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.

Matrix-analytic methods, tandem queues, batch arrival, queue length approximations, asymptotic error bound, large deviations theory, renewal theory, extreme value analysis
International Conference on Matrix-Analytic Methods in Stochastic Models

Vatamidou, E, Adan, I.J.B.F, Vlasiou, M, & Zwart, A.P. (2016). Asymptotic error bounds for truncated buffer approximations of a 2-node tandem queue. In Proceedings of the Ninth International Conference on Matrix-Analytic Methods in Stochastic Models..