Anyone who travelled through Heathrow during April is likely to have been affected by the huge problems being publicised at the moment and therefore I apologise in advance for bringing any bad memories back up to the surface. Yes, I mean the unacceptable queuing duration through Border Control. But what I’m interested in is whether Operational Research could have prevented it.

The queues have grown out of control, with some non-European flyers having to wait two and a half hours to get into the country. Official time limits were broken 107 times during the first 15 days of April.

Migration officers had to be flown in (luckily on internal flights from Manchester or they might not have got through control and onto the booths in time before their shift ended) meaning they only worked 4 hours out of 8 on Border Control. 80% of The Olympic Games’ visitors are expected to arrive via Heathrow, equating to 45% more passengers and at this rate people might not make it to the events! At least there may be some spare seats for those not lucky enough to receive any tickets in the ballot though!

So what’s gone wrong?

Downing Street blames the delays on the wet weather but BAA says that the Home Office is to blame for enforcing tougher security checks (which take a longer time) and staff cuts.

Surely OR analysis would have shown that these staff cuts would prevent the process from running smoothly; and would have been used to derive optimal staffing patterns with those remaining to meet the demand rather than shipping extras in last minute.

Even a simplified queuing theory model (such as an M/M/c) taking arrivals as independent (when of course they are not as passengers come off planes in groups) could have shown that reducing the staff numbers, whilst increasing the service time on passport checks would result in these long queues. Otherwise, some more sophisticated event based stochastic simulation could have given an indication of the outcome, taking into account the probability of different weather conditions and likelihood of delay, with separate models for EU/non-EU travellers.

Figure 1 shows the average arrival figures (data taken from US Customs and Border Protection for between May 2010-2012) over the course of a day for passengers in Chicago O’Hare airport. This airport was chosen as US data (but not UK) is readily available and it is one of the biggest in America, so comparable to Heathrow. However, it is a smaller version compared with Heathrow’s average of 4,000* arrivals per hour and so the graph would need to be scaled up (but a similar trend expected).

The green dashed line gives an indication of how delays to planes could affect arrivals in a simplistic form, based on the relationship with the number of booths open. In reality, delays would cause much more distortion to the data, forming higher peaks and troughs to put stress on the Border Control.

If we assume that staff are working at capacity during the busiest time (between 3 and 4pm), then it takes 1.5 minutes for each person to get through Border Control on average. This means to get 4,000 customers through in an hour, 100 border staff are needed.

Linear programming can fit shift patterns around these predicted arrivals trends as closely as possible, ensuring that the available staff are used in the best possible way.

So with more sophisticated OR techniques, (maybe they even were carried out but not taken notice of) this situation could have been much less severe.

To any of you who are flying off tonight to make the most of the long weekend, I wish you all the best and hope the queues do not spoil your break!


Photo taken by Herry Lawford