Asymptotic expansions for large closed queueing networks with multiple job classes

A closed BCMP queuing network consisting of R job classes (chains), K+1 single-server, fixed-rate nodes, and M _j class j jobs (j=1, 2, . . ., R) is considered. Asymptotic expansions are constructed for the partition function under assumptions (1) K≫1, (2) M_j ≫1 for each j, and (3) K/M_j =O(1). Analytic expressions for performance measures such as the mean queue length are also given. The approach employs the ray method and the method of matched asymptotic expansions. Numerical comparisons illustrate the accuracy of the approximations