Fundamentals of queueing theory (2nd ed.).
Fundamentals of queueing theory (2nd ed.).
An analytic approach to a general class of G/G/s queueing systems
Operations Research
Transient and busy period analysis of the GI/G/1 queue: the method of stages
Queueing Systems: Theory and Applications
Wide area traffic: the failure of Poisson modeling
IEEE/ACM Transactions on Networking (TON)
Reparameterisation issues in mixture modelling and their bearing on MCMC algorithms
Computational Statistics & Data Analysis
Calculation of the Steady State Waiting Time Distribution in GI/PH/c and MAP/PH/c Queues
Queueing Systems: Theory and Applications
Bayesian analysis of M/Er/1 and M/H_k/1 queues
Queueing Systems: Theory and Applications
Prediction in Markovian bulk arrival queues
Queueing Systems: Theory and Applications
An EM-based technique for approximating long-tailed data sets with PH distributions
Performance Evaluation - Internet performance symposium (IPS 2002)
Computational Statistics & Data Analysis
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Bayesian inference for the transient behaviour and duration of a busy period in a single server queueing system with general, unknown distributions for the interarrival and service times is investigated. Both the interarrival and service time distributions are approximated using the dense family of Coxian distributions. A suitable reparameterization allows the definition of a non-informative prior, and Bayesian inference is then undertaken using reversible jump Markov chain Monte Carlo methods. An advantage of the proposed procedure is that heavy-tailed interarrival and service time distributions such as the Pareto can be well approximated. The proposed procedure for estimating the system measures is based on recent theoretical results for the Coxian/Coxian/1 system. A numerical technique is developed for every MCMC iteration so that the transient queue length and waiting time distributions and the duration of a busy period can be estimated. The approach is illustrated with both simulated and real data.