On a question of Gross

Using the notion of weighted sharing of sets we prove two uniqueness theorems which improve the results proved by Fang and Qiu [H. Qiu, M. Fang, A unicity theorem for meromorphic functions, Bull. Malaysian Math. Sci. Soc. 25 (2002) 31-38], Lahiri and Banerjee [I. Lahiri, A. Banerjee, Uniqueness of meromorphic functions with deficient poles, Kyungpook Math. J. 44 (2004) 575-584] and Yi and Lin [H.X. Yi, W.C. Lin, Uniqueness theorems concerning a question of Gross, Proc. Japan Acad. Ser. A 80 (2004) 136-140] and thus provide an answer to the question of Gross [F. Gross, Factorization of meromorphic functions and some open problems, in: Proc. Conf. Univ. Kentucky, Lexington, KY, 1976, in: Lecture Notes in Math., vol. 599, Springer, Berlin, 1977, pp. 51-69], under a weaker hypothesis.     

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.     

Relationships between characteristics in periodic Poisson queues

We study single server periodic queues in the day equilibrium conditions. The following characteristics of interest are considered at time of dayt: V^p(t)-the work load, L^p(t)-the number of customers and u^p(t)-the departure rate. We give relationships between E[V^p(t)], E[L^p(t)] and u^p(t). We also prove that E[V^p(t)] < and E[L^p(t)] < provided the second moment of the service time is finite.     

Large deviation analysis of the single server queue

We establish the large deviation principle (LDP) for the virtual waiting time and queue length processes in the GI/GI/1 queue. The rate functions are found explicitly. As an application, we obtain the logarithmic asymptotics of the probabilities that the virtual waiting time and queue length exceed high levels at large times. Additional new results deal with the LDP for renewal processes and with the derivation of unconditional LDPs for conditional ones. Our approach applies in large deviations ideas and methods of weak convergence theory.This work was supported in part by AT&T Bell Labs.     

Rate conservation laws: A survey

We survey the rate conservation law, RCL for short, arising in queues and related stochastic models. RCL was recognized as one of the fundamental principles to get relationships between time and embedded averages such as the extended Little's formulaH=G, but we show that it has other applications. For example, RCL is one of the important techniques for deriving equilibrium equations for stochastic processes. It is shown that the various techniques, including Mecke's formula for a stationary random measure, can be formulated as RCL. For this purpose, we start with a new definition of the rate with respect to a random measure, and generalize RCL by using it. We further introduce the notion of quasi-expectation, which is a certain extension of the ordinary expectation, and derive RCL applicable to the sample average results. It means that the sample average formulas such asH=G can be obtained as the stationary RCL in the quasi-expectation framework. We also survey several extensions of RCL and discuss examples. Throughout the paper, we would like to emphasize how results can be easily obtained by using a simple principle, RCL.     

Stationary queues with one autonomous server

Given a stationary stochastic continuous demand of service σ(θ_tω) dt with ∫ σ(ω)P(dω) < 1, we construct real stationary point processes $\text{(T}{}_{\mathrm{n}}\text{, n ∈}\text{Z}\text{)[T}{}_{\mathrm{n}}\text{< T}{}_{\mathrm{n}}\text{+1, lim}{}_{\mathrm{\pm \infty }}\text{T}{}_{\mathrm{n}}\text{= ±∞]}$ such that

for a given constant D \2>0. These point processes correspond to a service discipline for which a single server services during the time intervals [T_n, T_n+1[ the demand of service accumulated during the proceding intervals [T_n?1, T_n[ and take a rest of fixed duration D.     

基于AHP权重和灰色服务器负载预测的云计算On-line迁移策略

为了克服云计算环境下由于实时用户任务的不确定性到来和服务器性能差异而导致的云计算环境的负载不均衡问题,提出了一种AHP权重获取和灰度算法预测服务器负载的云计算on-line虚拟机迁移策略。首先,设计了基于AHP和灰色服务器预测的虚拟机on-line迁移模型,提出了采用AHP获取虚拟机各资源需求权重,然后,采用灰色模型预测下一时刻的服务器负载,采用此权值向量与各无需迁移的服务器的空闲资源向量进行加权得到加权和,将具有最小加权和的物理服务器作为迁移的目标宿主机。最后,定义了基于AHP权重和灰色服务器负载预测的云计算on-line迁移算法。在CloudSim环境下进行实验,结果表明文中的迁移策略使得云计算在响应用户任务时,具有任务失败次数少、SLA违约率低和迁移成功率高的优点,同时与其它方法相比,具有负载均衡程度高的优点,具有较强的可行性。     

基于SRLG不相关的共享保护算法的研究

通过对共享保护算法的深入分析,使用K条最短路和迭代思想的方法,提出了两种共享风险链路组不相关的共享保护算法,并在仿真平台上对两种算法的性能进行了仿真.KWFF算法借鉴了传统的K条最短路策略,并且在每一个波长平面上,都对新到业务进行了K条工作路由的计算,极大挖掘了网络中潜在的波长资源.而IFF算法由于引入了迭代的思想,避免了共享风险链路组问题中,所特别有“陷阱”问题的出现,并且利用两套权重计算公式,在计算工作路由和保护路由的时候,充分考虑了网络资源的实时变化情况.通过仿真数据可以看到,与以往算法相比,KWFF和IFF算法大大降低了网络阻塞率,并且提高了网络资源的使用效率.     

涉及分担函数与分担值的正规定则

研究了涉及分担函数的正规定则,证明了:设F为定义在区域D内的一族亚纯函数,n,k是两个正整数,满足n≥k+3.如果对于F中任意一个函数f,(fn)(k)-z至多有一个不同的零点,则F在D内正规.此结论说明在(fn)(k)具有不动点的情形下,1990年杨乐在Notre Dame大学举行的学术会议上提出的断言仍然成立.