Macroscopic Traffic Flow Modelling on Roundabouts and Optimization
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Date
2015-07
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Addis Ababa University
Abstract
This dissertation is motivated by practical problem of traffic flow on roundabouts.
The study aimed at modelling traffic flow on roundabouts, proposing
an optimization strategy for traffic flow on roundabouts and investigating
the impact induced by short stay of pedestrians on the crosswalk on the
performance of the roundabout in regulating traffic flow problem. To this end,
macroscopic approach of traffic modelling has been used. To be specific, first
the roundabout was modelled as a sequence of 2 2 junctions with one main
lane and secondary incoming and outgoing roads. The evolution of traffic flow
on the road networks of the roundabout was modelled by Lighthill-Whitham-
Richards model. Then, we considered two cost functionals: the total travel time
and the total waiting time, which give an estimate of the time spent by drivers
on the network section. These cost functionals were minimized with respect to
the right of way parameter for the incoming roads. For each cost functional,
the analytical expression was given at each junction. We then solved numerically
the optimization problem and the traffic behaviour was studied on the
whole roundabout. The approach was numerically tested on a simple roundabout
with three incoming and three outgoing roads. Two different choices of
parameters were considered: instantaneously locally optimal and a well chosen
but fixed values. The simulation results have shown that the local optima parameter
value outperform the other choices, in improving the performances of
the network. This result indicate the effectiveness of the optimization strategy
compared to the case of fixed constant right of way parameters. In the second
case, we formulated the problem in discrete form. Then a cost functional that
measures the total travel time spent by drivers on the roundabout in discrete
form were introduced. Numerical tests were conducted for a roundabout with
four incoming and four outgoing roads. The simulation results show that gradient
based instantaneous optimal choice of the priority parameters produce
better results in improving the performance of the roundabout compared to
the fixed choices of priority parameters. In the third case, we considered the
roundabouts as alternatively periodic sequences of 21 and 12-type junctions
and external incoming and outgoing roads. The evolution of traffic flow
on the road networks of the roundabout was modelled by Lighthill-Whitham-
Richards model with extended flux to capture the presence of pedestrians on
crosswalk. To this end, we introduced three cost functionals that measure the
total mass of vehicle , average velocity, and total flux respectively on the network.
Then we analyzed the performance of the roundabout with and without
pedestrian through numerical simulation using Godunov scheme. The simulation
result indicated that, the presence of pedestrians on the crosswalk reduces
the performance of roundabout in controlling traffic flow problem.
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Keywords
Macroscopic Traffic Flow Modelling