Queues and Risk Models with Simultaneous Arrivals

Synchronized queues with deterministic arrivals

We consider m independent exponential servers in parallel, driven by the same deterministic input. This is a modification of the Flatto-Hahn-Wright model which turns out to be easily tractable. We focus on the time-stationary distribution of the number of customers which is obtained using the Palm inversion formula.

Single-server queues with spatially distributed arrivals

Consider a queueing system where customers arrive at a circle according to a homogeneous Poisson process. After choosing their positions on the circle, according to a uniform distribution, they wait for a single server who travels on the circle. The server’s movement is modelled by a Brownian motion with drift. Whenever the server encounters a customer, he stops and serves this customer. The se...

Analysis of Queues with Bat h Arrivals

The steady state distribution of quasi-birth-death pro esses an be eÆ iently obtained by matrix-geometri (MG) methods. Sin e a number of tele ommuni ation problems are modelled by pro esses with bat h arrivals, the extension of MG methods for these pro esses has pra ti al importan e. This paper presents an extension of MG methods whi h is e e tive for the analysis of quasi-birth-death pro esses...

Numerical analysis of queues with batch arrivals

Insurance risk models with marked Poisson arrivals

This presentation is intended to be a short course on inference and filtering in hidden Markov models (HMMs) and state space models. These models comprise a hidden (unobserved) Markov chain (either with discrete or continuous state space) that governs the distribution of an observed stochastic process. An example of a HMM is a regime-switching model for stock returns in which the stock return d...