A Spatial Analysis of Multimodal Transport in Kisii Town Using the LWR Model

Traffic flow in most urban areas is augmenting due to the growth in transport and continual demand for it. It is multimodal and includes use of different types of vehicles, motorcycles and even walking. The assessment of uninterrupted traffic flow is traditionally based on empirical methods. This study was based on the macroscopic model which is a mathematical model that formulates the relationships among traffic flow characteristics like density, flow, mean and speed of a traffic stream. The study considered traffic models first developed by Lighthill and Whitham [14] and later Richards [20] shortly called LWR traffic flow model. Simulation by use of this method enables control strategies of congestion dissipation and has suggested some recommended measures to rationalize the design of roads and implementation of regulations of road users considering some regulations and infrastructural gaps in Kisii town. This paper focuses on two finite difference schemes, that is, first order Explicit Upwind Difference Scheme-EUDS (forward time, backward space) and second order Lax-Wendroff Difference Scheme-LWDS (forward time, centred space) for solving first order PDE as well as the traffic density $\rho(t,x)$ was computed by solving LWR macroscopic conservation form of traffic flow model using both schemes. The conditions of stability were numerically verified and it is shown that LWDS is superior to EUDS in terms of time step selection. The results obtained were compared with average key data, which provided the initial and boundary conditions used for numerical simulation.