On Bayesian inference for the M/G/1 queue with efficient MCMC sampling
نویسندگان
چکیده
We introduce an efficient MCMC sampling scheme to perform Bayesian inference in the M/G/1 queueing model given only observations of interdeparture times. Our MCMC scheme uses a combination of Gibbs sampling and simple Metropolis updates together with three novel “shift” and “scale” updates. We show that our novel updates improve the speed of sampling considerably, by factors of about 60 to about 180 on a variety of simulated data sets. This paper proposes a new approach to computation for Bayesian inference for the M/G/1 queue (Markovian arrival process/General service time distribution/1 server). Inference for this model using ABC (Approximate Bayesian Computation) was previously considered by Bonassi (2013), Fearnhead and Prangle (2012), and Blum and Francois (2010). ABC, in general, does not yield samples from the exact posterior distribution. We use the strategy of considering certain unobserved quantities as latent variables, allowing us to use Markov Chain Monte Carlo (MCMC), which converges to the exact posterior distribution.
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