Approximations to the moments of the sojourn time in a tandem queue with overtaking

The sojourn time in a tandem queue with exponential servers and a Poisson arrival process is considered. Overtaking is possible since the first node is processor-shared and the second node is first-come-first served. Asymptotic approximations are constructed for the first two moments of the sojourn time conditioned on the number in each node on arrival. The present approximations are shown to be in good agreement with simulated results.