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A PHYSICIST WRITES . . .
(September 2003)
Dr Rachel Hooke [a fellow columnist] recently came up with a remarkable list of similarities between the progress of patients through the NHS and the flow of traffic on the roads — an additional consultant in a hospital is like opening up a new road or bypass, and so on. She ended by wondering if a physicist might have any thoughts on these matters.
Well, that tempts me to call on a physician or two to help me try to explain a motorway mystery. Picture an old-fashioned surgery, in Maidenhead perhaps, on a sunny Monday morning. There is no appointment system (I said it was old-fashioned). At the beginning of the day, the three GPs are easily able to see patients immediately they appear. But soon, because of people arriving from all directions, the gap between patients dwindles. It only takes one or two consultations to run on a bit for the waiting-room to start to fill.
The average consultation time per patient is now actually more than it was before, because of the delay while the next one is called. The receptionist tries to help people by offering to switch them to the doctor with the shortest queue, but this only causes more delay for others. Eventually though, everyone is seen in turn and patients emerge into the clear air quite understanding why they had to wait — and expecting to be delayed again at the pharmacy.
Meanwhile, what has been happening nearby on the eastbound M4, just beyond J8/9? At the beginning of the day, the three lanes are flowing freely and drivers are easily able to keep a decent distance from the vehicle in front. But soon, because of traffic arriving from all directions (the A404(M), the A308(M), the M4 west) the average time-gap reduces to two seconds or less. It only takes one or two drivers to brake a bit for the lanes to start to fill.
The average time between cars is now actually more than two seconds, because of their slow speed. Drivers try to help themselves by switching to the fastest lane, but this only causes more delay for others. Eventually though, everyone arrives at the front of the queue in turn and impatient drivers emerge onto the clear road quite mystified why they had to wait — and expecting to be delayed again at Slough.
I hope the queuing is less of a mystery to you now. There are other ways of looking at the problem. Perhaps the simplest is to say that if every driver is trying to keep a two-second gap in front, and more than 30 cars are trying to pass a given point per minute, then something has to give! Experts have also studied the way a ‘shock-wave’ of braking spreads backwards through heavy traffic, strengthening as it goes — while the driver who started it all disappears into the distance.
I was surprised to read that the variable speed limit on the M25 in Surrey is now eight years old. Apparently it has produced a noticeable reduction in the severity of the shock-waves, by encouraging drivers to proceed more smoothly when the traffic is heavy. So why hasn’t the system been tried out elsewhere — on other motorways, or on busy A-roads? By the time it is installed everywhere it is needed, we shall all be in a perpetual traffic jam.
Peter Soul
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