Optimal estimation of the states of modulated semi-synchronous integrated flow of events in condition of its incomplete observability

Bakholdina, Maria A.; Горцев, A. M.

doi:10.12988/ams.2015.5135

Cited by 7 publications

(1 citation statement)

References 21 publications

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“…Bakholdina1 and Gortsev [24]: Focused on the problem of optimal estimation of the states of the modulated semi-synchronous integrated flow of events. Burkatovskaya, Kabanova, and Vorobeychikov [251]: CUSUM algorithms for parameter estimation in queueing systems where the arrival process is an Markov-modulated Poisson process.…”

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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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