Proxel-based simulation is a new and deterministic approach to analysing discrete stochastic models and studying their behaviour. One of its main advantages is the intuitiveness with which it approaches models’ analysis. Even though the proxel-based method is a deterministic approach, unlike the other approaches in that class, it does not set up and solve partial differential equations, and pos...

The analysis of discrete stochastic models such as generally distributed stochastic Petri nets can be done by using state spacebased methods. They describe the behavior of a model by a Markov chain that can be solved mathematically. Formerly this approach often had to be discarded as unfeasible due to high memory and runtime costs. The recently developed Proxel-based algorithm is a state space-...

This paper considers parameter estimation of a class of discrete multi-variate phase-type distributions (DMPH). Such discrete phase-type distributions are based on discrete Markov chains with marked transitions introduced by He and Neuts (Stoch Process Appl 74(1):37–52, 1998) and is a generalization of the discrete univariate phase–type distributions. Properties of the DMPHs are presented. An E...

One of the classical topics in discrete mathematics and in computer science is the computation of the transitive closure and reduction of a directed graph. We provide a complete analysis of the random variables counting the size of the transitive closure and reduction in random acyclic digraphs. In particular we present closed forms for their probability distribution and moments, showing that t...

Given a digraph D = (V ,A) and an X ⊆ V , DX denotes the digraph obtained from D by reversing those arcs with exactly one end in X. A digraph D is called acyclically pushable when there exists an X ⊆ V such that DX is acyclic. Huang, MacGillivray and Yeo have recently characterized, in terms of two excluded induced subgraphs on 7 and 8 nodes, those bipartite permutation digraphs which are acycl...

In this article we construct bivariate discrete distribution in Z. We make use of a generalized trivariate reduction technique. The special case leading to bivariate Skellam distributions is studied in detail. Properties of the derived models as well as estimation are examined. Real data application is provided. Discussion of extensions to different models is also mentioned.

In this note we present a series expansion of inverse moments of a non-negative discrete random variate in terms of its factorial cumulants, based on the Poisson-Charlier expansion of a discrete distribution. We apply the general method to the positive binomial distribution and obtain a convergent series for its inverse moments with an error residual that is uniformly bounded on the entire inte...

The vertex arboricity $rho(G)$ of a graph $G$ is the minimum number of subsets into which the vertex set $V(G)$ can be partitioned so that each subset induces an acyclic graph‎. ‎A graph $G$ is called list vertex $k$-arborable if for any set $L(v)$ of cardinality at least $k$ at each vertex $v$ of $G$‎, ‎one can choose a color for each $v$ from its list $L(v)$ so that the subgraph induced by ev...

The simulation of discrete stochastic models using state space-based methods has recently become practical through the proxel-based simulation algorithm. Proxels implement the method of supplementary variables and generate a DTMC of the model’s state space. However, due to state space explosion the method does not yet work efficiently on larger models. By using discrete phase-type approximation...