Tail behaviour of the area under a random process, with applications to queueing systems, insurance and percolations

Rafał Kulik (1) , Zbigniew Palmowski (2)

1 Department of Mathematics and Statistics [Ottawa]
2 Mathematical Institute [Wroclaw]

The areas under the workload process and under the queueing process in a single-server queue over the busy period have many applications not only in queueing theory but also in risk theory or percolation theory. We focus here on the tail behaviour of distribution of these two integrals. We present various open problems and conjectures, which are supported by partial results for some special cases.

Mots clés: Queueing process; Risk process; Workload; Area; Busy period; 60G07

Domaines: Réseaux et télécommunications [cs.NI]

Rafał Kulik, Zbigniew Palmowski. Tail behaviour of the area under a random process, with applications to queueing systems, insurance and percolations. Queueing Systems, 2011, 68 (3-4), pp.275-284. ⟨10.1007/s11134-011-9242-1⟩. ⟨hal-00842610⟩