We study the phenomenon of entrainment in processor sharing networks, whereby, while individual network resources have sufficient capacity to met demand, the requirement for simultaneous availability… (More)

In this paper we consider the component structure of decomposable combinatorial objects, both labeled and unlabeled, from a probabilistic point of view. In both cases we show that when the generating… (More)

A bipartite random mapping TK,L of a finite set V = V1 ∪ V2, |V1| = K and |V2| = L , into itself assigns independently to each i ∈ V1 its unique image j ∈ V2 with probability 1/L and to each i ∈ V2… (More)

In this paper we investigate the asymptotic structure of a random mapping model with preferential attachment, T ρ n , which maps the set {1, 2, ..., n} into itself. The model T ρ n was introduced in… (More)

Dai, Li, and Wu proposed Rule k, a localized approximation algorithm that attempts to find a small connected dominating set in a graph. In this paper we consider the "average-case" performance of two… (More)

We consider the set of polynomials of degree n over a finite field and put the uniform probability measure on this set. Any such polynomial factors uniquely into a product of its irreducible factors.… (More)

In this paper we introduce a new random mapping model, T D̂ n , which maps the set {1, 2, ..., n} into itself. The random mapping T D̂ n is constructed using a collection of exchangeable random… (More)

Random costsC(i, j) are assigned to the arcs of a complete directed graph onn labeled vertices. Given the cost matrixC n =(C(i, j)), letT* k =T* k (C n ) be the spanning tree that has minimum cost… (More)

In this paper we consider a random mapping, T̂n,θ, of the finite set {1, 2, ..., n} into itself for which the digraph representation Ĝn,θ is constructed by: (1) selecting a random number, L̂n, of… (More)