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This is dependent on the arrival time of each of the vehicles as well as the wait time that is expected with each one. It was assumed that each of the cars would take an average of 3 minutes in wait time to fill up the tank. The RN1 and RN2 were created with the average time which each vehicle would arrive. Since these were based on the arrival time according to random intervals, this helped to give average times of the main time when each vehicle would arrive. To determine the wait time and the average time at the pump, there was a basis of seeing when the first vehicle would arrive at the pump filling station.
It was expected that no other car would be at the filling station at that time. If a car was at the station before the other, then the duration of waiting time was calculated with the outcome being a 3 minute time at the station and the remainder of the time being based on the amount of wait time that each vehicle had to take. This gave an average wait time for each of the vehicles and provided insight into the vehicles that were seeking fuel at random times. The vehicles which arrived first determined the wait time for the vehicles that arrived later.
For instance, if a vehicle arrived 2 minutes after a car before, then it was expected that there would be a wait time before the vehicle would fill up the gas. The advantage of the gas filling station comes with the expectations from the owner, which is that 65% arrive 4-5 minutes after the previous vehicle. This lowers the amount of wait time and allows the vehicle to be free. However, if a vehicle arrives within the 1-3 minute time frame, then there is an expected wait. If this occurs continuously then it is expected that the wait time will increase according to the number of vehicles, time spent at the pump and the wait in which the vehicle had from the previous vehicle that was filling up at the pump.
This caused some of the vehicles to wait for up to 9 minutes before having the opportunity to fill up their vehicle. However, this balanced out because of the five minute intervals that were between vehicles which caused some portions of the pump to not service vehicles at a given time. The assumptions made with this particular chart were based on several factors. The first was that it would take an average of 3 minutes for each vehicle to complete what is needed. However, it was also stated that this was the average of all vehicles as stated by the owner.
This fluctuation would change the wait time of all vehicles and would alter the results. It was also assumed that the vehicles arrived at the random intervals provided and would have to wait for the previous vehicles to finish filling. However, this would alter according to the speed of the last vehicle and the lining that was taking place with the vehicles. The system used within the gas station would
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