Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Markovian Transition Counting Processes: An Alternative to Markov
  Modulated Poisson Processes   Stochastic models for performance analysis, optimization and control of
queues hinge on a multitude of alternatives for input point processes. In case
of bursty traffic, one very popular model is the \textit{Markov Modulated
Poisson Process} (MMPP), however it is not the only option. Here, we introduce
an alternative that we call \textit{Markovian transition counting process}
(MTCP). The latter is a point process counting the number of transitions of a
finite continuous-time Markov chain.
  For a given MTCP one can establish an MMPP with the same first and second
moments of counts. In this paper, we show the other direction by establishing a
duality in terms of first and second moments of counts between MTCPs and a rich
class of MMPPs which we refer to as slow MMPPs (modulation is slower than the
events). Such a duality confirms the applicability of the MTCP as an
alternative to the MMPP which is superior when it comes to moment matching and
finding the important measures of the inter-event process. We illustrate the
use of such equivalence in a simple queueing example, showing that the MTCP is
a comparable and competitive model for performance analysis.

29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex