The Sydney Harbour Bridge has eight lanes for traffic each of which can be controlled by the RTA station manager to be used for either northbound or south-bound traffic-but never for both. Hence, the manager must decide at different times of the day just how many lanes to use for north-bound traffic and how many to be set up to allow south-bound traffic. Between the hours of 7 and 9 am, north bound cars arrive at the bridge at the rate of about 72 per minute. During the same morning rush hours, south-bound vehicles enter the bridge at a rate of about 126 per minutes. Each lane can allow an average 30 vehicles per minutes.
Assuming that vehicles entering the bridge form a queue and proceed to the first empty lane to pay the toll fee. The station manager does not want vehicles to wait in a queue for more than six seconds on average and does not want any queue to contain more than eight vehicles on average.
Is this achievable during the 7 to 9 am period? If not, would it be acheivable if an existing emergency is also used to carry traffic during this peak period?