Question
The management of a busy petrol station is concerned thatcustomers are being lost because of long waiting times sometimesrequired at their petrol pump. Over a two weeks period a carefulstudy has been taken of the arrival of cars and the length of timetaken to serve customers at the petrol station. The tables belowshow the arrival rates and the service time distribution:
Inter arrival time (minutes) | Percentage of customers | | Service time (minutes) | Percentage of customers | |
0 - <2 | 60 | | 0 - <4 | 20 | |
2 - <4 | 25 | | 4 - <6 | 30 | |
4 - <6 | 10 | | 6 - <8 | 20 | |
6 - <8 | 5 | | 8 - <10 | 15 | |
| | | 10 - <12 | 15 | |
- Assuming that the petrol station has only one pump and only onemember of staff attend the customers, simulate the arrival of thefirst 10 customers and calculate the following:
(a) Â Â Â 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.
| | | | 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 | | | | | | | | | |
2 | | | | | | | | | |
3 | | | | | | | | | |
4 | | | | | | | | | |
5 | | | | | | | | | |
6
| | | | | | | | | |
7 | | | | | | | | | |
8 | | | | | | | | | |
9 | | | | | | | | | |
10 | | | | | | | | | |
| | | | | | | | | |
