Markovian service process (MSP) is a model similar to the Markovian arrival process (MAP), where arrivals are replaced with service completions. The MSP can represent various queueing models such as vacation models, N -policy models and exceptional service models. We analyze MAP/MSP/1 queues and obtain a new sort of matrix-type factorization of the vector generating function for the stationary ...

The discrete-time batch Markovian arrival process (D-BMAP) was first defined in [2]. The D-BMAP can represent a variety of arrival processes which include, as special cases, the Bernoulli arrival process, the Markov-modulated Bernoulli process (MMBP), the discrete-time Markovian arrival process (D-MAP), and their superpositions. It is the discrete-time version of the versatile Markovian point p...

The non-Markovian correlation spectra of spontaneous emission of an excited two-level atom are derived including the effect of finite size of the atom and all the possible contribution of allowed multipole radiations. The emission process is then analyzed by the quantum stochastic trajectory approach. The non-Markovian effect is counted in by expanding the original system to an enlarged system ...

We consider the theoretical description of real-time counting of electrons tunneling through a Coulomb-blockade quantum dot using a detector with finite bandwidth. By tracing out the quantum dot we find that the dynamics of the detector effectively is non-Markovian. We calculate the cumulant generating function corresponding to the resulting non-Markovian rate equation and find that the measure...

Imagine that the particles in the system are each called either first class or second class. The evolution is the same as before, except that if a second-class particle attempts to go to a site occupied by a first-class particle, it is not allowed to do so, while if a first-class particle attempts to move to a site occupied by a second-class particle, the two particles exchange positions. In ot...