Skip to main content

Cumulative waiting in discrete-time queues and the area distribution of compact directed avalanches

As part of the Physics Department's Theory group seminar series, Michael J Kearney, University of Surrey, hosts a seminar on the above topic.

The dynamic (critical) behaviour of the discrete-time, single-server Geo/Geo/1 queueing system is analysed by exploiting a mapping onto a class of lattice polygons whose area-perimeter generating function obeys a known non-linear functional equation. By studying the asymptotic behaviour of this equation, the exact form of the tail of the distribution of the area swept out by the queue occupation process during a busy period (the cumulative waiting time) is determined. The results are applicable in a number of contexts; for example, they capture the critical scaling behaviour (by area) of a class of avalanche models in the compact directed percolation (CDP) universality class. The method also determines the extreme statistics of the corresponding (strongly correlated) fluctuating interface model.

Futher Information

Please contact Dawn Keaneywith any queries related to this event.