10 - <12 |
11 |
15 |
100 |
85 – 99 |
- Assuming that the petrol station has only one pump and only one member of staff attend the customers, simulate the arrival of the first 10 customers and calculate the following:
(a) Average inter-arrival time.
- Average service time.
- Average waiting time.
- Average queue length.
Use the random numbers given below for the simulation.
89,34,07,65,37,11,29,80,28,34,08,14,75,92,01,48,21,83,63,91.
my answer:
|
|
|
|
|
Service |
|
|
|||
|
Cust. No. |
Random Number |
Inter-Arrival Time |
Clock time |
Random Number |
Service Time |
Service Starts |
Service Ends |
Waiting Time |
Queue Length |
|
0
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
1
|
89 |
5 |
5 |
08 |
2 |
5 |
7 |
0 |
|
|
2
|
34 |
1 |
6 |
14 |
2 |
7 |
9 |
1 |
|
|
3
|
07 |
1 |
7 |
75 |
9 |
9 |
18 |
2 |
|
|
4
|
65 |
3 |
10 |
92 |
11 |
18 |
29 |
8 |
|
|
5
|
37 |
1 |
11 |
01 |
2 |
29 |
31 |
18 |
|
|
6 |
11 |
1 |
12 |
48 |
5 |
31 |
36 |
19 |
|
|
7
|
29 |
1 |
13 |
21 |
5 |
36 |
41 |
23 |
|
|
8
|
80 |
3 |
16 |
83 |
9 |
41 |
50 |
25 |
|
|
9
|
28 |
1 |
17 |
63 |
7 |
50 |
57 |
33 |
|
|
10
|
34 |
1 |
18 |
91 |
11 |
57 |
68 |
39 |
|
|
|
|
AVG = 1.8 |
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AVG= 6.3 |
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AVG= 16.8 |
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How to find the Queue Length??
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