Abstract: Queueing theory is a branch of applied probability that deals with queues of various types as one may encounter in a bank, a supermarket or a telecommunication network. We will consider management issues related to a simplified supermarket queue, consisting of two lines, one of them being an express line. Usually, such a system is hard to manage but we will show that number theory provides many "easy" examples. The connection is based on a very simple observation, that one of the most basic formulas in queueing thery, the Pollaczek-Khinchine formula, expresses the average waiting time of a single line system in terms of a Mellin transform evaluated at integer points.

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at Schreiber building 006