This dissertation is motivated by practical problem of traffic flow on roundabouts.rnThe study aimed at modelling traffic flow on roundabouts, proposingrnan optimization strategy for traffic flow on roundabouts and investigatingrnthe impact induced by short stay of pedestrians on the crosswalk on thernperformance of the roundabout in regulating traffic flow problem. To this end,rnmacroscopic approach of traffic modelling has been used. To be specific, firstrnthe roundabout was modelled as a sequence of 2 2 junctions with one mainrnlane and secondary incoming and outgoing roads. The evolution of traffic flowrnon the road networks of the roundabout was modelled by Lighthill-Whitham-rnRichards model. Then, we considered two cost functionals: the total travel timernand the total waiting time, which give an estimate of the time spent by driversrnon the network section. These cost functionals were minimized with respect tornthe right of way parameter for the incoming roads. For each cost functional,rnthe analytical expression was given at each junction. We then solved numericallyrnthe optimization problem and the traffic behaviour was studied on thernwhole roundabout. The approach was numerically tested on a simple roundaboutrnwith three incoming and three outgoing roads. Two different choices ofrnparameters were considered: instantaneously locally optimal and a well chosenrnbut fixed values. The simulation results have shown that the local optima parameterrnvalue outperform the other choices, in improving the performances ofrnthe network. This result indicate the effectiveness of the optimization strategyrncompared to the case of fixed constant right of way parameters. In the secondrncase, we formulated the problem in discrete form. Then a cost functional thatrnmeasures the total travel time spent by drivers on the roundabout in discreternform were introduced. Numerical tests were conducted for a roundabout withrnfour incoming and four outgoing roads. The simulation results show that gradientrnbased instantaneous optimal choice of the priority parameters producernbetter results in improving the performance of the roundabout compared tornthe fixed choices of priority parameters. In the third case, we considered thernroundabouts as alternatively periodic sequences of 21 and 12-type junctionsrnand external incoming and outgoing roads. The evolution of traffic flowrnon the road networks of the roundabout was modelled by Lighthill-Whitham-rnRichards model with extended flux to capture the presence of pedestrians onrncrosswalk. To this end, we introduced three cost functionals that measure therntotal mass of vehicle , average velocity, and total flux respectively on the network.rnThen we analyzed the performance of the roundabout with and withoutrnpedestrian through numerical simulation using Godunov scheme. The simulationrnresult indicated that, the presence of pedestrians on the crosswalk reducesrnthe performance of roundabout in controlling traffic flow problem.