On Queues and Numbers

We will consider the problem of managing a mini-market with! two checkout counters, one of them serving as an express lane. For many of the standard job size distributions such as the exponential distribution,
the problem of managing the mini-market is rather nasty. However, for some distributions, the! management problem becomes very easy. We will provide some examples coming from the Taniyama-Shimura conjecture and explain the general connection between mini-market queues and number theory, coming from a very basic computation of Riemann. If time permits we will discuss the problem of positivity of L-functions that comes up naturally in this context and describe the relation of super-market queues with Lorentzian geometry. The talk is self-contained, in particular no knowledge of managing a mini-market is necessary.