An Approximation for General Transit Time Function

People have unpleasant experience of driving through congested road network of urban areas, where transit time is not constant but flow-dependent. Network flow over time with flow-dependent transit times is more realistic than flow over time with fixed transit time on arcs which is an active area of research from last two decades. In traffic assignment problem, transmission time of the vehicles directly depends on the number of vehicles entering on the road. So, general transit time function is non-decreasing, convex and left-continuous. In this paper we discuss how a general transit time function can be approximated by the step function. It relaxes the inflow-dependent transit times to a bow graph. We calculate maximum bow flow by using temporally repeated flow for the given time horizon. Our aim is to show how flow value in step function converges to the flow value of general transit time function by increasing number of points in the domain of the step function.