American Journal of Computational Mathematics, 2016, 6, 55-65 Published Online June 2016 in SciRes. http://www.scirp.org/journal/ajcm http://dx.doi.org/10.4236/ajcm.2016.62007 How to cite this paper: Ali, A. and Andallah, L.S. (2016) Inflow Outflow Effect and Shock Wave Analysis in a Traffic Flow Si- mulation. American Journal of Computational Mathematics, 6, 55-65. http://dx.doi.org/10.4236/ajcm.2016.62007 Inflow Outflow Effect and Shock Wave Analysis in a Traffic Flow Simulation Ahsan Ali 1 , Laek Sazzad Andallah 2 1 Department of Electronics and Communications Engineering, East West University, Dhaka, Bangladesh 2 Department of Mathematics, Jahangirnagar University, Dhaka, Bangladesh Received 21 February 2016; accepted 24 April 2016; published 27 April 2016 Copyright © 2016 by authors and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/ Abstract This paper investigates the effect of inflow, outflow and shock waves in a single lane highway traf- fic flow problem. A constant source term has been introduced to demonstrate the inflow and out- flow. The classical Lighthill Whitham and Richards (LWR) model combined with the Greenshields model is used to obtain analytical and numerical solutions. The model is treated as an IBVP and numerical solutions are presented using Lax Friedrichs scheme. Godunov method is also used to present shock wave analysis. The numerical procedures adopted in this investigation yield results which are very much consistent with real life scenario in terms of traffic density and velocity. Keywords Macroscopic Model, Source Term, Shock Wave, Lax Friedrichs Scheme, Godunov Method 1. Introduction The problem of traffic congestion is becoming endemic due to increased levels of population. Traffic conditions in many major metropolitan areas are becoming increasingly congested, affecting the operational efficiency of whole networks as well as the travel cost of each trip. Therefore, traffic flow models are becoming more impor- tant in traffic engineering and the transportation policy making process. In an effort to minimize congestion, an accurate method for modeling the flow of traffic is imperative. Mainly two approaches are widely used in de- scribing traffic flow phenomena mathematically. The first one is the microscopic model which describes flow by tracking individual vehicles using car-following logic. On the other hand, macroscopic models are concerned with describing the flow-density relationship for a traffic stream (a group of vehicles). Macroscopic models are more suitable for modeling traffic flow since less supporting data and computation are needed. In this paper, we have studied macroscopic traffic flow models.