Fluid and diffusion limits for transient sojourn times of processor sharing queues with time varying rates

We provide an approximate analysis of the transient sojourn time for a processor sharing queue with time varying arrival and service rates, where the load can vary over time, including periods of overload. Using the same asymptotic technique as uniform acceleration as demonstrated in [12] and [13], we obtain fluid and diffusion limits for the sojourn time of the M_t/M_t/1 processor-sharing queue. Our analysis is enabled by the introduction of a “virtual customer” which differs from the notion of a “tagged customer” in that the former has no effect on the processing time of the other customers in the system. Our analysis generalizes to non-exponential service and interarrival times, when the fluid and diffusion limits for the queueing process are known.     

基于移动Agent技术的医学图像检索方法

针对现有医学图像检索方法中，检索算法速度较慢、准确性较低以及远程检索时占用大量带宽等问题，设计并实现了一种基于移动Agent技术的医学图像检索方法，重点讨论了该方法实现的关键技术，包括提升框架下的M带整数小波变换和提取多通道纹理特征的检索算法．模拟实验结果表明，该方法实时性较强，占用网络带宽较少，采用的算法运算速度提高近10倍、运算复杂度降低约50％，提取的纹理特征能充分表达图像内容，较好地满足了医学图像的检索要求，实现了对医学图像库快速较准确的检索．     

On polynomial symbols for subdivision schemes

Given a dilation matrix A :ℤ^d→ℤ^d, and G a complete set of coset representatives of 2π(A ^−Tℤ^d/ℤ^d), we consider polynomial solutions M to the equation ∑ _g∈G M(ξ+g)=1 with the constraints that M≥0 and M(0)=1. We prove that the full class of such functions can be generated using polynomial convolution kernels. Trigonometric polynomials of this type play an important role as symbols for interpolatory subdivision schemes. For isotropic dilation matrices, we use the method introduced to construct symbols for interpolatory subdivision schemes satisfying Strang–Fix conditions of arbitrary order. Research partially supported by the Danish Technical Science Foundation, Grant No. 9701481, and by the Danish SNF-PDE network.     

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.     

On the departure process of a leaky bucket system with long-range dependent input traffic

Due to the strong experimental evidence that the traffic to be offered to future broadband networks will display long-range dependence, it is important to study the possible implications that such traffic may have for the design and performance of these networks. In particular, an important question is whether the offered traffic preserves its long-range dependent nature after passing through a policing mechanism at the interface of the network. One of the proposed solutions for flow control in the context of the emerging ATM standard is the so-called leaky bucket scheme. In this paper we consider a leaky bucket system with long-range dependent input traffic. We adopt the following popular model for long-range dependent traffic: Time is discrete. At each unit time a random number of sessions is initiated, having the distribution of a Poisson random variable with mean λ. Each of these sessions has a random duration τ, where the integer random variable τ has finite mean, infinite variance, and a regularly varying tail, i.e., P(τ >К) ~ К^-Lα L(К), where 1 < α < 2 L(·) is a slowly varying function. Once a session is initiated, it generates one cell at each unit of time until its termination. We examine the departure process of the leaky bucket policing mechanism driven by such an arrival process, and show that it too is long-range dependent for any token buffer size and any - finite or infinite - cell buffer size. Moreover, upper and lower bounds for the covariance sequence of the output process are established. The above results demonstrate that long-range dependence cannot be removed by the kinds of flow control schemes that are currently being envisioned for broadband networks. This revised version was published online in June 2006 with corrections to the Cover Date.     

Asymptotic analysis of a large closed queueing network with discriminatory processor sharing

In this paper the steady-state behavior of a closed queueing network with multiple classes and large populations is investigated. One of the two nodes of the network simply introduces random delays and the discipline in the other node is discriminatory processor sharing. The network is not product-form, so not even the steady-state behavior is known. We assume that the usage is moderately heavy, and obtain two-term asymptotic approximations to the mean number of jobs, and the mean sojourn time, of each class of jobs in the processor node. We also obtain the leading term in the asymptotic approximation to the joint distribution of the number of jobs in the processor node, which is a zero-mean multivariate Gaussian distribution around a line through the origin.     

On meromorphic functions that share three values of finite weights

A uniqueness theorem for two distinct non-constant meromorphic functions that share three values of finite weights is proved, which generalizes two previous results by H.X. Yi, and X.M. Li and H.X. Yi. As applications of it, many known results by H.X. Yi and P. Li, etc. could be improved. Furthermore, with the concept of finite-weight sharing, extensions on Osgood-Yang's conjecture and Mues' conjecture, and a generalization of some prevenient results by M. Ozawa and H. Ueda, ect. could be obtained.     

Algebraic structure of association schemes of prime order

Finite groups of prime order must be cyclic. It is natural to ask what about association schemes of prime order. In this paper, we will give an answer to this question. An association scheme of prime order is commutative, and its valencies of nontrivial relations and multiplicities of nontrivial irreducible characters are constant. Moreover, if we suppose that the minimal splitting field is an abelian extension of the field of rational numbers, then the character table is the same as that of a Schurian scheme.     

Optimal production and rationing decisions in supply chains with information sharing

This paper considers a two-echelon capacitated supply chain with two non-identical retailers and information sharing. We characterize the optimal inventory policies. We also study the benefits of the optimal stock rationing policy over the first come first served (FCFS) and the modified echelon-stock rationing (MESR) policies.     

DISSIPATIVE SCHEMES WITH PROPERTY OF INHERITING HOMOCLINIC ORBITS FOR 2N-DIMENSIONAL HAMILTONIAN SYSTEMS

1　ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｉｓｐａｐｅｒｉｓｄｅｖｏｔｅｄｔｏｓｔｕｄｙｗｈａｔｋｉｎｄｏｆｄｉｓｃｒｅｔｅｓｃｈｅｍｅｓｏｆｔｈｅｆｏｌｌｏｗｉｎｇ 2ｎ ｄｉｍｅｎ ｓｉｏｎａｌＨａｍｉｌｔｏｎｉａｎｓｙｓｔｅｍｓｗｉｔｈｐａｒａｍｅｔｅｒｉｎｎｏｒｍａｌｆｏｒｍ ｕ=Ｊ2ｎ Ｈ ｕＴ,　　Ｈ =Ｈ(ｕ ,λ) ,(1 )ｗｈｅｒｅｕ∈Ｒ2ｎ,λ∈Ｒ ,Ｈ∈Ｃｋ+1(Ｒ2ｎ×Ｒ ,Ｒ) ,ｋ≥ 6,ａｎｄＪ2ｎ =0Ｉｎ-Ｉｎ 0 ,Ｉｎ:ｕｎｉｔｍａｔｒｉｘｏｆｏｒｄｅｒｎｈａｓｔｈｅｐｒｏｐｅｒｔｙｏｆｉｎｈｅｒｉｔｉｎｇｈｏｍ…