Bayesian Inference and Prediction in an M/G/1 with Optional Second Service

Mohammadi, Abdolreza; Salehi-Rad, M. R.

doi:10.1080/03610918.2011.588358

Cited by 8 publications

(6 citation statements)

References 16 publications

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“…Despite its breadth of almost 300 publications from 1955, only two articles have been identified as being applied to healthcare: [24,48]. Both works are concerned with customers who can re-enter services during their time in the queuing system, which is mainly of value when considering the effect of unpredictable behaviour in intensive care units, for instance.…”

Section: Handling Incomplete Queue Datamentioning

confidence: 99%

“…Both works are concerned with customers who can re-enter services during their time in the queuing system, which is mainly of value when considering the effect of unpredictable behaviour in intensive care units, for instance. [24] seeks to approximate service and re-service densities through a Bayesian approach and by filtering out those customers seeking to be serviced again. On the other hand, [48] considers an extension to the M/M/c queue with direct re-entries.…”

Section: Handling Incomplete Queue Datamentioning

confidence: 99%

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Segmentation analysis and the recovery of queuing parameters via the Wasserstein distance: a study of administrative data for patients with chronic obstructive pulmonary disease

Wilde,

Knight,

Gillard

et al. 2020

Preprint

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This work uses a data-driven approach to analyse how the resource requirements of patients with chronic obstructive pulmonary disease (COPD) may change, quantifying how those changes impact the hospital system with which the patients interact. This approach is composed of a novel combination of often distinct modes of analysis: segmentation, operational queuing theory, and the recovery of parameters from incomplete data. By combining these methods as presented here, this work demonstrates that potential limitations around the availability of fine-grained data can be overcome. Thus, finding useful operational results despite using only administrative data.The paper begins by finding a useful clustering of the population from this granular data that feeds into a multi-class M/M/c model, whose parameters are recovered from the data via parameterisation and the Wasserstein distance. This model is then used to conduct an informative analysis of the underlying queuing system and the needs of the population under study through several what-if scenarios.The analyses used to form and study this model consider, in effect, all types of patient arrivals and how those types impact the system. With that, this study finds that there are no quick solutions to reduce the impact of COPD patients on the system, including adding capacity to the system. In this analysis, the only effective intervention to reduce the strain caused by those presenting with COPD is to enact external policies which directly improve the overall health of the COPD population before they arrive at the hospital.

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Section: Handling Incomplete Queue Datamentioning

confidence: 99%

Section: Handling Incomplete Queue Datamentioning

confidence: 99%

Segmentation analysis and the recovery of queuing parameters via the Wasserstein distance: a study of administrative data for patients with chronic obstructive pulmonary disease

Wilde,

Knight,

Gillard

et al. 2020

Preprint

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“…M/G/∞ (Random translation models in general) [32] [193] [55] [109] M/GI/1 [1] E k /G/1 [95] M/G/c [76] Harris [124]: An overview paper presented the statistical analysis of queueing systems with emphasis on the estimation of input and service parameters and/or distributions.…”

Section: Classification By Modelmentioning

confidence: 99%

Parameter and State Estimation in Queues and Related Stochastic Models: A Bibliography

Asanjarani,

Nazarathy,

Pollett

2017

Preprint

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This is an annotated bibliography on estimation and inference results for queues and related stochastic models. The purpose of this document is to collect and categorise works in the field, allowing for researchers and practitioners to explore the various types of results that exist.This bibliography attempts to include all known works that satisfy both of these requirements:• Works that deal with queueing models.• Works that contain contributions related to methodology of parameter estimation, state estimation, hypothesis testing, confidence interval and/or actual data-sets of application areas.Our attempt is to make this bibliography exhaustive, yet there are possibly some papers that we have missed. As it is updated continuously, additions and comments are welcomed.The sections below categorise the works based on several categories. A single paper may appear in several categories simultaneously. The final section lists all works in chronological order along with short descriptions of the contributions.This bibliography is maintained at http://www.maths.uq.edu.au/˜pkp/papers/Qest/Qest.html and may be cited as such. We welcome additions and corrections.There are additional works not mentioned in this bibliography that are mildly related. This includes methods for parameter estimation of point processes, methods for parameter estimation of stochastic matrix analytic models as well as inference, estimation and tomography of communication networks not directly modelled as queueing networks.6 Chronological order with brief descriptions 1955 Cox [70]: An overview paper of queueing theory outlining the philosophy of estimating parameters of input processes vs. performance processes. 1957 Benes [32]: Transient M/M/∞ full observation over a fixed interval. Clarke [64]: M/M/1 MLE with full observation. The first paper. Sampling until "busy time" reaches a pre-assigned value yields closed form MLEs. 1961 Billingsley [39]: Book on inference of Markov chains. 1965 Cox [71]: An overview paper on parameter estimation, separate analysis of input and service mechanism and problems connected with the sampling of queueing process. Kovalenko [167]: Wolff [264]: Large sample theory for birth-death queues. 1966 Lilliefors [173]: Confidence intervals for standard performance measurements based on parameter error. 1967 Greenberg [114]: Different ways of determining for how long to observe a stationary M/M/1 queue (e.g. fixed number of arrivals, fixed total observation time, etc... 1968 Daley [73]: The serial correlation coefficients of queue sizes in a stationary GI/M/1 queue are studied. Daley [74]: The serial correlation coefficients of a (stationary) sequence of waiting times in a stationary M/M/1, M/G/1 and GI/G/l queueing system are studied. 1970 Brown [46]: Estimating the G in M/G/∞ with arrival and departure times without known what customers they related to. Ross [226]: Discusses identifying the distributions of GI/G/k uniquely based on observation of the queueing process. 1971 Pakes [205]: The serial correlation coefficients ...

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“…For a detailed appraisal of classical techniques for estimation and applications of mixture distributions, we refer to studies by Sultan et al [7], Abu-Zinadah [8], and Kamaruzzaman et al [9] among others. On the other hand, the estimation of parameters in Bayesian framework for a mixture of two distributions has been considered by many researchers [10][11][12][13][14][15][16][17][18][19][20][21]. Contrary to the two-component mixture modeling, some authors have discussed situations where data are assumed to follow a three-component mixture of suitable probability distributions [22][23][24][25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

On Estimation of Three-Component Mixture of Distributions via Bayesian and Classical Approaches

Tahir

Almanjahie

Abid

et al. 2021

Mathematical Problems in Engineering

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In this study, we model a heterogeneous population assuming the three-component mixture of the Pareto distributions assuming type I censored data. In particular, we study some statistical properties (such as various entropies, different inequality indices, and order statistics) of the three-component mixture distribution. The ML estimation and the Bayesian estimation of the mixture parameters have been performed in this study. For the ML estimation, we used the Newton Raphson method. To derive the posterior distributions, different noninformative priors are assumed to derive the Bayes estimators. Furthermore, we also discussed the Bayesian predictive intervals. We presented a detailed simulation study to compare the ML estimates and Bayes estimates. Moreover, we evaluated the performance of different estimates assuming various sample sizes, mixing weights and test termination times (a fixed point of time after which all other tests are dismissed). The real-life data application is also a part of this study.

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Bayesian Inference and Prediction in an M/G/1 with Optional Second Service

Cited by 8 publications

References 16 publications

Segmentation analysis and the recovery of queuing parameters via the Wasserstein distance: a study of administrative data for patients with chronic obstructive pulmonary disease

Segmentation analysis and the recovery of queuing parameters via the Wasserstein distance: a study of administrative data for patients with chronic obstructive pulmonary disease

Parameter and State Estimation in Queues and Related Stochastic Models: A Bibliography

On Estimation of Three-Component Mixture of Distributions via Bayesian and Classical Approaches

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