Single-Server Queueing System with Markov-Modulated Arrivals and Service Times

Key words: Markov-modulated queues, waiting time, heavy traffic.

Models of Alternating Renewal Process at Discrete Time

We study a class of models used with success in the modelling of climatological sequences. These models are based on the notion of renewal. At first, we examine the probabilistic aspects of these models to afterwards study the estimation of their parameters and their asymptotical properties, in particular the consistence and the normality. We will discuss for applications, two particular classes of alternating renewal processes at discrete time. The first class is defined by laws of sojourn time that are translated negative binomial laws and the second class, suggested by Green is deduced from alternating renewal process in continuous time with sojourn time laws which are exponential laws with parameters α^0 and α^1 respectively.

Detecting Precipitation Climate Changes: An Approach Based on a Stochastic Daily Precipitation Model

2002 Mathematics Subject Classification: 62M10.

Time to Extinction in Branching Processes and its Application in Epidemiology

2010 Mathematics Subject Classification: Primary 60J80; Secondary 92D30.