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Multiclass Hammersley–Aldous–Diaconis process and multiclass-customer queues

Pablo A. Ferrari, James B. Martin (2009)

Annales de l'I.H.P. Probabilités et statistiques

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 departure process in a batch-arrival queue with finite buffer capacity and threshold-type control mechanism

Wojciech M. Kempa, Dariusz Kurzyk (2022)

Kybernetika

Non-stationary behavior of departure process in a finite-buffer M X / G / 1 / K -type queueing model with batch arrivals, in which a threshold-type waking up N -policy is implemented, is studied. According to this policy, after each idle time a new busy period is being started with the N th message occurrence, where the threshold value N 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...

On a discrete modified M / G I / c / queue

Anatolij Dvurečenskij (1987)

Aplikace matematiky

The busy period distribution of a discrete modified queue M / G I / c / , with finitely or infinitely many severs , and with different distribution functions of customer service times is derived.

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