Abstract
A tandem Jackson network with a processor-sharing (PS) node followed by either another PS node or a first-in first-out (FIFO) node is considered. It is assumed that both nodes are in heavy traffic. Three-term asymptotic approximations to the distribution of the total sojourn (response) time through the two nodes are computed. The leading term in the asymptotic approximation corresponds to the heavy traffic limit, in which the effects of “overtaking” disappear. The correction terms in the approximations give a quantitative measure of the erects of overtaking, which occurs due to the presence of the PS node(s).
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