arXiv subjects

Moez Draief

Publications and source records attributed to Moez Draief.

20 records · Page 2Linked to original sources

arXiv2007

Services within a busy period of an M/M/1 queue and Dyck paths

We analyze the service times of customers in a stable M/M/1 queue in equilibrium depending on their position in a busy period. We give the law of the service of a customer at the beginning, at the end, or in the middle of the busy period. It enables as a by-product to prove that the process of instants of beginning of services is not Poisson. We then proceed to a more precise analysis. We consider a family of polynomial generating series associated with Dyck paths of length 2n and we show that they provide the correlation function of the successive services in a busy period with (n+1) customers.

cs.DM↗

arXiv2005

The Single Server Queue and the Storage Model: Large Deviations and Fixed Points

We consider the coupling of a single server queue and a storage model defined as a Queue/Store model in Draief et al. 2004. We establish that if the input variables, arrivals at the queue and store, satisfy large deviations principles and are linked through an {\em exponential tilting} then the output variables (departures from each system) satisfy large deviations principles with the same rate function. This generalizes to the context of large deviations the extension of Burke's Theorem derived in Draief et al. 2004.

math.PR↗