Monday, 10 October 2016

The best angle for traffic light louvres

Certain traffic signals in the UK are covered with louvres so that the light in the signal is only visible when your eye is aligned with the gap between the louvres.  Not everyone is happy with them.  In an online discussion, I found the following explanation:
The proper use for the louvred aspects on signal heads is to avoid conflicting signals being displayed. For example, if you have a pedestrian crossing within a few yards of a signal controlled junction, if there is a chance that drivers may misread an aspect being shown on the pedestrian signals [green] as the aspect for the junction then the louvres are fitted to ensure that you only see it from a certain distance from the stop line. This is also the case for the pedestrian aspects as well if the phasing is not all the same and you have another button to push in the centre refuge. It may appear 'difficult' to see in some circumstances but it does avoid confusion as you are required to check you are on green before proceeding.
However, not all drivers were happy with the introduction of such louvres, because they were driving trucks and the angle of the louvres was set for the benefit of car drivers, much lower on the ground.  The discussions did not mention the problem for cyclists, whose eye level is also higher than for car drivers.  As a cyclist in Exeter, there are some louvred lights that I cannot see unless I am close to them, because the light is "directed" down towards a car driver.  Geometry says that if the driver is supposed to first see the light when they are 40ft away, a cyclist or truck driver is likely to be about 20ft away when they see it.
 The louvres in this picture are set horizontally, with openings at the base.  Other examples do not have the openings, and have louvres set at an angle ... and as the angle is a number, there is mathematics involved and someone should try and optimise that number.   What criteria to use?  I leave it as an exercise in multiple objective decision-making

Scheduling electrical power supplies - the effect of on-demand TV

When a popular TV programme comes to an end, viewers rush to put the kettle on for a hot drink.  For some programmes, the resulting surge in demand for electricity put a strain on the power system, and so the power companies had generators ready to be brought online to meet the demand.  One of my industrial contacts worked for a power supplier, and we discussed the problem that his business faced.  It was an interesting application of O.R., and like so much O.R., it was hidden from view.  The company needed to know TV schedules, and forecasts of viewer numbers and the step in numbers between programmes, and what fraction of those who stopped viewing would use high wattage equipment. Occasionally, I used this as an example for students to consider how they would tackle such a forecasting and scheduling problem.
However, changing habits in TV viewing have reduced the size of "end-of-programme" surges.  Many people watch programmes on catch-up TV, so want their hot drinks at a time which bears no resemblance to the end of the original programme.
Fifteen years ago, the surge (called a "pick-up" in the power companies) after an episode of the popular soap, EastEnders, could be up to 660Megawatts.  Now there is still a surge, but only 200Megawatts.
Jeremy Caplin, the Energy Forecasting Manager for the National Grid, has the overall responsibility for developing models for forecasting demand.  He was recently quoted as saying: "We see as many spikes in demand, but they are much, much smaller than they were.  The way that people watch TV has meant that they have come down in size."  Nonetheless, during the summer's Olympic Games, there were many sizeable spikes, because so many people wanted to see events as they happened.
From an O.R. perspective, the integration of forecasting and resource allocation is an interesting case of several techniques coming together to deal with a problem, and it is one which occurs several times each day.
Besides forecasting the surges, the forecasters at the National Grid have had to forecast the effect on solar farms of a partial eclipse of the sun, and there is an infographic available (below) of the changed demand during the 1999 total eclipse of the sun when crowds of people stopped using power to watch the eclipse.

Putting on the kettle is not the only activity that follows a popular TV programme.  I met an engineer who had studied the variation in the flow in sewers during advertising breaks and at the end of TV programmes.