Asymptotic analysis and simple approximation of the loss probability of the GIX/M/c/K queue

We consider the GIX/M/c/K queues with partial rejection or total rejection, and find an asymptotic behavior of loss probability of the GIX/M/c/K queue as K tends to infinity. The asymptotic loss probability is expressed only in terms of the roots of the characteristic equation and the boundary probabilities of the corresponding GIX/M/c queue. Numerical examples show that the asymptotic loss probability is a quite accurate approximation for the loss probability of the GIX/M/c/K queue even when the system capacity K is moderate.