HEAVY TRAFFIC APPROXIMATIONS FOR A SYSTEM OF INFINITE SERVERS WITH LOAD BALANCING

1999 ◽  
Vol 13 (3) ◽  
pp. 251-273 ◽  
Author(s):  
Philip J. Fleming ◽  
Burton Simon
Keyword(s):  
State Space ◽  
Heavy Traffic ◽  
Joint Probability ◽  
Mass Function ◽  
Accurate Estimate ◽  
The State ◽  
Probability Mass Function ◽  
Traffic Loads ◽  
Wide Range ◽  
Heavy Traffic Approximations

We consider an exponential queueing system with multiple stations, each of which has an infinite number of servers and a dedicated arrival stream of jobs. In addition, there is an arrival stream of jobs that choose a station based on the state of the system. In this paper we describe two heavy traffic approximations for the stationary joint probability mass function of the number of busy servers at each station. One of the approximations involves state-space collapse and is accurate for large traffic loads. The state-space in the second approximation does not collapse. It provides an accurate estimate of the stationary behavior of the system over a wide range of traffic loads.

Approximate Maximum Entropy Joint Feature Inference Consistent with Arbitrary Lower-Order Probability Constraints: Application to Statistical Classification

2000 ◽  
Vol 12 (9) ◽  
pp. 2175-2207 ◽  
Author(s):  
David J. Miller ◽  
Lian Yan
Keyword(s):  
Maximum Entropy ◽  
Lower Order ◽  
Joint Probability ◽  
Feature Space ◽  
Mass Function ◽  
Multilayer Perceptrons ◽  
Small Subset ◽  
Probability Mass Function ◽  
Order Probability ◽  
Probability Constraints

We propose a new learning method for discrete space statistical classifiers. Similar to Chow and Liu (1968) and Cheeseman (1983), we cast classification/inference within the more general framework of estimating the joint probability mass function (p.m.f.) for the (feature vector, class label) pair. Cheeseman's proposal to build the maximum entropy (ME) joint p.m.f. consistent with general lower-order probability constraints is in principle powerful, allowing general dependencies between features. However, enormous learning complexity has severely limited the use of this approach. Alternative models such as Bayesian networks (BNs) require explicit determination of conditional independencies. These may be difficult to assess given limited data. Here we propose an approximate ME method, which, like previous methods, incorporates general constraints while retaining quite tractable learning. The new method restricts joint p.m.f. support during learning to a small subset of the full feature space. Classification gains are realized over dependence trees, tree-augmented naive Bayes networks, BNs trained by the Kutato algorithm, and multilayer perceptrons. Extensions to more general inference problems are indicated. We also propose a novel exact inference method when there are several missing features.

Heavy Traffic Analysis of Approximate Max-Weight Matching Algorithms for Input-Queued Switches

2021 ◽  
Vol 48 (3) ◽  
pp. 109-110
Author(s):  
Yu Huang ◽  
Longbo Huang
Keyword(s):  
Approximation Algorithms ◽  
State Space ◽  
Queue Length ◽  
Heavy Traffic ◽  
Traffic Analysis ◽  
The State ◽  
Heavy Traffic Analysis ◽  
Heavy Traffic Limit

In this paper, we propose a class of approximation algorithms for max-weight matching (MWM) policy for input-queued switches, called expected 1-APRX. We establish the state space collapse (SSC) result for expected 1-APRX, and characterize its queue length behavior in the heavy-traffic limit.

scholarly journals On Some Compound Random Variables Motivated by Bulk Queues

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Romeo Meštrović
Keyword(s):  
Random Variables ◽  
Random Variable ◽  
Mass Function ◽  
Probability Mass Function ◽  
Time Of Arrival ◽  
Uniform Random Variable ◽  
Wide Range ◽  
Bulk Queue ◽  
Probability Mass ◽  
Number Of Customers

We consider the distribution of the number of customers that arrive in an arbitrary bulk arrival queue system. Under certain conditions on the distributions of the time of arrival of an arriving group (Y(t)) and its size (X) with respect to the considered bulk queue, we derive a general expression for the probability mass function of the random variableQ(t)which expresses the number of customers that arrive in this bulk queue during any considered periodt. Notice thatQ(t)can be considered as a well-known compound random variable. Using this expression, without the use of generating function, we establish the expressions for probability mass function for some compound distributionsQ(t)concerning certain pairs(Y(t),X)of discrete random variables which play an important role in application of batch arrival queues which have a wide range of applications in different forms of transportation. In particular, we consider the cases whenY(t)and/orXare some of the following distributions: Poisson, shifted-Poisson, geometrical, or uniform random variable.

scholarly journals State-Space Algorithms for Estimating Spike Rate Functions

2010 ◽  
Vol 2010 ◽  
pp. 1-14 ◽  
Author(s):  
Anne C. Smith ◽  
Joao D. Scalon ◽  
Sylvia Wirth ◽  
Marianna Yanike ◽  
Wendy A. Suzuki ◽  
...  
Keyword(s):  
State Space ◽  
Goodness Of Fit ◽  
State Space Model ◽  
Rate Function ◽  
Spike Rate ◽  
The State ◽  
Space Model ◽  
Wide Range ◽  
Neurophysiological Data ◽  
Rate Functions

The accurate characterization of spike firing rates including the determination of when changes in activity occur is a fundamental issue in the analysis of neurophysiological data. Here we describe a state-space model for estimating the spike rate function that provides a maximum likelihood estimate of the spike rate, model goodness-of-fit assessments, as well as confidence intervals for the spike rate function and any other associated quantities of interest. Using simulated spike data, we first compare the performance of the state-space approach with that of Bayesian adaptive regression splines (BARS) and a simple cubic spline smoothing algorithm. We show that the state-space model is computationally efficient and comparable with other spline approaches. Our results suggest both a theoretically sound and practical approach for estimating spike rate functions that is applicable to a wide range of neurophysiological data.

SINGLE VEHICLE ROUTING PROBLEMS WITH A PREDEFINED CUSTOMER ORDER, UNIFIED LOAD AND STOCHASTIC DISCRETE DEMANDS

2012 ◽  
Vol 27 (1) ◽  
pp. 1-23 ◽  
Author(s):  
Dimitrios G. Pandelis ◽  
Constantinos C. Karamatsoukis ◽  
Epaminondas G. Kyriakidis
Keyword(s):  
Optimal Policy ◽  
Dynamic Programming Algorithm ◽  
Joint Probability ◽  
Mass Function ◽  
Programming Algorithm ◽  
Probability Mass Function ◽  
Discounted Cost ◽  
Horizon Problem ◽  
Customer Order ◽  
Single Vehicle

We consider the problem of finding the optimal routing of a single vehicle that delivers K different products to N customers that are served according to a particular order. It is assumed that the demands of the customers for each product are discrete random variables, and the total demand of each customer for all products cannot exceed the vehicle capacity. The joint probability mass function of the demands of each customer is known. It is assumed that all products are stored together in the vehicle's single compartment. The policy that serves all customers with the minimum total expected cost is found by implementing a suitable dynamic programming algorithm. We prove that this policy has a specific threshold-type structure. Furthermore, we study a corresponding infinite-time horizon problem in which the service of the customers is not completed when the last customer has been serviced but it continues periodically with the same customer order. The demands of each customer for the products have the same distributions at different periods. The discounted cost optimal policy and the average-cost optimal policy have the same structure as the optimal policy in the finite-horizon problem. Numerical results are given that illustrate the structural results.

RESEARCH ON INVESTMENT AND INNOVATION ACTIVITY IN UKRAINE: TRENDS AND PROBLEMS

2018 ◽  
Vol 1 (01) ◽  
pp. 5-73
Author(s):  
Anatoliy Ivanovich Bogdanenko
Keyword(s):  
State Policy ◽  
Innovation System ◽  
State Regulation ◽  
The State ◽  
Innovation Activity ◽  
Legal Principles ◽  
Innovation Activities ◽  
Wide Range ◽  
Intellectual Potential ◽  
Innovation Processes

In the monograph the theoretical identification of concepts and categorical series of state regulation of investment-innovation processes are investigated; the directions of optimization of the state policy of innovation and investment development management in Ukraine are determined; the organizational and legal principles of the state regulation of development of intellectual potential of the population are substantiated; the areas of development and improvement of the national innovation system as an object of state policy are highlighted and assessed. The monograph will be interesting for scholars, lecturers, doctoral and graduate students, and will also be useful to practical politicians, journalists and media workers and a wide range of readers interested in investment and innovation activities.

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