A ﬂuid queueing system in which the ﬂuid ﬂow in to the buffer is regulated by the state of the background queueing process is considered. In this model, the arrival and service rates follow chain sequence rates and are controlled by an exponential timer. The buffer content distribution along with averages are found using continued fraction methodology. Numerical results are illustrated to analyze the trend of the average buffer content for the model under consideration. It is interesting to note that the stationary solution of a ﬂuid queue driven by a queue with chain sequence rates does not exist in the absence of exponential timer.
Authors:Rolando Cavazos-Cadena and Daniel Hernández-Hernández
This note concerns the asymptotic behavior of a Markov process obtained from normalized products of independent and identically
distributed random matrices. The weak convergence of this process is proved, as well as the law of large numbers and the central
Summary First we give a construction of bridges derived from a general Markov process using only its transition densities. We give sufficient conditions for their existence and uniqueness (in law). Then we prove that the law of the radial part of the bridge with endpoints zero derived from a special multidimensional Ornstein--Uhlenbeck process equals the law of the bridge with endpoints zero derived from the radial part of the same Ornstein--Uhlenbeck process. We also construct bridges derived from general multidimensional Ornstein--Uhlenbeck processes.
Authors:Bernard Roynette, Pierre Vallois, and Marc Yor
, 1987. Théorie du potentiel associée â une résolvante. Théorie des processus de Markov. [Potential theory associated with a resolvent. Theory of Markovprocesses], Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], 1417