William Hartston learns about Queuing Theory
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Has it ever occurred to you, as you wait at the supermarket check- out wondering how much longer it will take the man at the front to find his credit card, or the cashier to catch the attention of a staff member to help her find out the price of half a pound of loose bar-codes, that what you are experiencing is simply an interaction of the negative exponential distribution of time taken to serve each customer, and a Poisson distribution of arrival times of shoppers? To put it in mathematical language, you are standing in a "queue".

So if you really want to know how much longer you will have to wait, it is all explained in a new book by Brian Bunday, head of the maths department at Bradford University.

With its pages full of calculus and probability theory, An Introduction to Queuing Theory may be beyond the average shopper but the implications of this branch of maths touch us all.

The basic question is what happens when people arrive somewhere in a random stream and wait to be served. You know how often, on average, they will turn up, and how long, on average, it will take to serve each one, but some will take longer than others and the intervals between one customer and the next are unpredictable.

Queuing Theory is the mathematics of such situations and, as the book makes clear, the social and moral problems of queues have their basis in probability theory.

We tried to contact Dr Bunday. The Hodder Headline publishing group answered the phone after 17 rings, then transferred us to the publicity department for the Arnold imprint under which his book appears. That call was met, after six rings, by a recording inviting us to leave a message or press zero. We pressed zero and got back to the switchboard after another 12 rings. The operator transferred us to another number, but, after a dozen rings, there was no reply.

Perhaps someone at Hodder should read its own book. You can predict that sort of thing with Queuing Theory.