Queue for the Loo!

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A curious article appeared in New Scientist magazine on the topic of relative lengths of queues for men and women's public lavatories. What was curious was not the fact that women spend 2.3 times as long in the loo as men do, nor that the queues for women's conveniences are five times as long as those for the gents, nor even that those two figures are connected in precisely the way predicted by the mathematical theory of queuing.

No, what was curious was first that it has taken the New Scientist so long to catch up with this obvious application of queuing theory, and second that they have not yet found the solution to the dilemma it poses. Queuing theory all comes down to a question of optimal allocation of resources. Suppose, for example, the average lavatorial sojourn lasts four minutes and we have, on average, 15 people arriving every hour. If they time their arrivals with perfect regularity at precise four-minute intervals, then the cubicle would never be unoccupied and nobody would ever have to wait. One would exit as the next was going in. Unfortunately, however, people tend to arrive at random timings. This leads to periods in which the loo is unoccupied, and the important point is that it can never recover from its moments of vacancy.

Since it is, on average, in use for 60 minutes per hour, once it has slipped a few minutes behind, things can only get worse and the queues can only get longer and longer.

As soon as mathematical queuing theory was formulated some two or three decades ago, I realised its implications for the utilisation of lavatorial facilities. In other areas of human patience, a queue may be no more than a minor irritation, but here, above all, it may result in profound discomfort or even disaster.

For that reason we have, for several years now, been operating a bookings system at Loonytunes Towers for the use of the lavatory. Through a ballot, the residents and members of staff have been allocated sufficient four-minute periods to satisfy their needs, and further appointments may be booked by entering the relevant times on a register kept outside the toilet block. Visitors to the Towers are sent an updated list of available slots on which they may enter their preferred times, together with second and third preferences in case of over-booking. We are currently working on an Internet bookings system
to enable anyone dropping in impetuously to make all the necessary arrangements before they arrive.

Frankly, it astonishes me that the rest of civilisation has not adopted this idea yet. We can make bookings for tennis courts and hairdressers where waiting would scarcely cause any hardship. Why cannot we do the same to overcome the queuing inconvenience of our public conveniences?

I must go now. I have an important appointment to keep.


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