The network for routing the query is based on Markov process. If we want to model the time taken to answer a query , is Probabilistic timed automaton a better model?
A stochastic queue would be indicated. Look up queueing theory. Start here: "http://en.wikipedia.org/wiki/Queueing_theory". If you wanted to use a number of probabilistic timed automatons, you would then have the complexity of having to build in the appropriate statistical properties.