In this extended abstract we consider the use of Bernstein polynomials (BPs) for the approximation of distributions and transient probabilities of continuous time Markov chains (CTMCs). We show that while standard BPs are not appropriate to this purpose it is possible to derive from them a family of functions, called in the sequel Bernstein expolynomials (BEs), which enjoys those properties tha...

We present a model checking procedure for the CSL until operator on the CTMCs that underly Jackson queueing networks. The key issue lies in the fact that the underlying CTMC is infinite in as many dimensions as there are queues in the JQN. We need to compute the transient state probabilities for all goal states and for all possible starting states. However, for these transient probabilities no ...

In this paper, we study a finite capacity Markovian multi-server queuing system with discouraged arrivals, reneging, and retention of reneging customers. The transient state probabilities of the queuing system are obtained by using a computational technique based on the 4th order RungeKutta method. With the help of the transient state probabilities, we develop some important measures of perform...

For reaction-diffusion processes without exclusion, in which the particles can exist in the same site of a one-dimensional lattice, we study all the integrable models which can be obtained by imposing a boundary condition on the master equation of the asymmetric diffusion process. The annihilation process is also added. The Bethe ansatz solution and the exact N-particle conditional probabilitie...

Three-valued accounts of conditionals frequently promise (a) to conform to the probabilistic view that conditionals are evaluated by conditional probabilities, and (b) to yield a plausible account of compounds of conditionals. However, McGee (1981) shows that probabilistic validity, the conception of validity most naturally associated with the probabilistic view, cannot be characterized by a fi...

We investigate time evolution of S-wave charmonium populations under a time-dependent homogeneous magnetic field and evaluate survival probabilities the low-lying charmonia to goal estimating strength at heavy-ion collisions. Our approach implements mixing between different spin eigenstates transitions radially excited states. show that can change even by an extremely short field. Furthermore, ...

1 Introduction Suppose that n individuals, labeled 1,..., n 9 wish to assign consensual probabilities to a sequence of events E u ..., E k which partition some set of possibilities. Let their subjective assignments be registered in an n x k matrix P = (Pij), where py denotes the subjective probability assigned by individual / to event Ej. The question of how to aggregate the probabilities in P ...

Stochastic model checking requires the computation of steady-state or transient distribution for finite or infinite Markov chains for the evaluation of some formulas implying probabilities. However the numerical analysis of Markov chains is much less efficient than the sophisticated algorithmic techniques such as MTBDD developed for the deterministic model checking. We propose to simplify the n...

This paper investigates handover and fresh call blocking probabilities for subscribers moving along a road in a traffic jam passing through consecutive cells of a wireless network. It is observed and theoretically motivated that the handover blocking probabilities show a sharp peak in the initial part of a traffic jam roughly at the moment when the traffic jam starts covering a new cell. The th...

Most Markov chains that describe networks of stochastic reactions have a huge state space. This makes exact analysis infeasible and hence the only viable approach, apart from simulation, is approximation. In this paper we derive a product form approximation for the transient probabilities of such Markov chains. The approximation can be interpreted as a set of interacting time inhomogeneous Mark...