Question

Write a FORTRAN program to simulate the daily activity at a gas station. Assuming that one customer is served every six minutes, what is the average waiting time per customer?

Answer 1

SOLUTION :

This is a problem in discrete simulation. A random number generator is used in the program to model the arrival of customers. Since the gas station attendant cannot know if the stream of customers will be continuous, randomness of arrivals is assumed.
To calculate the average waiting time, the program should compute the waiting time of each individual car, add the times, and divide that sum by the total number of cars. The first arrival incurs no waiting time, but all subsequent arrivals must wait six minutes for each car in front of them. To obtain an average the service time remaining for each car, the total waiting time for all the cars, and the number of cars that are lined up must be found.
For each simulated minute, the program must reduce the service time SERV by one and check to see if another car has arrived. If so, the waiting time for that last car is given by SERV. WAIT - the total waiting time, is increased by adding SERV to it, while the number of cars, CARTOT, is Increased by one, and SERV is increased by six minutes. The parameter N is the number of minutes to be simulated (N cannot contain more than 6 digits).
Another assumption made is that customers arrive each minute with a probability of 0.1. To simplify the problem, it is assumed that there is only one gas pump at this station.
Note, that several values of N can be entered in the DATA section. The program procedure will be done for each of those time intervals. In order to end the program, enter N ≤ 0 as the last value.
C GASOLINE LINE SIMULATION

INTEGER WAIT, SERV, CARTOT, TIME

5 READ (5,1)N

1 FORMATE (I6)

C DO WHILE N GREATER THAN ZERO

IF (N. LE. 0) GO TO 99

SERV = 0

WAIT = 0

CARTOT = 0

DO 10 TIME = 1,N

SERV = MAX (SERV − 1,0)

22 2 CALL RAND (X)

IF (X.GT.0.1) GO TO 22

CARTOT = CARTOT + 1

WAIT = WAIT + SERV

SERV = SERV + 6

10 CONTINUE

AVWAIT = FLOAT (WAIT)/FLOAT (CARTOT)

WRITE (6,101) CARTOT,AVWAIT

101 FORMAT (IX,'AVERAGE WAIT FOR EACH OF THE',

16,'CUSTOMERS IS', F6.2,'MINUTES.')

GO TO 5

C END DO-WHILE

99 STOP

END