Some Circumstances in Which Vehicles Will Reach Their Destinations Earlier by Starting Later

Since the speed of travel on a road usually decreases as flow increases, there are often advantages in extending the period over which travelers on a road system begin their journeys, but, since travelers often wish to reach their destinations almost simultaneously, there are also advantages in reducing the period over which they spread their journeys. This suggests that there may be an optimum period during which vehicles should begin their journeys on a road system in order to reach their destinations within the shortest possible time. An analysis of the situation suggests that, if n vehicles spread their entry times into a road system uniformly over a period of time t and travel an average distance l , then the time from the first vehicle entering to the last vehicle arriving at its destination is a minimum when ( l / v 2 )( dv / dq ) + ( t 2 / nl ) = 0, where v is the average speed when the flow is q vehicles per unit time. The average journey time (also measured from the entry time of the first vehicle is minimal when ( l / v 2 )( dv / dq ) + ( t 2 /2 nl ) = 0. These considerations have been applied to the case of vehicles entering a city center during peak travel periods. The calculations suggest that the “optimum” duration of entry times is associated with a particular average speed of travel, which is itself dependent on the value of fA / n , where f is the fraction of the surface area A of the city center used for roads.