Antonis Economou. Queueing Systems with binomial transitions: Modeling and analysis of synchronized events

Abstract. In many queueing systems, there exist synchronized events concerning the
behavior of the customers, related in particular with services,
abandonments, routing etc. For example consider a system where all the
customers are served concurrently and at service completion epoch every
one of them is satisfied and departs with probability p or repeats his
service with probability p=1-p. Then the number of customers in system is
reduced at service completion epochs according to a binomial distribution.
Similarly, consider a system where the present customers decide
concurrently if they will abandon the system or not at certain time
points. Again, the number of customers in system is reduced at these
points according to a binomial distribution. Similar phenomena occur in
Mathematical Biology in the study of population processes subject to
binomial catastrophes.

I will present several models of this type that lead to spatially
inhomogeneous Markov chains with binomial transitions. I will also present various techniques for the analysis of such models for the exact or algorithmic computation of their stationary, busy period and sojourn time distributions.

The talk is based on various joint papers with (1) S. Kapodistria, (2) I. Adan and S. Kapodistria, (3) J. Artalejo and M.J. Lopez-Herrero.