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.
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.
31784785
Tiger: Educational Research in the Age of the Internet
13369698
Make-to-stock systems with backorders: IPA gradients
We consider single-stage, single-product make-to-stock systems with random demand and random service (production) rate, where demand shortages at the inventory facility are backordered. The make-to-stock system is modeled as a stochastic fluid model (SFM), in which the traditional discrete arrival, service and departure stochastic processes are replaced by corresponding stochastic fluid-flow rate processes. IPA (infinitesimal perturbation analysis) gradients of various performance metrics are derived with respect to parameters of interest (here, base-stock level and production rate), and are showed to be unbiased and easy to compute. The (random) IPA gradients are obtained via sample path analysis under very mild assumptions, and are inherently nonparametric in the sense that no specific probability law need be postulated. The formulas derived can be used in simulation, as well as in real-life systems.
14058950
A Profit-Based Business Model for Evaluating Rule Interestingness
Different types of rules are mined from transaction databases often with the goal of improving sales and services. In this paper, we link the interestingness of rules with the context of business marketing. We consider the profits generated from some specific marketing strategies that are developed based on particular discovered rules. This leads to a profit-based business model for evaluating rule interestingness. With this additional utility, we investigate some relationships between different marketing strategies and fundamental properties of rules for profit increasing.
748152
On-line testing of multi-source noise-induced errors on the interconnects and buses of system-on-chips
With processors and system-on-chips using nano-meter technologies, several design and test efforts have been recently developed to eliminate and test for many emerging DSM (deep sub-micron) noise effects. In this paper, we show the emergence of multi-source noise effects, where multiple DSM noise sources combine to produce functional and timing errors even when each separate noise source itself does not. We show the dynamic nature of multi-source noise, and the need for on-line testing to detect such noise errors. We propose a double-sampling data checking based low-cost on-line error detection circuit to test for such noise effects in on-chip buses. Based on the proposed circuit, an effective and efficient testing methodology has been developed to facilitate online testing for generic on-chip buses. The applicability of this methodology is demonstrated through embedding the on-line detection circuit in a bus design. The validated design shows the effectiveness of the proposed testing methodology for multi-source noise-induced errors in global interconnects and buses.
43233125
CRD: A New Data Mining Method in Deductive Databases