In this paper the equivalence between various divisible load-scheduling policies and continuous time Markov chains is demonstrated. The problem is to show optimal divisible load schedules for various network topologies have Markov chain analogs. This paper is a continuation of our initial short paper [1] that introduced this unification between divisible load theory and Markov chain models for ...

A random variableX is geometrically infinitely divisible iff for every p ∈ (0, 1) there exists random variable Xp such that X d = ∑T (p) k=1 Xp,k, where Xp,k’s are i.i.d. copies of Xp, and random variable T (p) independent of {Xp,1, Xp,2, . . .} has geometric distribution with the parameter p. In the paper we give some new characterization of geometrically infinitely divisible distribution. The...

In the class of abelian groups a subclass of two-divisible-groups is singled out, and in the latter, a subclass of uniquely-two-divisible-groups. With every such a group a special geometrical structure, more precisely the structure of “congruence of vectors” is correlated. The notion of “affine vector space” (denoted by AffVect) is introduced. This term is defined by means of suitable axiom sys...

Based on congruences mod p and on properties of Bernoulli polynomials and Bernoulli numbers, several conditions are derived for x, k > 2 to satisfy the Diophantine equation 1k + 2k H-\(x 1 )* = xk . It is proved that ord2(x 3) = orà2k + 3 and that x cannot be divisible by any regular prime. Furthermore, by using the results of experiments with the above conditions on an SGI workstation it is pr...

This paper presents an off-line divisible e-cash scheme where a user can withdraw a divisible coin of monetary value 2 that he can parceled and spend anonymously and unlinkably. We present the construction of a security tag that allows to protect the anonymity of honest users and to revoke anonymity only in case of cheat for protocols based on a binary tree structure without using a trusted thi...

In a recent article Pillai (1990, Ann. Inst. Statist. Math., 42, 157-161) showed that the distribution 1-E~(-x~), 0 < c~ _< 1; 0 _< x, where E~(x) is the Mittag-Lettter function, is infinitely divisible and geometrically infinitely divisible. He also clarified the relation between this distribution and a stable distribution. In the present paper, we generalize his results by using Bernstein fun...