7415922
A numerically stable algorithm for two server queue models
In this paper, we consider a queueing system in which there are two exponential servers, each having his own queue, and arriving customers will join the shorter queue. Based on the results given in Flatto and McKean, we rewrite the formula for the probability that there are exactlyk customers in each queue, wherek = 0, 1,…. This enables us to present an algorithm for computing these probabilities and then to find the joint distribution of the queue lengths in the system. A program and numerical examples are given.
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.
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.
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.
5956143
Fast Update Algorithm for IP Forwarding Table Using Independent Sets
This paper describes a new update algorithm for Internet Protocol (IP) forwarding tables. The update algorithm is so general that it can be combined with many IP address lookup algorithms for fast update. This is done by partitioning the IP forwarding table into independent sets. Each independent set can be looked as a set of disjoint ranges, therefore any data structure for disjoint ranges search can be combined with this algorithm to support fast update. This algorithm achieves fast update by avoiding the worst-case update scenario. The number of independent sets is small, hence, the number of parallel data structures is small.
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.
3140808
Voxels on Fire
We introduce a method for the animation of fire propagation and the burning consumption of objects represented as volumetric data sets. Our method uses a volumetric fire propagation model based on an enhanced distance field. It can simulate the spreading of multiple fire fronts over a specified isosurface without actually having to create that isosurface. The distance field is generated from a specific shell volume that rapidly creates narrow spatial bands around the virtual surface of any given isovalue. The complete distance field is then obtained by propagation from the initial bands. At each step multiple fire fronts can evolve simultaneously on the volumetric object. The flames of the fire are constructed from streams of particles whose movement is regulated by a velocity field generated with the hardware-accelerated Lattice Boltzmann Model (LBM). The LBM provides a physically-based simulation of the air flow around the burning object. The object voxels and the splats associated with the flame particles are rendered in the same pipeline so that the volume data with its external and internal structures can be displayed along with the fire.
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.
37471711
Coarsening Classification Rules on Basis of Granular Computing
The task of classification, as a well-studied field of machine learning and data mining, has two main purposes: describing the classification rules in the training dataset and predicting the unseen new instances in the testing dataset. Normally, one expects a high accuracy for precisely descriptive use. However, a higher accuracy is intended to generate longer rules, which are not easy to understand, and may overfit the training instances. This motivates us to propose the approach of coarsening the classification rules, namely, reasonably sacrifice the accuracy of description in a controlled level in order to improve the comprehensibility and predictability. The framework of granular computing provides us a formal and systematic methodology for doing this. In this paper, a modified PRISM classification algorithm is presented based on the framework of granular computing.
38902380
Construction Algorithm of Principal Curves in the Sense of Limit
Principal curves have been defined as self-consistent, smooth, one-dimensional curves which pass through the middle of a multidimensional data set. They are nonlinear generalization of the first Principal Component. In this paper, we take a new approach by defining principal curves as continuous curves based on the local tangent space in the sense of limit. It is proved that this new principal curves not only satisfy the self-consistent property, but also are the unique existence for any given open covering. Based on the new definition, a new practical algorithm for constructing principal curves is given. And the convergence properties of this algorithm are analyzed. The new construction algorithm of principal curves is illustrated on some simulated data sets.
2480088
Melting and flowing in multiphase environment
Abstract This paper presents a method to simulate the melting and flowing phenomena with different materials in multiple phases. In such a multiphase environment, solid objects are melted because of heating and the melted liquid flows while interacting with the ambient air flow. Our simulation is based on a modified lattice Boltzmann method (LBM), where the fluid dynamics of the air flow and the melted liquid is modeled within a common lattice framework. Therefore, no particular front tracking methods are required for the liquid–air interface. The liquid–solid and air–solid interfaces are implemented as curved boundaries in the LBM, which can accommodate arbitrarily shaped solid objects. Heat transfer is incorporated with a finite difference discretization of a standard diffusion–advection equation simulating the temperature evolution. The temperature and body forces (gravity and surface tension) are easily applied by adopting a new version of the LBM: multiple-relaxation-time LBM (MRTLBM). The melting and flowing behavior is controlled by the heat source, the viscosity and the body forces. All the numerical computations in our method are local and parallelizable, therefore, interactive speed is achieved by hardware acceleration on the contemporary graphics hardware (GPU).