### A tale of two tails

**Briggs, K ***(BT Technology)*

Wednesday 27 March 2013, 13:40-14:20

Seminar Room 1, Newton Institute

#### Abstract

In the design and modelling of industrial processes, a common requirement is (loosely expressed) that "the worst case is not too bad", or, more precisely, "the probability of very bad cases occurring is sufficiently small". Mathematically, this means that for some random variable X depending on parameters alpha, Prob[X_alpha>x] must be shown to be less than epsilon for some specified x and epsilon (typically x is large, and epsilon small). I shall describe two practical problems of this type. The first concerns trip-planning on transport systems with random delay, where the requirement is to arrive close to a specific target time, with the probability of arriving very late being very small. The second (which is work in progress), concerns the management of radio spectrum in the case of many small devices all sharing the same channel. Here the requirement is that the probability of seriously bad interference occurring is less than some specified bound.

#### Presentation

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