For a star like network (central server system) with state dependent branching we compute the cycle time distribution. The Laplace-Stieltjes transform of this distribution is of product form. This allows to define a recursive algorithm for evaluation of cycle time moments of any order.

This article analyzes discrete Markov processes that arise in some general control problems of a storage (or a dam) with an infinite capacity. Employing a special step-wise structure of the transition matrices of these processes, the author obtains conditions for their ergodicity and develops an implementable algorithm for finding the generating function of the corresponding...

In this paper, we investigate a class of first order impulsive integro-differential equations subject to certain nonlinear boundary conditions and prove, with the help of upper and lower solutions, that the problem has a solution lying between the upper and lower solutions. We also develop monotone iterative technique and show the existence of multiple solutions of a class of...

This paper deals with a multi-channel queueing system with a finite waiting room but without losses. The latter is achieved by a temporary interruption of the input flow activity until the waiting room is ready to place a new customer. In addition, the input flow on its busy period is non-recurrent: It is state dependent and may be controlled over relevant times of decision...

We report some results on nonstandard potentials and their application to solution of the Stefan problem.

A class of linear difference equations with variable coefficients is considered. Sufficient conditions and necessary conditions for the oscillation of the solutions are established. In the special cases where the coefficients are constant or periodic the conditions become both necessary and sufficient.

In this paper we consider the question of existence of solutions for a large class of nonlinear differential inclusions on Banach space arising from control theory.

The properties of the solution set of stochastic inclusions xt−xs∈clL2(∫stFτ(xτ)dτ

In classical Little's formula L=λW used in queueing, the parameter λ serves as the intensity of the input process. In various applications this parameter may not be known. The author discusses important classes of modulated input processes, where this parameter can be found.

We discuss the existence, uniqueness, and continuous dependence on data, of anti-periodic traveling wave solutions to higher order two-dimensional equations of Korteweg-deVries type.

In this paper we develop the monotone method in the presence of lower and upper solutions for the problem u(n)(t)=f(t,u(t));u(i)(a)−u(i)(b)=λi∈ℝ,i=0,…,n−1 where f is a Carathéodory function. We obtain sufficient conditions for f to guarantee the existence and approximation of solutions between a lower solution α and an upper solution β for n≥3 with either α≤β or α≥β.

If a1,a2,…,an are independent, normally distributed random variables with mean 0 and variance 1, and if vn is the mean number of zeros on the interval (0,2π) of the trigonometric polynomial a1cosx

We study two-parameter coordinate-wise C0-semigroups and their generators, as well as two-parameter evolutions and differential equations up to the second order for them. These results are applied to obtain the Hille-Yosida theorem for homogeneous Markov fields of the Feller type and to establish forward, backward, and mixed Kolmogorov equations for nonhomogeneous diffusion...

We consider a system of finite number of particles that are moving in Rd under mutual interaction. It is assumed that the particles are subjected to some additional random forces which cause diffusion motion of the particles. The latter is described by a system of stochastic differential equations of the first order for noninertia particles and the second order for inertial...

In the present paper we study nonlocal problems for ordinary differential equations with a discontinuous coefficient for the high order derivative. We establish sufficient conditions, known as regularity conditions, which guarantee the coerciveness for both the space variable and the spectral parameter, as well as guarantee the completeness of the system of root functions. The...

We consider an initial value problem for impulsive differential-difference equations, and obtain sufficient conditions for the existence, uniqueness, and continuability of solutions of such problem.

We start from an earlier paper evaluating the overall sojourn time to derive the local sojourn time in stationary regime, in a single server tandem queue of (m

A separable spin glass model whose exchange integral takes the form Jij=J(ξi1ξj2

Based on the G-H-KKM selections, some nonempty intersection theorems and their applications to minimax inequalities are presented.

We study MX/G/1 nonpreemptive and preemptive-resume priority queues with/without vacations under random order of service (ROS) discipline within each class. By considering the conditional waiting times given the states of the system, which an arbitrary message observes upon arrival, we derive the Laplace-Stieltjes transforms of the waiting time distributions and explicitly obtain...

Using recent results in tandem queues and queueing networks with renewal input, when successive service times of the same customer are varying (and when the busy periods are frequently not broken up in large networks), the local queueing delay of a single server queueing network is evaluated utilizing new concepts of virtual and actual delays (respectively). It appears that...