Moment estimation of customer loss rates from transactional data.
In the Hammersley–Aldous–Diaconis process, infinitely many particles sit in ℝ and at most one particle is allowed at each position. A particle at x, whose nearest neighbor to the right is at y, jumps at rate y−x to a position uniformly distributed in the interval (x, y). The basic coupling between trajectories with different initial configuration induces a process with different classes of particles. We show that the invariant measures for the two-class process can be obtained as follows. First,...
Non-stationary behavior of departure process in a finite-buffer -type queueing model with batch arrivals, in which a threshold-type waking up -policy is implemented, is studied. According to this policy, after each idle time a new busy period is being started with the th message occurrence, where the threshold value is fixed. Using the analytical approach based on the idea of an embedded Markov chain, integral equations, continuous total probability law, renewal theory and linear algebra, a...
The busy period distribution of a discrete modified queue , with finitely or infinitely many severs , and with different distribution functions of customer service times is derived.