scholarly journals Simple and Yet Efficient Estimators for Markovian Multiserver Queues

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Emilio Suyama ◽  
Roberto C. Quinino ◽  
Frederico R. B. Cruz
Keyword(s):  
Maximum Likelihood ◽  
Arrival Rate ◽  
Research Area ◽  
Service Rate ◽  
Traffic Intensity ◽  
Moment Estimator ◽  
Likelihood Estimator ◽  
Future Developments ◽  
Multiserver Queues

Estimators for the parameters of the Markovian multiserver queues are presented, from samples that are the number of clients in the system at arbitrary points and their sojourn times. As estimation in queues is a recognizably difficult inferential problem, this study focuses on the estimators for the arrival rate, the service rate, and the ratio of these two rates, which is known as the traffic intensity. Simulations are performed to verify the quality of the estimations for sample sizes up to 400. This research also relates notable new insights, for example, that the maximum likelihood estimator for the traffic intensity is equivalent to its moment estimator. Some limitations of the results are presented along with a detailed numerical example and topics for future developments in this research area.

scholarly journals Traffic Intensity Estimation in Finite Markovian Queueing Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Frederico R. B. Cruz ◽  
Márcio A. C. Almeida ◽  
Marcos F. S. V. D’Angelo ◽  
Tom van Woensel
Keyword(s):  
Queueing Systems ◽  
Arrival Rate ◽  
Research Area ◽  
Service Rate ◽  
Intermediate Step ◽  
Single Server ◽  
Traffic Intensity ◽  
Finite Sample ◽  
Jeffreys Prior ◽  
Accurate Performance

In many everyday situations in which a queue is formed, queueing models may play a key role. By using such models, which are idealizations of reality, accurate performance measures can be determined, such as traffic intensity (ρ), which is defined as the ratio between the arrival rate and the service rate. An intermediate step in the process includes the statistical estimation of the parameters of the proper model. In this study, we are interested in investigating the finite-sample behavior of some well-known methods for the estimation of ρ for single-server finite Markovian queues or, in Kendall notation, M/M/1/K queues, namely, the maximum likelihood estimator, Bayesian methods, and bootstrap corrections. We performed extensive simulations to verify the quality of the estimators for samples up to 200. The computational results show that accurate estimates in terms of the lowest mean squared errors can be obtained for a broad range of values in the parametric space by using the Jeffreys’ prior. A numerical example is analyzed in detail, the limitations of the results are discussed, and notable topics to be further developed in this research area are presented.

The convexity of a general performance measure for multiserver queues

1987 ◽  
Vol 24 (03) ◽  
pp. 725-736 ◽  
Author(s):  
Arie Harel ◽  
Paul Zipkin
Keyword(s):  
Queueing Systems ◽  
Arrival Rate ◽  
Performance Measure ◽  
Service Rate ◽  
Service Time Distribution ◽  
Multiserver Queues ◽  
General Performance ◽  
Production Models ◽  
Convexity Properties ◽  
Special Case

This paper examines a general performance measure for queueing systems. This criterion reflects both the mean and the variance of sojourn times; the standard deviation is a special case. The measure plays a key role in certain production models, and it should be useful in a variety of other applications. We focus here on convexity properties of an approximation of the measure for the M/G/c queue. For c ≧ 2 we show that this quantity is convex in the arrival rate. Assuming the service rate acts as a scale factor in the service-time distribution, the measure is convex in the service rate also.

scholarly journals The Dependence of Airport Profit on Passenger Satisfaction and Operational Efficiency

2017 ◽  
Vol 5 (2) ◽  
pp. 11
Author(s):  
Roman Vokáč ◽  
Milan Lánský ◽  
Stanislav Szabo
Keyword(s):  
Cost Reduction ◽  
High Efficiency ◽  
Arrival Rate ◽  
Air Transport ◽  
Process Efficiency ◽  
Service Rate ◽  
Basic Process ◽  
Passenger Satisfaction ◽  
Key Factor

<p>Since the airports are in fact commercial companies, their main objective is to make profit. Therefore, it is important for the airports to identify the business activities that may increase the income as well as those that may reduce the costs. The terminal process, handling the passengers’ baggage both on their departure and arrival, is a basic process at all airports that are intended for the commercial air transport. The quality of the terminal process provided by the airports has a significant impact on the passengers especially in terms of their satisfaction. In this text, the passenger satisfaction is regarded as a key factor of the terminal process affecting a whole range of other areas. Its high efficiency leads to cost reduction from the perspective of the airport. As it is proposed here, there is a connection between the passenger satisfaction and the process efficiency. For example, the queues that form due to the check-in process may be a result of the imbalance between the passenger arrival rate and the service rate. Therefore, there is a necessity of improving not only the passenger satisfaction but also the process efficiency.</p>

scholarly journals Consensual Affine Transformations for Partial Valuation Aggregation

2019 ◽  
Vol 33 ◽  
pp. 2612-2619
Author(s):  
Hermann Schichl ◽  
Meinolf Sellmann
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Reliable Information ◽  
New Method ◽  
Global Information ◽  
Affine Transformations ◽  
Likelihood Estimator ◽  
Numerical Comparisons ◽  
Aggregation Methods

We consider the task of aggregating scores provided by experts that each have scored only a subset of all objects to be rated. Since experts only see a subset of all objects, they lack global information on the overall quality of all objects, as well as the global range in quality. Inherently, the only reliable information we get from experts is therefore the relative scores over the objects that they have scored each. We propose several variants of a new aggregation framework that takes this into account by computing consensual affine transformations of each expert’s scores to reach a globally balanced view. Numerical comparisons with other aggregation methods, such as rank-based methods, Kemeny-Young scoring, and a maximum likelihood estimator, show that the new method gives significantly better results in practice. Moreover, the computation is practically affordable and scales well even to larger numbers of experts and objects.

scholarly journals A pricing problem with unknown arrival rate and price sensitivity

2020 ◽  
Vol 92 (1) ◽  
pp. 77-106
Author(s):  
Athanassios N. Avramidis
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Demand Uncertainty ◽  
Inverse Function ◽  
Arrival Rate ◽  
System Size ◽  
Likelihood Estimator ◽  
Worst Case ◽  
Lipschitz Continuous ◽  
The One

Abstract We study a pricing problem with finite inventory and semi-parametric demand uncertainty. Demand is a price-dependent Poisson process whose mean is the product of buyers’ arrival rate, which is a constant $$\lambda $$ λ , and buyers’ purchase probability $$q(p)$$ q ( p ) , where p is the price. The seller observes arrivals and sales, and knows neither $$\lambda $$ λ nor $$q$$ q . Based on a non-parametric maximum-likelihood estimator of $$(\lambda ,q)$$ ( λ , q ) , we construct an estimator of mean demand and show that as the system size and number of prices grow, it is asymptotically more efficient than the maximum likelihood estimator based only on sale data. Based on this estimator, we develop a pricing algorithm paralleling (Besbes and Zeevi in Oper Res 57:1407–1420, 2009) and study its performance in an asymptotic regime similar to theirs: the initial inventory and the arrival rate grow proportionally to a scale parameter n. If $$q$$ q and its inverse function are Lipschitz continuous, then the worst-case regret is shown to be $$O((\log n / n)^{1/4})$$ O ( ( log n / n ) 1 / 4 ) . A second model considered is the one in Besbes and Zeevi (2009, Section 4.2), where no arrivals are involved; we modify their algorithm and improve the worst-case regret to $$O((\log n / n)^{1/4})$$ O ( ( log n / n ) 1 / 4 ) . In each setting, the regret order is the best known, and is obtained by refining their proof methods. We also prove an $$\Omega (n^{-1/2})$$ Ω ( n - 1 / 2 ) lower bound on the regret. Numerical comparisons to state-of-the-art alternatives indicate the effectiveness of our arrivals-based approach.

The convexity of a general performance measure for multiserver queues

1987 ◽  
Vol 24 (3) ◽  
pp. 725-736 ◽  
Author(s):  
Arie Harel ◽  
Paul Zipkin
Keyword(s):  
Queueing Systems ◽  
Arrival Rate ◽  
Performance Measure ◽  
Service Rate ◽  
Service Time Distribution ◽  
Multiserver Queues ◽  
General Performance ◽  
Production Models ◽  
Convexity Properties ◽  
Special Case

This paper examines a general performance measure for queueing systems. This criterion reflects both the mean and the variance of sojourn times; the standard deviation is a special case. The measure plays a key role in certain production models, and it should be useful in a variety of other applications.We focus here on convexity properties of an approximation of the measure for the M/G/c queue. For c ≧ 2 we show that this quantity is convex in the arrival rate. Assuming the service rate acts as a scale factor in the service-time distribution, the measure is convex in the service rate also.

Comparing Short-Memory Charts to Monitor the Traffic Intensity of Single Server Queues

2018 ◽  
Vol 33 (1) ◽  
pp. 1-21 ◽  
Author(s):  
Marta Santos ◽  
Manuel Cabral Morais ◽  
António Pacheco
Keyword(s):  
Quality Control ◽  
Control Charts ◽  
Queueing Systems ◽  
Arrival Rate ◽  
Service Rate ◽  
Single Server ◽  
Traffic Intensity ◽  
Statistical Process ◽  
Single Server Queues ◽  
Short Memory

Abstract This paper describes the application of simple quality control charts to monitor the traffic intensity of single server queues, a still uncommon use of what is arguably the most successful statistical process control tool. These charts play a vital role in the detection of increases in the traffic intensity of single server queueing systems such as the {M/G/1} , {GI/M/1} and {GI/G/1} queues. The corresponding control statistics refer solely to a customer-arrival/departure epoch as opposed to several such epochs, thus they are termed short-memory charts. We compare the RL performance of those charts under three out-of-control scenarios referring to increases in the traffic intensity due to: a decrease in the service rate while the arrival rate remains unchanged; an increase in the arrival rate while the service rate is constant; an increase in the arrival rate accompanied by a proportional decrease in the service rate. These comparisons refer to a broad set of interarrival and service time distributions, namely exponential, Erlang, hyper-exponential, and hypo-exponential. Extensive results and striking illustrations are provided to give the quality control practitioner an idea of how these charts perform in practice.

Large-sample confidence intervals of information-theoretic measures in linguistics

2020 ◽  
Vol 6 (1) ◽  
pp. 19-54
Author(s):  
Ryan Ka Yau Lai ◽  
Youngah Do
Keyword(s):  
Maximum Likelihood ◽  
Corpus Linguistics ◽  
Delta Method ◽  
Confidence Bounds ◽  
Likelihood Estimator ◽  
Information Theoretic ◽  
Leibler Divergence ◽  
Information Theoretic Measures ◽  
Data Points ◽  
Measure Of Uncertainty

This article explores a method of creating confidence bounds for information-theoretic measures in linguistics, such as entropy, Kullback-Leibler Divergence (KLD), and mutual information. We show that a useful measure of uncertainty can be derived from simple statistical principles, namely the asymptotic distribution of the maximum likelihood estimator (MLE) and the delta method. Three case studies from phonology and corpus linguistics are used to demonstrate how to apply it and examine its robustness against common violations of its assumptions in linguistics, such as insufficient sample size and non-independence of data points.

The Comparison Between the Bayes Estimator and the Maximum Likelihood Estimator of the Reliability Function for Negative Exponential Distribution

2018 ◽  
pp. 439
Author(s):  
Hazim Mansour Gorgees ◽  
Bushra Abdualrasool Ali ◽  
Raghad Ibrahim Kathum
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Exponential Distribution ◽  
Reliability Function ◽  
Bayes Estimator ◽  
Likelihood Estimator ◽  
Monte Carlo Simulation Technique ◽  
Negative Exponential Distribution ◽  
Negative Exponential ◽  
Better Than

     In this paper, the maximum likelihood estimator and the Bayes estimator of the reliability function for negative exponential distribution has been derived, then a Monte –Carlo simulation technique was employed to compare the performance of such estimators. The integral mean square error (IMSE) was used as a criterion for this comparison. The simulation results displayed that the Bayes estimator performed better than the maximum likelihood estimator for different samples sizes.

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