SOJOURN TIME TAILS IN THE M/D/1 PROCESSOR SHARING QUEUE

We consider the sojourn time V in the M/D/1 processor sharing (PS) queue and show that P(V > x) is of the form Ce−gx as x becomes large. The proof involves a geometric random sum representation of V and a connection with Yule processes, which also enables us to simplify Ott's [21] derivation of the Laplace transform of V. Numerical experiments show that the approximation P(V > x) ≈ Ce−gx is excellent even for moderate values of x.

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