Asymptotic error bounds for truncated buffer approximations of a 2-node tandem queue.

We consider the queue lengths of a tandem queueing network. The number of customers in the system can be modelled as QBD with a doubly-innite state-space. Due to the innite phase-space, this system does not have a product-form solution. A natural approach to nd a numerical solution with the aid of matrix analytic methods is by truncating the phase-space; however, this approach imposes approximation errors. The goal of this paper is to study these approximation errors mathematically, using large deviations and extreme value theory. We obtain a simple asymptotic error bound for the approximations that depends on the truncation level. We test the accuracy of our bound numerically.