Road, rail, data and many other networks suffer from congestion. Industry uses very detailed models to establish capacity needs and manage traffic, but more academic researchers have also had considerable success with minimal stripped-down models designed to expose the nature of collective behaviour emerging on the network. Modelling of road networks has received most attention, with emphasis on the phenomenon of stop waves on highways and gridlock in cities – in both cases this stems from the limited capacity of the network to hold traffic.
This project will consider rail networks where the limiting factor is the throughput of trains across busy junctions (typically stations) and trains cannot be rerouted, leading to queueing. When there is plenty of track capacity to hold the queueing trains there is no gridlock, but still the queues themselves interact and evolve in non-trivial ways which this project aims to explore.
The project will involve formulating both an agent based model of trains and a delay-differential equation model of queues, comparing the two through simulations and attempting to match to real time data from Dutch Railways. 
 Biham, Ofer; Middleton, A. Alan; Levine, Dov (November 1992). "Self-organization and a dynamical transition in traffic-flow models". Phys. Rev. A (American Physical Society) 46 (10): R6124–R6127. arXiv:cond-mat/9206001
(and more references can be found via
 Ming Li, Zhong-Jun Ding, Rui Jiang, Mao-Bin Hu, Bing-Hong Wang, “Traffic flow in a Manhattan-like urban system”, J. Stat. Mech. (2011) P12001. arXiv:1109.4628
 See spoorkaart.mwnn.nl
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