On Exact Asymptotics for a Stationary Sojourn Time Distribution in a Tandem of Queues with Light-Tailed Service Times

We study the asymptotics of the stationary sojourn time $Z$ of a “typical customer” in a tandem of single-server queues. It is shown that in a certain “intermediate” region of light-tailed service time distributions, $Z$ may take a large value mostly due to a large value of a single service time of one of the customers. Arguments used in the paper also allow us to obtain an elementary proof of the logarithmic asymptotics for the tail distribution of the stationary sojourn time in the whole class of light-tailed distributions.