Auxiliary variables for Bayesian inference in multi-class queueing networks

Queueing networks describe complex stochastic systems of both theoretical and practical interest. They provide the means to assess alterations, diagnose poor performance and evaluate robustness across sets of interconnected resources. In the present paper, we focus on the underlying continuous-time Markov chains induced by these networks, and we present a flexible method for drawing parameter inference in multi-class Markovian cases with switching and different service disciplines. The approach is directed towards the inferential problem with missing data, where transition paths of individual tasks among the queues are often unknown. The paper introduces a slice sampling technique with mappings to the measurable space of task transitions between the service stations. This can address time and tractability issues in computational procedures, handle prior system knowledge and overcome common restrictions on service rates across existing inferential frameworks. Finally, the proposed algorithm is validated on synthetic data and applied to a real data set, obtained from a service delivery tasking tool implemented in two university hospitals.