Bayesian Service Demand Estimation with Gibbs Sampling

Performance modelling of web applications involves the task of estimating service demands of requests at physical resources, such as CPUs. In this paper, we propose a service demand estimation algorithm based on a Markov Chain Monte Carlo (MCMC) technique, Gibbs sampling. Our methodology is widely applicable as it requires only queue length samples at each resource, which are simple to measure. Additionally, since we use a Bayesian approach, our method can use prior information on the distribution of parameters, a feature not available with existing demand estimation approaches. The main challenge of Gibbs sampling is to efficiently evaluate the conditional expression required to sample from the posterior distribution of the demands. This expression is shown to be the equilibrium solution of a multiclass closed queueing network. We define a novel approximation to efficiently obtain the normalising constant to make the cost of its evaluation acceptable for MCMC applications. Experimental evaluation based on simulation data with different model sizes demonstrates the effectiveness of Gibbs sampling for service demand estimation.