Analysis of buffer reservation holding times under a processor sharing queueing discipline and setup control

The authors model the buffer reservation (allocation) holding time as the sojourn time in an M/M/1/K processor sharing queue, where K corresponds to the limit on the number of active virtual circuits sharing a congested trunk´s bandwidth. They evaluate the exact results for the M/M/1/K processor sharing sojourn time distribution and show that it is of phase-type. Numerical results demonstrate the amount of smoothing induced by the limit K, as well as the robustness of the overload performance. For the case of general holding time distributions, in the absence of contention from other virtual circuits, i.e. the M/G/1/K processor sharing queue, the authors present an approximate method for evaluating the coefficient of variation of the sojourn time distribution, and compare these results with simulations