Bayesian inference for the transient behavior 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
