Markovian Arrival Processes - Batch Markov Arrival Process

Batch Markov Arrival Process

The batch Markovian arrival process (BMAP) is a generalisation of the Markovian arrival process by having arrivals of size greater than one. The homogeneous case has rate matrix,


Q=\left[\begin{matrix}
D_{0}&D_{1}&D_{2}&D_{3}&\dots\\
0&D_{0}&D_{1}&D_{2}&\dots\\
0&0&D_{0}&D_{1}&\dots\\
\vdots & \vdots & \ddots & \ddots & \ddots
\end{matrix}\right]\; .

An arrival of size occurs every time a transition occurs in the sub-matrix . Sub-matrices have elements of, the rate of a Poisson process, such that,


0\leq _{i,j}<\infty\;\;\;\; 1\leq k

0\leq _{i,j}<\infty\;\;\;\; i\neq j

_{i,i}<0\;

and


\sum^{\infty}_{k=0}D_{k}\boldsymbol{1}=\boldsymbol{0}

Read more about this topic:  Markovian Arrival Processes

Famous quotes containing the words batch, arrival and/or process:

    And so it goes, back and forth, good church-members all, which means that their banter contains nothing off-color, and by the same token, nothing that was coined later than the first batch of buffalo nickels.
    Robert Benchley (1889–1945)

    National literature does not mean much these days; now is the age of world literature, and every one must contribute to hasten the arrival of that age.
    Johann Wolfgang Von Goethe (1749–1832)

    Language is a process of free creation; its laws and principles are fixed, but the manner in which the principles of generation are used is free and infinitely varied. Even the interpretation and use of words involves a process of free creation.
    Noam Chomsky (b. 1928)