A BMAP/SM/1 queueing system with Markovian arrival input of disasters is considered. After a disaster arrival all customers leave the system instantaneously and a server is recovered during a random period of time. We consider both variants of accumulating and losing the customers arriving during a recovery period. Numerically stable algorithm for calculation of the stationary state distribution of embedded Markov chain is presented.

This paper investigates the mathematical model of multi-server retrial queueing system with the Batch Markovian Arrival Process (BMAP), the Phase type (PH) service distribution and the finite buffer. The sufficient condition for the steady state distribution existence and the algorithm for calculating this distribution are presented. Finally, a formula to solve loss probability in the case of complete admission discipline is derived.

Basic idea of Randall-Sundrum brane world model I and II is reviewed with detailed calculation. After introducing the brane world metric with exponential warp factor, metrics of Randall-Sundrum models are constructed. We explain how Randall-Sundrum model I with two branes makes the gauge hierarchy problem much milder, and derive Newtonian gravity in Randall-Sundrum model II with a single brane by considering small fluctuations.