Sojourn time asymptotics in the M/G/1 processor sharing queue

We show for the M/G/1 processor sharing queue that the service time distrib ution is regularly varying of index -nu, nu non-integer, iff the sojourn ti me distribution is regularly varying of index -nu. This result is derived f rom a new expression for the Laplace-Stieltjes transform of the sojourn tim e distribution. That expression also leads to other new properties for the sojourn time distribution. We show how the moments of the sojourn time can be calculated recursively and prove that the kth moment of the sojourn time is finite iff the kth moment of the service time is finite. In addition, w e give a short proof of a heavy traffic theorem for the sojourn time distri bution, prove a heavy traffic theorem for the moments of the sojourn time, and study the properties of the heavy traffic limiting sojourn time distrib ution when the service time distribution is regularly varying. Explicit for mulas and multiterm expansions are provided for the case that the service t ime has a Pareto distribution.