Traffic & Transport
The Voorhees law of traffic: when overtaken slow cars seem to always catch up at a red light | Motoring
It is a situation experienced by many motorists: one driver overtakes another only to find the slower car is right behind them when they reach a red light. Now a researcher has used mathematics to reveal why the situation feels inevitable.
Dr Conor Boland from Dublin City University has called his work “The Voorhees law of traffic”.
The name is a nod to the character Jason Voorhees from the American horror film franchise Friday the 13th.
“I always thought of him because he seems to just walk everywhere … His victims are running away, they’re sprinting, but he just catches them,” Boland said.
However, in the case of cars it is traffic lights rather than stones or tree branches that prevent the “escape” of the faster individual.
Writing in the journal Royal Society Open Science, Boland explains that as two cars travelling at different speeds encounter a traffic light, the spacing between them can either increase, stay the same, partly decrease or be completely lost, depending on the colour of the traffic light, its duration, the time advantage of the faster car and the overall time it takes for the traffic lights to complete a cycle.
Assuming that the traffic light changes colour based on a set time cycle rather than a sensor, and that the cars are travelling on a single-lane road, the results reveal that, taking into account the probabilities of each of the four scenarios, on average the possible gains and losses in spacing between the cars balance exactly.
That means, on average, the lead of one car over the other remains the same after the light as before.
The results suggest the idea the slower car will inevitably catch up at the lights is something of an illusion.
“Recurrent encounters are known to be disproportionately salient in human perception, particularly when they follow an attempted separation or avoidance,” Boland writes.
Put simply, it is probably just more memorable for a driver when the car they overtook catches up with them again.
However, when drivers encounter a succession of independent traffic lights – as might occur in towns and cities – the situation is different.
As Boland explains, here the eventual catchup of the slower car at at least one of the lights becomes statistically near-certain. That’s because the probability that the slower car never catches up relies on multiplying the probability of no catchup for each traffic light – meaning the more lights, the less overall chance no catchup will occur.
Boland said the results have implications for road safety, suggesting speeding past others does not necessarily give an advantage.
Kit Yates, professor of mathematical biology and public engagement at the University of Bath who was not involved in the work, welcomed the study.
“It’s something I, as a slower driver, often think about. Was it really worth it for that car that sped to overtake me? When I catch them up at the lights I smugly think, ‘No, it wasn’t.’ So it’s good that someone has sat down and modelled how and when this happens,” he said.
However, Yates added that in his experience, catching up to a faster car does not seem to happen constantly, or to be surprising when it does occur.
He also noted that the study made a number of assumptions, among them that cars travel at constant speed between lights with no acceleration when a light changes to green or deceleration when it changes to red.
“But as the old adage goes, ‘all models are wrong, but some are useful’ and I think this one is definitely useful to explain why slower cars can often catch up with quicker ones,” Yates said.
Traffic & Transport
London tube strike to go ahead after 11th-hour talks fail to find resolution | London Underground
The strike on the London Underground will go ahead on Tuesday after a day of talks failed to avert industrial action.
About half of London’s tube drivers will take action, bringing widespread transport disruption to the capital. A second strike is planned for Thursday.
Hopes of a resolution were high after previous threatened action was suspended in May. However, despite 11th-hour negotiations at Acas between RMT union representatives and Transport for London (TfL), RMT drivers will strike on Tuesday and Thursday in a dispute over the introduction of a four-day working week.
TfL urged customers to check before travel, although it hopes to run about half of all tube services. Drivers in Aslef, a slight majority of those working on the tube, have welcomed the four-day week proposals and will not be on strike, limiting the impact of the RMT’s action.
Nonetheless, no service is expected on the Circle or Piccadilly lines, or in central sections of the Metropolitan and Central lines, during the strike. Tube services will also finish earlier and later than usual on functioning lines.
Other rail services, including the Elizabeth line, the London Overground and the Docklands Light Railway, will run as normal. Buses will operate as usual but are likely to be very busy and slowed by additional traffic on the roads.
The RMT union blamed TfL’s “refusal to engage meaningfully” with concerns over the proposed working patterns. A spokesperson said: “Despite our best efforts in ACAS talks, TfL have failed to provide assurances on our members deeply held concerns around fatigue, reduced flexibility, shift lengths and the impact these proposals could have in a safety-critical role like tube driving.
“We remain available for meaningful talks, but strike action tomorrow will now go ahead.”
A TfL spokesperson said: “It is bitterly disappointing that despite five hours of meetings with the RMT at ACAS and repeated assurances that the four-day working week proposals will remain voluntary, RMT has chosen to continue with its disruptive strike action. We will do all we can to provide as much service as possible during this action.”
TfL’s chief operating officer, Claire Mann, said: “Our proposals are, and have always been, clear. The completely voluntary four-day week has been designed to improve work-life balance and any of our tube drivers who do not wish to take up the new proposed way of working and associated changes to working arrangements can remain on a five-day working pattern.”
The strikes will take effect for 24 hours from 00.01 on both Tuesday and Thursday – potentially slightly less disruptive than the previous walkouts that ran over two 24-hour periods starting from midday, affecting four days in April.
Business groups said that even the threat of strikes had already been disruptive. Ed Richardson of BusinessLDN said: “For many businesses that rely on people visiting in person, the impact of these strikes will have already been felt through cancelled bookings and people changing their plans.
“We urge both sides to reach a sustainable agreement to put an end to the damaging uncertainty hanging over businesses and London’s economy.”
Traffic & Transport
London tube strikes to go ahead on Tuesday and Thursday, RMT says | London Underground
Strikes by drivers on London Underground next week will go ahead, the RMT union has announced, paving the way for more days of transport disruption.
Two 24-hour stoppages are to take place, from 00.01 to 23.59 on Tuesday 2 June and Thursday 4 June, because of differences over a planned four-day week.
An RMT spokesperson said: “Strike action by London Underground drivers next week is scheduled to go ahead following TfL’s continued refusal to engage meaningfully with the union’s concerns over the proposed compressed four-day working arrangements.
“Our members have raised serious concerns around fatigue, longer shifts, reduced flexibility and the impact these proposals could have in a safety-critical role.”
Transport for London said it expected services on most tube lines during the strike, but has told commuters to expect disruption. It added that other services including the Elizabeth line, London Overground, DLR and tram would run as scheduled, but would be busier than normal.
TfL has said its proposals for a four-day week would be trialled on a voluntary basis. Its proposal has been endorsed by the Aslef union, which represents a slight majority of tube drivers.
Claire Mann, the chief operating officer at TfL, said it was disappointed that the RMT was continuing its industrial action.
“We still believe that the points they have raised can be worked out in time, through more detailed discussions and we are continuing to talk to the union’s representatives to find a way to avoid disruption to London,” she said.
She urged the RMT to work with TfL to resolve the dispute, adding: “A significant number of drivers have indicated that they want us to progress plans for the pilot of this new working pattern on the Bakerloo line, bringing benefits both for our colleagues and our customers.”
The RMT’s opposition to London Underground plans for a voluntary four-day week has already led to industrial action, most recently in April.
Hopes were raised that differences between the two sides might soon be resolved when the RMT called off at the last minute a two-day strike planned for mid-May.
However, at the same time the union also moved forward further strikes planned for 16 and 18 June to 2 and 4 June, saying the dispute was not over and that it was prepared to take more industrial action if the two sides failed to make sufficient progress.
The RMT said it remained “available for meaningful talks” with TfL, but cautioned London Underground against carrying out what it called a change to drivers’ working conditions “while refusing to properly address legitimate safety and workplace concerns”.
Previous waves of industrial action by the RMT over the four-day week proposals had found little public sympathy and had also mystified Aslef, which felt the proposal presented a significant improvement in working conditions for tube drivers.
Traffic & Transport
HS2: white elephant or vital addition to Britain’s rail network? | HS2
Simon Jenkins’ argument is shortsighted and ignores the fundamental reason that HS2 was designed in the first place – the west coast mainline is full and the UK is rattling towards its worst transport bottleneck (HS2 is the wildest white elephant in British history. Please put it out of its misery, 21 May). Cost and schedule overruns invite legitimate scrutiny and reflect failures that must be addressed. But they do not invalidate the need for additional rail capacity that will deliver transformational benefits to the north, including vital freight capacity and improved regional connectivity.
With unemployment on the rise, major infrastructure programmes aren’t just about capacity and connectivity. They are critical to creating high-quality careers and supporting the UK supply chain. HS2 is already doing both. From tunnel facilities in Hartlepool to working with local West Midlands firms, HS2 is supporting more than 30,000 jobs, sustaining highly skilled workers and apprenticeships, and strengthening small and medium-sized enterprises across every region. The bridges, viaducts and tunnels delivered so far are a testament to this country’s continued engineering excellence.
These benefits are rarely discussed, yet cannot be ignored. HS2 is already starting to generate £20bn in development benefits across the West Midlands and west London. Abandoning HS2 now would not save money. It would leave taxpayers with an enormous bill while delivering none of the benefits that the project will continue to provide. Cancellation costs and the inevitable need for an alternative solution to the capacity crisis would impose their own huge bills, leaving the north permanently disadvantaged and sending a damaging signal that Britain no longer has the confidence to deliver major infrastructure at all.
The question is not whether HS2 should be cancelled, it is what a congested, unreliable rail network would ultimately cost this country. The priority now is for industry, government and HS2 Ltd to work together to deliver HS2 within its revised scope.
Deb Carson
Head of operations, High Speed Rail Group
Simon Jenkins is right to call HS2 “the wildest white elephant in British history”, but the same culture of institutional denial and sunk-cost thinking is already metastasising elsewhere in Britain’s rail sector. East West Rail, particularly the controversial eastern section route option known as CS3, risks becoming HS2 in miniature: another prestige infrastructure scheme insulated from scrutiny while taxpayers are expected to foot the bill indefinitely.
The most alarming aspect is that the Department for Transport continues to resist freedom of information requests seeking disclosure of the business case underpinning CS3. If ministers and officials genuinely believed that the numbers stacked up, they would publish them. Instead, campaigners and affected communities are left piecing together fragments of evidence while decisions of enormous consequence are made behind closed doors.
What has emerged already should concern anyone serious about public value. The scheme’s own figures reportedly point towards a benefit-cost ratio as low as 0.3 – an extraordinary admission for a project supposedly justified on economic grounds. A railway that returns barely 30p of value for every pound spent would never survive scrutiny in the private sector, yet in Whitehall such projects acquire a momentum of their own, propelled by consultants, lobbying networks and a revolving-door culture of rail industry cheerleaders recycling between public agencies and infrastructure bodies.
Meanwhile, billions are frittered away on speculative masterplans, consultations and promotional exercises while local transport priorities struggle for funding. Like HS2, East West Rail has become insulated from the basic question that should govern all public expenditure: is this genuinely the best use of scarce national resources?
Britain urgently needs ministers prepared to think the unthinkable. Cancelling failing projects is not weakness, it is responsible government. East West Rail deserves the same ruthless reassessment now being demanded of HS2 before even more public money disappears into another avoidable infrastructure fiasco.
Stephen Mallinson
Little Eversden, Cambridgeshire
I completely disagree with Simon Jenkins on HS2. While it is disgraceful that the project has cost so much and been poorly managed, he does not offer an alternative to the problems facing existing railways. The west coast mainline is full to capacity. There is no easy way of increasing the number of seats available without building a new line. If HS2 is not built, it will simply mean even worse overcrowding on all services between London, Birmingham and Manchester. Fares will have to be set higher to limit demand, as has been the system since the second world war, regardless of whether the railway is nationalised or not. If we are to follow Jenkins’ advice on cancelling the project, we are dooming future generations to higher rail fares, worse road congestion and even more crowded trains.
Alex Stewart
London
More than 20 years ago, I had a conversation with a colleague at the Northwest Regional Development Agency. We were pretty junior in that organisation, so our opinions counted for nothing. We agreed that while there was an argument for increasing rail capacity, there was no argument that we could see for a high-cost option to shave a few minutes off the journey time from Manchester to London. My colleague expressed his reservations in a pithy manner inappropriate for a family newspaper.
A London meeting realistically meant a day away from our Warrington office, and a half-hour saving would not change that. So the high-speed train went ahead as a costly vanity project for engineers and politicians. It remains so today, and Simon Jenkins is quite right to call for it to be cancelled.
Julian Roberts
Great Bookham, Surrey
Simon Jenkins is correct to call for the grossly expensive HS2 vanity project to be scrapped. HS2 was first mooted in 2009 and, we are informed, will possibly be operational between 2036 and 2039. In 2009, work started on a 34-mile bridge and tunnel linking Hong Kong and Macau. That is was open to the public in 2018. The incompetent management and oversight of major infrastructure projects in the UK is pathetic and highly embarrassing.
David Campbell
Portishead, Somerset
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