ML and Bayes estimation in a two-phase tandem queue with a second optional service and random feedback

Ghorbani-Mandolakani, Mehrzad; Rad, Mohammad Reza Salehi

doi:10.1080/03610926.2014.887107

Cited by 6 publications

(1 citation statement)

References 12 publications

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“…Ghorbani-Mandolakani and Salehi Rad [104]: Derives the ML and Bayes estimators of traffic intensity and asymptotic confidence intervals for mean system size of a two-phase tandem queueing model with a second optional service and random feedback and two heterogeneous servers. Morozov, Nekrasova, Peshkova, and Rumyantsev [195]: Develops a novel approach to confidence estimation of the stationary measures in high performance multi-server queueing systems.…”

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

Asanjarani,

Nazarathy,

Pollett

2017

Preprint

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Pricing Policy for Registration Service

Jin

Yue

2021

Resource Management and Performance Analysis of Wireless Communication Networks

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Equilibrium balking strategies in unobservable queues with multiple vacations and an optional service

Yang,

Dai,

2024

RAIRO-Oper. Res.

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This paper examines equilibrium mixed strategies in unobservable Markovian queues featuring a second optional service with server vacations, where arriving customers may choose to join or balk the system. All customers arriving at the system receive the essential service, and some customers opt for the second service after the first service has been completed. Once all customers in the system have been served, the server takes the first of multiple vacations. If no customers are waiting upon from the vacation, then the server takes another vacation. In unobservable queues, arriving customers cannot know the queue length; however, the information pertaining to the server state may be available. By examining unobservable queues (fully unobservable and almost unobservable cases), it is possible to formulate an equilibrium joining strategy as well as the socially optimal probability of joining a fully unobservable queue. This paper also presents numerical examples illustrating how system parameters affect mixed equilibrium and socially optimal balking strategies.

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ML and Bayes estimation in a two-phase tandem queue with a second optional service and random feedback

Cited by 6 publications

References 12 publications

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

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

Pricing Policy for Registration Service

Equilibrium balking strategies in unobservable queues with multiple vacations and an optional service

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