Maximum likelihood estimates in an M/M/c queue with heterogeneous servers

Acharya, Sarat Kumar; Rodríguez-Sánchez, Sara V.; Villarreal-Rodríguez, César Emilio

doi:10.1504/ijmor.2013.054735

Cited by 4 publications

(2 citation statements)

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“…이러한 제약 극복을 위해 Larson의 대기행 렬 추론 엔진(QIE, queue inference engine) [4][5][6] 을 필두로 다양한 대기행렬 추론 방법이 대안으로 제안되었다. Baccelli et al [2] 은 기존에 연구되었던 대부분의 추론연 구들을 통합하여 발표하였으며 최근에는 베이시안 추론 (Bayesian inference) 방법 [10,11] 과 최대공산(maximum likelihood) [1] 을 이용한 방법도 연구된 바 있다. 그러나 이 러한 방법들은 대부분 분포적 특성을 가정한 모수적 접 근 방법(parametric approach)들이다.…”

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An Inference Method of a Multi-server Queue using Arrival and Departure Times

Park¹

2016

Journal of the Korea Society for Simulation

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This paper presents inference methods for inner operations of a multi-server queue when historical data are limited or system observation is restricted. In a queueing system analysis, autocorrelated arrival and service processes increase the complexity of modeling. Accordingly, numerous analysis methods have been developed. In this paper, we introduce an inference method for specific situations when external observations exhibit autocorrelated structure and and observations of internal operations are difficult. We release an assumption of the previous method and provide lemma and theorem to guarantee the correctness of our proposed inference method. Using only external observations, our proposed method deduces the internal operation of a multi-server queue via non-parametric approach even when the service times are autocorrelated. The main internal inference measures are waiting times and service times of respective customers. We provide some numerical results to verify that our method performs as intended.

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An Inference Method of a Multi-server Queue using Arrival and Departure Times

Park¹

2016

Journal of the Korea Society for Simulation

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“…Acharya, Rodrguez-Snchez and Villarreal-Rodrguez [2]: Presents the derivation of maximum likelihood estimates for the arrival rate and service rates in a stationary M/M/c queue with heterogeneous servers.…”

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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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Inference of a Multi-server Queue Using External Observations

Park,

Kim

2024

Communications in Computer and Information Science

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Maximum likelihood estimates in an M/M/c queue with heterogeneous servers

Cited by 4 publications

References 29 publications

An Inference Method of a Multi-server Queue using Arrival and Departure Times

An Inference Method of a Multi-server Queue using Arrival and Departure Times

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

Inference of a Multi-server Queue Using External Observations

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