Bayesian estimation of traffic intensity based on queue length in a multi-server M/M/s queue

Cruz, Frederico R. B.; Quinino, Roberto da Costa; Ho, Linda Lee

doi:10.1080/03610918.2016.1236953

Cited by 34 publications

(15 citation statements)

References 2 publications

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“…[4][5][6] In general, basic queueing models are applied as approximations for complex computer and telecommunication networks, 7,8 manufacturing and service systems, [9][10][11][12] and, more recently, health care systems, [13][14][15] among others. [4][5][6] In general, basic queueing models are applied as approximations for complex computer and telecommunication networks, 7,8 manufacturing and service systems, [9][10][11][12] and, more recently, health care systems, [13][14][15] among others.…”

Section: Introductionmentioning

confidence: 99%

“…[4][5][6] In general, basic queueing models are applied as approximations for complex computer and telecommunication networks, 7,8 manufacturing and service systems, [9][10][11][12] and, more recently, health care systems, [13][14][15] among others. 9 Queueing models in general and M∕M∕s queues in particular are especially useful when predicting performance measures from the systems they model, such as the empty system probability (P 0 ), expected number of customers in the systems (L), expected number of customers in the queue (L q ), expected time in the system (W), and expected time in the queue (W q ). Despite their simplicity, these models may find application in real-life systems.…”

Section: Introductionmentioning

confidence: 99%

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Control charts for traffic intensity monitoring of Markovian multiserver queues

Cruz

Quinino

2019

Quality & Reliability Eng

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A number of recent research studies have applied queueing theory as an approximate modeling tool to mathematically describe industrial systems, which include manufacturing, distribution, and service, for instance. Among the main observable characteristics in queues, the number of users in the system can be controlled to keep waiting times as minimal as possible. The design of efficient control charts is an attempt to monitor and control such systems. Control charts are proposed to monitor infinite queues with Markovian arrivals, exponential service times, and s identical parallel servers. The proposed charts monitor traffic intensities, which are the ratio between the arrival rate and the service rate, estimated through the number of users in the queueing system at random epochs. The effectiveness and efficiency of the proposed approaches in terms of the average run lengths are established by a comprehensive set of Monte Carlo simulations. KEYWORDS attribute control charts, average run length, Markovian queues, quality control wileyonlinelibrary.com/journal/qre [Colour figure can be viewed at wileyonlinelibrary.com] [Colour figure can be viewed at wileyonlinelibrary.com] Frederico R. B. Cruz holds a bachelor's degree in electrical engineering (1988) as well as a master's degree (1991) and a doctorate (1997) in computer science from the Universidade Federal de Minas Gerais, where he is a full professor in the Department of Statistics and conducts research in operations research.Roberto C. Quinino has a PhD in production engineering from the Universidade de São Paulo (1998). He is currently a full professor at the Universidade Federal de Minas Gerais. He develops research on quality control and marketing engineering with an emphasis on stochastic modeling applications acting on the following subjects: Taguchi online, Markov chains, misclassification, optimization, control chart planning, regression analysis, planning of experiments, and conjoint analysis. He supervises undergraduate, specialization, master's, and doctoral students. He has published papers in several international journals.

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Section: Introductionmentioning

confidence: 99%

“…[4][5][6] In general, basic queueing models are applied as approximations for complex computer and telecommunication networks, 7,8 manufacturing and service systems, [9][10][11][12] and, more recently, health care systems, [13][14][15] among others. 9 Queueing models in general and M∕M∕s queues in particular are especially useful when predicting performance measures from the systems they model, such as the empty system probability (P 0 ), expected number of customers in the systems (L), expected number of customers in the queue (L q ), expected time in the system (W), and expected time in the queue (W q ). Despite their simplicity, these models may find application in real-life systems.…”

Section: Introductionmentioning

confidence: 99%

Control charts for traffic intensity monitoring of Markovian multiserver queues

Cruz

Quinino

2019

Quality & Reliability Eng

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“…To better illustrate an application of the method, a numerical application based on the data considered in Table 7, collected in a large supermarket network Table 6: Average length (L) and coverage (C) of 95% confidence intervals for and = 20. in a region of interest [12], is provided. The goal is to evaluate traffic intensity, which, for managerial reasons, should not exceed 87%; if it does, users may leave.…”

Section: Numerical Examplementioning

confidence: 99%

“…Therefore, the inference process for estimating starts with (2) and assumes an a priori beta distribution, that is, ( ) ∼ Beta( , ), which has been successfully used in inference in other Markovian queues [12,13] and results in the following a posteriori distribution:…”

Section: Betamentioning

confidence: 99%

“…It is impossible to discuss inference in queues without mentioning the pioneering work of Clarke in the 1950s, who describes maximum likelihood estimators for the arrival rates and service times in simple queues, and the work of Schruben and Kulkarni in the 1980s, who consider the problem of bias in queue estimation. It is also important to mention the Bayesian papers on the subject, including that of Muddapur in the 1970s, who published one of the first results that extended Clark's methodology, the series of papers from Armero and Bayarri [3,4], Armero and Conesa [5][6][7][8], Choudhury and Borthakur [9], and, more recently, Chowdhury and Mukherjee [10,11], Cruz et al [12], and Quinino and Cruz [13]. These are only a few examples of the papers in this important research area.…”

Section: Introductionmentioning

confidence: 99%

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Traffic Intensity Estimation in Finite Markovian Queueing Systems

Cruz

Almeida

D’Angelo

et al. 2018

Mathematical Problems in Engineering

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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 ( ), 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 for single-server finite Markovian queues or, in Kendall notation, / /1/ 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.

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