Integral representations and asymptotics for infinite- and finite-capacity queues described by the unfinished work I

We continue our study of a finite-capacity queue with customer loss. We construct asymptotic expansions for the transient probability distribution of the unfinished work. It is assumed that the system's capacity of unfinished work is large. We consider all possible initial conditions and several cases of the model parameters. We also give asymptotic approximations for the rate at which customers are lost. The results are obtained by using integral representations and the saddle point method.