Another approach to asymptotic expansions for large closed queueing networks

The paper considers the same closed Jackson network as in Knessl and Tier. It consists of a large number of customers, a single infinite server queue and a large number of single server queues with constant service rates. Asymptotic expansions for the normalization constant (partition function) are derived by the saddle point method from its integral representation in the complex space. In contrast with Knessl and Tier such an approach provides a rigorous and simple derivation for the dominant term.