Heavy Traffic Analysis of the Sojourn Time in Tandem Queues with Overtaking.

We consider a tandem Jackson network with a processor-sharing (PS) node followed by either another PS node or a first in first out (FIFO) node. It is assumed that both nodes are in heavy traffic. We compute two-term asymptotic approximations to the distribution of the total sojourn (response) time through the two nodes. The second term in our approximation gives a quantitative measure of the effects of ``overtaking'', which occurs due to the presence of the PS node(s).