Figure It Out 70: The price of misery Welcome to “Figure It Out”, a weekly email from the Operational Research (OR) team taking a light-hearted look at the numbers behind the news. On Monday morning, 18 October, I was on the Jubilee line on the London Underground and had a journey to work like no other I have ever experienced. I was stuck on a very crowded train for nearly two and half hours due to a power failure. We eventually had to evacuate the train and walk through a fairly dark tunnel for more than twenty minutes to the nearest station. The headline in the Evening Standard that night was the “Walk of fear”.
Light at the end of tunnel as we arrived at St.John’s Wood (Source: Sky News) Whilst waiting in the train we were given no indication of how long we would be waiting, even though the decision to evacuate was made quite early on. After hearing many announcements about the evacuation, it made me think, whether Transport for London (TFL) could have an emergency team on standby to help us. As a good Operational Research consultant I started to do some sums around the issue at hand. I estimated that there are around three and half million passenger journeys made each day. We were told that 5 trains were affected and this meant around 4,000 people. This results in a probability of a passenger journey being affected by this on Monday as 0.11%. If half the passengers have to make the “walk of fear” this results in a 0.06% chance of a passenger having to make the walk in the tunnel. I guessed that this happens only once a year, therefore the chance of being involved falls to 0.00024%. This may sound low, but when it happens to you, it is not a nice thing. Especially as it took nearly two hours for TFL to assemble a team and get them in place to carry out the rescue. The team that turned up to eventually help us consisted of about six TFL staff, four policemen, and four members of the ambulance service. So if TFL were to establish an emergency team to be on permanent standby, it would need to consist of at least six members. If we take the average UK salary to be about £26,000, one team would cost £156,000 annually (there would of course be additional costs). It is important to note that one team would not be sufficient to cover the whole underground system. There are about 526 trains running during the peak hours of the service serving 270 stations. The team would probably need to get around London via the roads. The average speed in London is about 10 miles per hour, so it is likely that at least five teams would probably be needed. The annual cost of five teams would therefore be about £780,000. This in turn would increase the cost to TFL which in turn would eventually be passed onto us the consumers, at the cost of around 22p per day. Whilst this may not sound like much, it would effectively be an increase of at least 2% in my daily travel costs, and all to just reduce the time spent in a tunnel by 1 hour on something that has a probability of 0.00024% of happening. Given these numbers I decided that I would just keep the money in my pocket and suffer the extra hours wait. On Tuesday I decided that I had enough of the Jubilee and took the Victoria line instead – and you may have heard more trains had to be evacuated causing more disruption. For more Blogs related to the London Underground, refer to Going Underground’s Blog. Previous work by the OR Team has given us the experience to help TFL and the emergency services plan for such a future eventuality. We have done ambulance modelling across the country over the last couple of years, helping them with a wide variety of problems including the optimum number of ambulance vehicles and what are the drivers to increase the utilisation of these vehicles. We have also done simulation models about evacuations of more difficult to reach places such as oil rigs. This has helped to identify areas of weakness in the emergency plans. To find out more please contact Russell Hodge or Nigel Lewis.