11954710
Balancing Queues by Mean Field Interaction
Consider a queueing network with N nodes in which queue lengths are balanced through mean-field interaction. When N is large, we study the performance of such a network in terms of limiting results as N goes to infinity.
7249461
Equilibrium probability calculations for a discrete-time bulk queue model
Many problems in management science and telecommunications can be solved by the analysis of aDX/Dm/1 queueing model. In this paper, we use the zeros, both inside and outside the unit circle, of the denominator of the generating function of the model to obtain an explicit closed-form solution for the equilibrium probabilities of the number of customers in the system. The moments of the number of customers in the queue or in the system are also studied. When there are infinitely many zeros outside the unit circle, we propose an approximation method using polynomials. This method yields correct values for a finite number of the probabilities, the number depending on the degree of the polynomial approximation.
8245310
Packet classification using independent sets
This paper describes a new algorithm for packet classification using the concept of independent sets. The algorithm has very small memory requirements. The search speed is neither sensitive to the rule table nor to the percentage of wildcards in the fields. It also scales well from two dimensional classifiers to high dimensional ones. In particular, the algorithm is inherently parallel. Hardware tailored to this algorithm can achieve very fast search speed.
10152279
An on-chip IP address lookup algorithm
This paper proposes a new data compression algorithm to store the routing table in a tree structure using very little memory. This data structure is tailored to a hardware design reference model presented in this paper. By exploiting the low memory access latency and high bandwidth of on-chip memory, high-speed packet forwarding can be achieved using this data structure. With the addition of pipeline in the hardware, IP address lookup can only be limited by the memory access speed. The algorithm is also flexible for different implementation. Experimental analysis shows that, given the memory width of 144 bits, our algorithm needs only 400kb memory for storing a 20k entries IPv4 routing table and five memory accesses for a search. For a 1M entries IPv4 routing table, 9Mb memory and seven memory accesses are needed. With memory width of 1,068 bits, we estimate that we need 100Mb memory and six memory accesses for a routing table with 1M IPv6 prefixes.
7393635
On a decomposition for infinite transition matrices
Heyman gives an interesting factorization of I-P, where P is the transition probability matrix for an ergodic Markov chain. We show that this factorization is valid if and only if the Markov chain is recurrent. Moreover, we provide a decomposition result which includes all ergodic, null recurrent as well as the transient Markov chains as special cases. Such a decomposition has been shown to be useful in the analysis of queues.
12919460
Decay rate for a PH/M/2 queue with shortest queue discipline
In this paper, we consider a PH/M/2 queue in which each server has its own queue and arriving customers join the shortest queue. For this model, it has been conjectured that the decay rate of the tail probabilities for the shortest queue length in the steady state is equal to the square of the decay rate for the queue length in the corresponding PH/M/2 model with a single queue. We prove this fact in the sense that the tail probabilities are asymptotically geometric when the difference of the queue sizes and the arrival phase are fixed. Our proof is based on the matrix analytic approach pioneered by Neuts and recent results on the decay rates.
7784369
Network bandwidth requirements for scalable on-demand streaming
Recently proposed streaming protocols are able to deliver multimedia files on-demand with the required server bandwidth growing only logarithmically with the file request rate. The same efficiencies are achieved for network bandwidth if delivery is over a true broadcast channel. This paper considers the required network bandwidth for on-demand streaming over multicast delivery trees. We consider both simple canonical delivery trees, and more complex cases in which delivery trees are constructed using both existing and new algorithms for various randomly generated network topologies and client site locations. Our results quantify the potential savings from the use of multicast trees that are configured to minimize network bandwidth rather than the latency to the content server. Further, we show that it is possible to achieve reasonably close to the minimum possible bandwidth usage for both network and server simultaneously, with a practical on-demand streaming protocol.
15310670
A Recent-Biased Dimension Reduction Technique for Time Series Data
There are many techniques developed for tackling time series and most of them consider every part of a sequence equally. In many applications, however, recent data can often be much more interesting and significant than old data. This paper defines new recent-biased measures for distance and energy, and proposes a recent-biased technique based on DWT for time series in which more recent data are considered more significant. With such a recent-biased technique, the dimension of time series can be reduced while effectively preserving the recent-biased energy. Our experiments have demonstrated the effectiveness of the proposed approach for handling time series.
6467988
Empirical and Theoretical Comparisons of Selected Criterion Functions for Document Clustering
This paper evaluates the performance of different criterion functions in the context of partitional clustering algorithms for document datasets. Our study involves a total of seven different criterion functions, three of which are introduced in this paper and four that have been proposed in the past. We present a comprehensive experimental evaluation involving 15 different datasets, as well as an analysis of the characteristics of the various criterion functions and their effect on the clusters they produce. Our experimental results show that there are a set of criterion functions that consistently outperform the rest, and that some of the newly proposed criterion functions lead to the best overall results. Our theoretical analysis shows that the relative performance of the criterion functions depends on (i) the degree to which they can correctly operate when the clusters are of different tightness, and (ii) the degree to which they can lead to reasonably balanced clusters.
1449662
A tool for teaching curve design
This paper describes a tool for teaching curve design. This tool is a component of the software tools to be used in a computing with geometry course [3, 4] that is being developed under the support of National Science Foundation. Curve design is important in computer graphics, animation, and computer aided design. Unfortunately, curve design requires very involved mathematics even though many curve design concepts are intuitive. As a result, it has been a challenging job for instructors teaching curves and surfaces in computer graphics, computer aided design, and other related courses. During past years, there have not been very many efforts dedicated to curve design tool development. Yen [7] produced a well-received video program explaining important concepts of B-spline curves and surfaces and Rockwood and Chambers [6] published a multimedia tutorial on computer aided geometric design. The former only provides a one-way communication, while the latter restricts users to a predefined environment with very limited interaction for users to carry out experiments. To fill this gap, our tool provides students with a fully interactive environment in which they are free to design, modify, and manipulate curved objects and perform experiments without constraints.In the following, Section 2 presents design issues, Section 3 discusses general features, Section 4 enumerates basic elements, Section 5 covers advanced topics, and Section 6 is our conclusion. Interested readers should consult [1, 2, 5] for mathematical background details.
42162120
Digitizing Old Photographs for the Web
In the last few years, both small family photo collections and huge library and museum collections have been digitized and made available on the Web. In this article, we discuss reasons for digitizing. We describe an ongoing project in which children and adults in a technology-oriented after-school program in rural Michigan are digitizing photographs for a local historical society.