Analysis of a Multiserver Queue with Setup Times

This paper deals with the analysis of an M/M/c queueing system with setup times. This queueing model captures the major characteristics of phenomena occurring in production when the system consists in a set of machines monitored by a single operator. We carry out an extensive analysis of the system including limiting distribution of the system state, waiting time analysis, busy period and maximum queue length. AMS subject classification: 90B22, 60K25     

Time-Reversed Dynamical Entropy and Irreversibility in Markovian Random Processes

A concept of time-reversed entropy per unit time is introduced in analogy with the entropy per unit time by Shannon, Kolmogorov, and Sinai. This time-reversed entropy per unit time characterizes the dynamical randomness of a stochastic process backward in time, while the standard entropy per unit time characterizes the dynamical randomness forward in time. The difference between the time-reversed and standard entropies per unit time is shown to give the entropy production of Markovian processes in nonequilibrium steady states.     

随机环境中的马氏链状态分类

给出了随机环境中马氏链的特征数和状态的定义,讨论了状态间的传递性,自反性,对称性,是经典马氏链相应结果的一般化.并运用位势方法研究了状态间的关系,它们在极限理论的研究中非常有用.     

A simple Markov chain structure for the evolution of credit ratings

We focus on continuous Markov chains as a model to describe the evolution of credit ratings. In this work it is checked whether a simple, tridiagonal type of generator provides a good approximation to a general one. Three different tridiagonal approximations are proposed and their performance is checked against two generators, corresponding to a volatile and a stable period, respectively. Copyright © 2007 John Wiley & Sons, Ltd.     

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.     

相互粒子系统中的负相关(英文)

主要研究相互粒子系统中概率测度的负相关.我们得到判定概率测度是负相关的一个充分必要条件.最后证明了具有负相关的概率测度的线性组合及乘积测度仍是负相关的.     

Traces of harmonic functions,capacities, and traces of symmetric Markov processes

We derive explicit isomorphism formulas between weighted Dirichlet integrals for harmonic functions and boundary Dirichlet forms. Applications yield results on traces of Markov processes and convergence quasieverywhere of harmonic functions.     

Perfect information two-person zero-sum markov games with imprecise transition probabilities

Based on an extension of the controlled Markov set-chain model by Kurano et al. (in J Appl Prob 35:293–302, 1998) into competitive two-player game setting, we provide a model of perfect information two-person zero-sum Markov games with imprecise transition probabilities. We define an equilibrium value for the games formulated with the model in terms of a partial order and then establish the existence of an equilibrium policy pair that achieves the equilibrium value. We further analyze finite-approximation error bounds obtained from a value iteration-type algorithm and discuss some applications of the model.     

Converging Marriage in Honey-Bees Optimization and Application to Stochastic Dynamic Programming

In this paper, we first refine a recently proposed metaheuristic called “Marriage in Honey-Bees Optimization” (MBO) for solving combinatorial optimization problems with some modifications to formally show that MBO converges to the global optimum value. We then adapt MBO into an algorithm called “Honey-Bees Policy Iteration” (HBPI) for solving infinite horizon-discounted cost stochastic dynamic programming problems and show that HBPI also converges to the optimal value.     

STRONG LAW OF LARGE NUMBERS AND ASYMPTOTIC EQUIPARTITION PROPERTY FOR NONSYMMETRIC MARKOV CHAIN FIELDS ON CAYLEY TREES

Some strong laws of large numbers for the frequcncies of occurrence of states and ordered couples of states for nonsymmetric Markov chain fields(NSMC)on Cayley trees are studied.In the proof,a new technique for the study of strong liinit theorems of Markov chains is extended to the case of Markov chain fields.The asymptotic equiparti- tion properties with almost everywhere(a.e.)convergence for NSMC on Cayley trees are obtained.