On Bayesian Inference for Markovian Queueing Models

Public Deposited
Resource Type
  • We are concerned with an M/M/- queueing model. Particularly, we focus on such models with join the shortest queue policy and N parallel queues. Assuming the steady-state case, a Bayesian paradigm is used in estimating the queueing system's parameters when full data or only queue lengths data are provided. We start with the case N=2 queues and found maximum likelihood estimators and Bayesian estimators for the system's parameters when full data about arrival times, departures times, and jobs' paths is provided. When only queue lengths data is provided, we estimate the traffic intensity of the JSQ-2 model using its asymptotic behaviour studied by Flatto [46]. Also, we provide Bayesian estimation for the traffic intensity using a new approximation to JSQ-2 queue length distribution. Indeed, a generalized bivariate geometric distribution (as proposed by [48]) is employed with an improper prior and a new proposed generalized bivariate beta distribution. When N is large enough, using the mean filed performance of the JSQ-N studied by Dawson et al. [47], we estimate the traffic intensity of JSQ-N model considering both maximum likelihood estimators and Bayesian estimators with different prior beliefs of the parameters. Numerical results are provided to show the accuracy of our estimators for JSQ-N for both cases N=2 and large enough N. Furthermore, we introduce a first study of privacy preserving analysis on a sensitive data released by a queueing model M/M/1. In fact, we propose, in the context of Differential Privacy [56], a Bayesian framework, inspired by [58], to generate private synthetic data, private service and arrival time rates from M/M/1 queueuing data. Keywords: Bayesian inference, Queueing models, Differential Privacy, Join the Shortest Queue (JSQ), Generalized bivariate beta distribution, Mean filed performance.

Thesis Degree Level
Thesis Degree Name
Thesis Degree Discipline
Rights Notes
  • Copyright © 2022 the author(s). Theses may be used for non-commercial research, educational, or related academic purposes only. Such uses include personal study, research, scholarship, and teaching. Theses may only be shared by linking to Carleton University Institutional Repository and no part may be used without proper attribution to the author. No part may be used for commercial purposes directly or indirectly via a for-profit platform; no adaptation or derivative works are permitted without consent from the copyright owner.
Date Created
  • 2022


In Collection: