Abstract
Consider a single server queueing model which is observed over a continuous time interval (0,T], where T is determined by a suitable stopping rule. Let θ be the unknown parameter for the arrival process and hat {theta }_{T} be the maximum likelihood estimator of θ. The main goal of this paper is to obtain a moderate deviation result of the maximum likelihood estimator for the single server queueing model under certain regular conditions.
Highlights
Statistical analysis on queueing theory has come a long way in the past sixty years
Consider a single server queueing model which is observed over a continuous time interval
The problem of estimation of the unknown parameter using maximum likelihood estimation has been discussed in the literature over the last several years
Summary
Statistical analysis on queueing theory has come a long way in the past sixty years. A key component for the estimation of queueing parameter is maximum likelihood estimation. The first theoretical treatment of the estimation problem was given by Clarke (1957), who derived maximum likelihood estimates of arrival and service rates in an M/M/1 queueing system. Acharya and Singh (2019) studied the asymptotic properties of the maximum likelihood estimator from single server queues using the martingale technique. Singh and Acharya (2019) discussed the bound for the equivalence of the Bayes and maximum likelihood estimator and obtained the bound on the difference between the Bayes estimator from their true values of arrival and service rate parameter in an M/M/1 queue. Our main aim in this paper is to study the problem of moderate deviations for the maximum likelihood estimator for single server GI /G/1 queueing model.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
