Disconnected networks & the rail replacement bus

Too many regions in the UK suffer unreliable rail networks, due to lack of connectivity and redundancy. This is exposed  each weekend when thousands of passengers suffer the ordeal of the rail replacement bus. The truth is that too much of the UK rail network scores poorly on measures of network robustness and connectivity and whole regions are vulnerable to the loss of single links – planned or otherwise.  What can we learn from other networks, such as the internet, or the brain of a roundworm to make our networks more robust?

A team at UCL geography has demonstrated how  network design affects resilience to random and systematic  failures.   Essentially they remove a part of the transport network, and see what this does for connectivity in a spatiotemporal model.

The study, which is free to view, including all the data as part of the Royal Society Open Science City Analytics special, looked at the time taken between locations on a number of networks and how these temporal distances can be effected by removal of particular node or links of the transport system.  Observing that the most efficient and robust networks can be seen in nature (think DNA packing, networks in the brain) the team compared three metro systems with the network of the brain of the roundworm C Elegans.
C. Elegans has a robust brain network
They also used compared other types of communication network, such as a university phone scheme.  Bad news was that the London tube network didn’t appear to be very robust compared to Paris and unsurprisingly C Elegan’s brain has the most resilient network.
Absence of rail connectivity between lines in North London.
Part of the reason is that the Paris metro network has more of the grid structure where’as much of the London underground’s outer branches suffer from a lack of connectivity.  This means rerouting strategies are difficult. In many cases the UK rail network suffers from this lack of resilience.  (Incidentally I get that the Paris and London systems serve a different purpose, ans the outer reaches of LU are most analogous to RER or Transilien.  Nevertheless, it is useful to see how network forms are vulnerable to having nodes and links removed).
NY subway in Brooklyn appears to offer more connectivity than LU in North London – its branches join at the ends.  Urban form has a major role in this.
The UCL team innovate by incorporating temporal network structures.  For example it uses the London Underground’s published timetable API as its network.  Previous studies have looked at the spatial network of transit systems and made similar comparisons about network resilience.  Derrible and Kennedy (2010) applied the network science concepts of scaling and small world behaviour as well as their own measure of robustness to transport networks.  They found that although networks tend to become more robust as more interchange points are added (as networks get larger),  some systems do better for their size than others.  For example, of the largest systems (London, Paris, Tokyo, Moscow, Seoul,) with the most interchange points, Tokyo was found to be the most robust.  The Tokyo metro has a large number of connections between lines, and a large number of interchanges relative to the total number of stations.
This stems from an idea in network science called scale free networks.  In real world networks such as the world wide web, there are fewer bigger hubs and this follows a power law distribution.  An accessible yet detailed description of this can be found in this excellent online book by Albert-László Barabási.
Comparison of a random network and a scale-free network. The latter is observed in real-world networks
In a transport network you expect a smaller number of interchange stations compared with non-interchange and very few stations where a large number of lines connect. This number of stations and interchanges follows a power law.
Another way of looking at networks is the number of changes required between nodes.  In essence networks with connected hubs are more resilient to random and systematic failure.  On the rail network it could be argued that hubs are more likely to be closed as these are where wear is highest and enhancement schemes are more likely to occur.  My own experiences travelling between London and East Anglia demonstrate this.   The more critical link on the network (i.e. into London) is usually the one closed.  The reason the most critical link on the Great Eastern Mainline (GEML)is most likely to be closed is because it is the focus of Crossrail and electrification works.  Also the busiest links must suffer more frequent failure, simply because of greater use.
The problem with my journey between London and Ipswich, the rail network simply offers no reasonable alternative to the mainline, despite the relatively close proximity of other lines.  Historically the East Anglian network was more robust.
In 1950 the East Anglian rail network had more redundancy (The Railway Executive 1950)
Today whenever work has to be done on the GEML, there is no way to reroute trains resulting in the need for replacement buses. These buses are unsatisfactory because they usually result in multiple interchanges.  We know that people don’t like interchanging (there is high interchange penalty in transport economics lingo) so it is no surprise that most people choose to drive.  The long term impact is a loss of faith in the public transport system.  In contrast I took a train to Portsmouth on a Sunday recently, and it has to be rerouted via Chertsey due to engineering, and all this did was extend the journey time.  Although the journey was longer, my productive working time on the train wasn’t disturbed by interchanges.  This is much better, but the Southwestrains area has a more connected network.  In truth, the network exists for GEML trains to reroute via Cambridge, but these cross country lines are not electrified.  Imaginative solutions like running Diesel loco hauled sets on engineering weekends are probably ruled out for practical reasons like driver knowledge, rolling stock balancing or simply cost.
So what about filling in some network gaps to improve robustness? Barabási suggests we might benefit from linking second tier husbs as a means to protect against random failure and hub attack (which I think is analogous to the higher likelihood of engineering or failure on hubs).
In my experience of planning rail schemes, network resilience is under represented as an objective.  The big network planning models used in the Southeast already have their hands full dealing with the complex interactions between journey time, crowding and station access.
The lack of attention to robustness might stems from  viewing planning for failure as an admission of failure.  In reality, even the most mechanically reliable system would still suffer failures beyond anyone’s control.  The UK transport sheme appraisal framework WebTAG requires consideration of reliability, but it’s generally framed in terms of some kind of timetabled lateness.  A value is calculated from the time saved by trains being slightly less late on average  This seems different from the idea of network connectivity.
Much of the potential rail network resilience was lost with Beeching cuts.  The problem is the difficulty of predicting and monetising the benefits of having network resilience.  The good news is that the Crossrail 2 route clearly improves network resilience in outer London as it enables rerouting both in the South (between the Southwest mainline, Northern Line) and in the North (where it ties the Victoria, Piccadilly and Great Northern Lines).  Outside of the capital its harder to see these schemes developing.    Business cases for lines like East-West rail will evaporate once autonomous vehicles become ubiquitous in less densely populated areas.  This will make it harder to fund connective routes in places like East Anglia.  On the other hand, where the economic or political costs of disconnectivity due to lack of resilience get too great, there may be no choice.  Network Rail are investigating alternatives to the Great Western Line in Devon, which is vulnerable to coastal storms but is the sole rail link to Devon.
Dawlish Coast – clearly vulnerable, yet vital for network connectivity
The pre-Beeching network in the Southwest had more resilience. Now only one route remains to Cornwall
 Network connectivity resilience  is very much at the vanguard of transport planning.  As the academic work on networks continues we should get a handle on the cost of a disconnected network, and the frequency of disconnectivity. From this point the network science might be a tool to prioritise links which hold together more robust connectivity.  Perhaps we won’t ever attain the robustness exhibited by the puny brain of C Elegans, but hopefully we might be able to banish the rail replacement bus.

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