Asymptotic behaviour of the tandem queueing system with identical service times at both queues

Consider a tandem queue consisting of two single-server queues in series, w ith a Poisson arrival process at the first queue and arbitrarily distribute d service times, which for any customer are identical in both queues. For t his tandem queue, we relate the tail behaviour of the sojourn time distribu tion and the workload distribution at the second queue to that of the (resi dual) service time distribution. As a by-result, we prove that both the soj ourn time distribution and the workload distribution at the second queue ar e regularly varying at infinity of index 1 - nu, if the service time distri bution is regularly varying at infinity of index -nu (nu > 1). Furthermore, in the latter case we derive a heavy-traffic limit theorem for the sojourn time S-(2) at the second queue when the traffic load rho up arrow 1. It st ates that, for a particular contraction factor Delta(rho), the contracted s ojourn time Delta(rho )S-(2) converges in distribution to the limit distrib ution H((.)) as rho up arrow 1 where H(w) = exp{-w(1-nu)}/1+nuw(1-nu).