A heavy-traffic comparison of shared and segregated buffer schemes for queues with the head-of-line processing-sharing discipline

In the head-of-line processor sharing discipline, the server completes the work from a given channel at a rate depending only on the number of other channels with work in the system. The authors compare the buffer requirements of shared and nonshared buffer schemes, when both schemes provide head-of-the-line processor sharing service among channels. Modeling the two schemes as Brownian flow systems, they derive heavy-traffic approximations predicting large benefits from sharing buffers. This contrasts with previous, analogous results predicting much smaller benefits from sharing buffers under more commonly studied processor-sharing disciplines that give each message in the system an equal processing rate regardless of the number of other messages in the system from the same channel