The curse of the sat-nav system

In the UK, and I guess in most other countries, satellite navigation systems (sat-navs) are a blessing and a curse. Surprisingly little has been published about the design of the algorithms used in them, though essentially they use modified forms of Dijkstra's method, which is also the dynamic programming approach. A fellow blogger has commented on some of the stories from the UK, Belgium and the Netherlands.

Over a meal on Friday evening, friends were talking about stories which don't reach the national papers. They mentioned the large number of small sites for caravans (there is a club which has private use of fields in many farms) which have the warning "Do not use sat nav" in their guide-book. Another friend mentioned that a passenger ferry across a river, at the end of a lane, is marked as accessible to vehicles.

There are several problems with sat-navs that these stories highlight. Most obvious is that data can be incorrect, and once published, is hard to retract. Next is that data may change; roads can be closed for repair, and even online updates may not help, even if the user chooses to subscribe to such a facility. But from an O.R. point of view, there is the question of the wrong algorithm. Many of the problems could be dealt with if the algorithm took into account the kind of vehicle, which would mean solving a constrained shortest path problem ... and for nearly all cases, that would mean using the normal algorithm on a modified dataset. But that would increase the price of the system.

So we end up with people cursing the system, damage to property thanks to incorrectly routed vehicles, a cost to society with special road signs trying to stop vehicles routed with sat-nav ....

Governments, swimming pools and models

The UK government has announced that it intends to subsidise swimming pools in England, with the aim of making entry free of charge to all the pools which are managed by councils. The subsidy will be introduced gradually, starting with the over-60s and under-16s. By 2012, everyone will be able to use public swimming pools free of charge. This excludes pools owned by companies, sports clubs, hotels and educational establishments. This is to try and encourage more people to take part in sport, and it is claimed that the most likely form of exercise for people to take up is swimming. There will also be money for new Olympic sized swimming pools.

Now I enjoy swimming, and go to the pool several times each week. When I started work at the university, one of the free perks of the job was being able to stroll to the open-air pool that was five minutes walk away from my office, and swim. The pool was free for staff and students. Now there is a charge, and I have moved my regular swimming to the public pool managed by Exeter city council. But, even though the pool was free, it didn't mean that everyone used it. Removing the charge for some goods or service doesn't automatically bring in more customers.

So I wonder what kind of modelling has been done by the UK government in advance of this announcement. The claim is that it will bring two million more people into regular exercise. As an O.R. person, I wonder what model yielded that figure, about 3% of the UK population. And how do you really measure "regular"? If the figure is accurate, what does it mean for the numbers of people using a typical swimming pool on a typical day? Most pools have lane swimming for serious swimming. Before 9am, Exeter's pool has two "fast" lanes, one "medium" and one "slow". The fast lanes are crowded when there are six or seven people in each, the medium one can take a few more, and swimming in the slow one is awkward when there are 20 in it. Can you recognise a queueing problem here? When does the congestion in a service system get so bad that arrivals turn away?

Swimming pools provide several further O.R. related questions. I used to ask one of my modelling classes how big the hot water tank that feeds the showers should be for a set of public showers. For simplicity, these showers often have no control over temperature, simply an on-off button or tap. So the water temperature cannot fluctuate too much. Therefore, the heating system must be able to maintain the water temperature within a small range, putting design limitations on it.

Another problem comes with lane swimming. There is a heuristic which says that it is safer if alternate lanes go in opposite senses, clockwise, anti-clockwise, clockwise ... across the pool. Why? Because adjacent lanes are swimming together, and a swimmer only needs to avoid those coming towards themselves on one side, not two. But overtaking in lane swimming is an art, which leads to models of congestion. Assuming that I am two metres tall, then if I make a turn after the person in front of me, then to overtake them, I need to swim an extra two metres in the time that it takes for us both to complete a length -- unless they give way. So you need to be in the region of 10% faster than the person ahead to complete overtaking in a normal pool. And if there is a third person behind, then that person will see congestion. It is rather like two similar speed trucks overtaking on a two or three lane road -- it takes time and there are people held up behind. Swimming has the complication of turning at the ends of the pool. But there's a research possibility: "The similarities and differences of lane swimming and overtaking trucks." You read it here first!