有向图上的随机游动

设G=(V,Г)是有向图,G上的随机游动X(G)定义如下:位于某个顶点上的一个粒子将以等概率转移到该顶点的所有后继顶点.令M(j,n)表示随机游动X(G)在前n步内访问顶点j的平均次数,用W(j)表示随机游动X(G)到达顶点j所需要的平均步效.我们对M(j,n)和W(j)的值进行了估计,证明了M(j,n)=O(n),并给出了W(j)的上界.     

关于任意随机变量序列泛函的强极限定理

本文在k是固定的正整数，{fn}是R^k 1上的Borel可测函数列时，得到了任意随机变量序列{Xrn≥0}的泛函{fn(Xn-k,…,Xn)}的强极限定理，它是Chung的关于独立随机变量序列的强大数律的推广，作为推论，得到了k重非齐次马尔科夫链的一类强极限定理．     

分布式配送系统在运输时间均匀分布条件下的性能分析

本文在运输时间不确定的前提下，对分布式配送系统在两个部件和最终产品早到无限制的情形下建立了随机优化模型。我们在极小化库存费用的同时以满足定时送货要求为目标，讨论了如何确定运输提前期，并给出了敏感性分析结果。     

A queueing system with linear repeated attempts,bernoulli schedule and feedback

We analyse a single-server retrial queueing system with infinite buffer, Poisson arrivals, general distribution of service time and linear retrial policy. If an arriving customer finds the server occupied, he joins with probabilityp a retrial group (called orbit) and with complementary probabilityq a priority queue in order to be served. After the customer is served completely, he will decide either to return to the priority queue for another service with probability ϑ or to leave the system forever with probability =1−ϑ, where 0≤ϑ<1. We study the ergodicity of the embedded Markov chain, its stationary distribution function and the joint generating function of the number of customers in both groups in the steady-state regime. Moreover, we obtain the generating function of system size distribution, which generalizes the well-knownPollaczek-Khinchin formula. Also we obtain a stochastic decomposition law for our queueing system and as an application we study the asymptotic behaviour under high rate of retrials. The results agree with known special cases. Finally, we give numerical examples to illustrate the effect of the parameters on several performance characteristics.     

Generalized binomial and negative binomial distributions of order<Emphasis Type="Italic">k</Emphasis> by the<Emphasis Type="Italic">l</Emphasis>-overlapping enumeration scheme

In this paper, we investigate the exact distribution of the waiting time for ther-th ℓ-overlapping occurrence of success-runs of a specified length in a sequence of two state Markov dependent trials. The probability generating functions are derived explicitly, and as asymptotic results, relationships of a negative binomial distribution of orderk and an extended Poisson distribution of orderk are discussed. We provide further insights into the run-related problems from the viewpoint of the ℓ-overlapping enumeration scheme. We also study the exact distribution of the number of ℓ-overlapping occurrences of success-runs in a fixed number of trials and derive the probability generating functions. The present work extends several properties of distributions of orderk and leads us a new type of geneses of the discrete distributions.     

Permanence for non-autonomous food chain systems with delay

In this paper we first establish a new general criterion for the permanence of Kolmogorov-type systems of nonautonomous functional differential equations. Then, as applications of this criterion we study the permanence of a class of n-species general nonautonomous food chain systems with delay and new sufficient condition are established.     

Single-server queues with spatially distributed arrivals

Consider a queueing system where customers arrive at a circle according to a homogeneous Poisson process. After choosing their positions on the circle, according to a uniform distribution, they wait for a single server who travels on the circle. The server's movement is modelled by a Brownian motion with drift. Whenever the server encounters a customer, he stops and serves this customer. The service times are independent, but arbitrarily distributed. The model generalizes the continuous cyclic polling system (the diffusion coefficient of the Brownian motion is zero in this case) and can be interpreted as a continuous version of a Markov polling system. Using Tweedie's lemma for positive recurrence of Markov chains with general state space, we show that the system is stable if and only if the traffic intensity is less than one. Moreover, we derive a stochastic decomposition result which leads to equilibrium equations for the stationary configuration of customers on the circle. Steady-state performance characteristics are determined, in particular the expected number of customers in the system as seen by a travelling server and at an arbitrary point in time.     

One-dimensional Ising chain with competing interactions: Exact results and connection with other statistical models

We study the ground state properties of a one-dimensional Ising chain with a nearest-neighbor ferromagnetic interactionJ ₁, and akth neighboranti-ferromagnetic interactionJ _k . WhenJ _k/J₁=–1/k, there exists a highly degenerate ground state with a residual entropy per spin. For the finite chain with free boundary conditions, we calculate the degeneracy of this state exactly, and find that it is proportional to the (N+k–1)th term in a generalized Fibonacci sequence defined by,F _N ^(k) =F _N–1 ^(k) +F _N–k ^(k) . In addition, we show that this one-dimensional model is closely related to the following problems: (a) a fully frustrated two-dimensional Ising system with a periodic arrangement of nearest-neighbor ferro- and antiferromagnetic bonds, (b) close-packing of dimers on a ladder, a 2× strip of the square lattice, and (c) directed self-avoiding walks on finite lattice strips.Work partially supported by grants from AFOSR and ARO.     

On the use of two QMR algorithms for solving singular systems and applications in Markov chain modeling

Recently, Freund and Nachtigal proposed the quasi-minimal residual algorithm (QMR) for solving general nonsingular non-Hermitian linear systems. The method is based on the Lanczos process, and thus it involves matrix—vector products with both the coefficient matrix of the linear system and its transpose. Freund developed a variant of QMR, the transpose-free QMR algorithm (TFQMR), that only requires products with the coefficient matrix. In this paper, the use of QMR and TFQMR for solving singular systems is explored. First, a convergence result for the general class of Krylov-subspace methods applied to singular systems is presented. Then, it is shown that QMR and TFQMR both converge for consistent singular linear systems with coefficient matrices of index 1. Singular systems of this type arise in Markov chain modeling. For this particular application, numerical experiments are reported.     

Asymptotic properties of multistate random walks. I. Theory

A calculation is presented of the long-time behavior of various random walk properties (moments, probability of return to the origin, expected number of distinct sites visited) formultistate random walks on periodic lattices. In particular, we consider inhomogeneous periodic lattices, consisting of a periodically repeated unit cell which contains a finite number of internal states (sites). The results are identical to those for perfect lattices except for a renormalization of coefficients. For walks without drift, it is found that all the asymptotic random walk properties are determined by the diffusion coefficients for the multistate random walk. The diffusion coefficients can be obtained by a simple matrix algorithm presented here. Both discrete and continuous time random walks are considered. The results are not restricted to nearest-neighbor random walks but apply as long as the single-step probability distributions associated with each of the internal states have finite means and variances.