Mittag-Leffler queues and an application to the fractional double auction model

Georgiou Nicos, University of Sussex

We will present three non-equivalent queueing models in continuous time that each generalise the classical M/M/1 queue in a different way. Inter-event times in all models are Mittag-Leffler dis- tributed. For each of the models we answer the question of the queue being at zero infinitely often (the ‘recurrent’ or ‘stable’ regime) or not (the ‘transient’ regime). Aside from this question, the different analytical properties of each models allow us to answer a number of questions such as ex- istence and description of equilibrium distributions, mixing times, asymptotic behaviour of return probabilities and moments and functional limit theorems. In the final part of the talk, we will dis- cuss a double auction model that has Mittag-Leffler inter-event times and is based on this fractional queue model. This is joint work with Jacob Butt and Enrico Scalas

Area: CS29 - Advances in Stochastic Control and System Modeling (Bernardo D'Auria)

Keywords: fractional calculus, queuing systems, double auction model

Please Login in order to download this file