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

As network speeds increase and the data traffic becomes more diverse, the need arises for service disciplines that offer fair treatment to diverse applications, while efficiently using resources at high speeds. Disciplines that approximate round-robin or processor-sharing service per channel are well suited for data networks because, over a wide range of time scales, they allocate bandwidth fairly among channels without needing to distinguish between different types of applications. This study is among the few to address head-of-line processor sharing. In most previous models of processor-sharing disciplines, the system immediately serves any arriving message at a rate depending only on the number of messages in the system regardless of how these messages are distributed among the channels. This model is commonly called pure processor sharing. In our model, the server completes the work from a given channel at a rate depending on the number of other channels with work in the system. That is, the service rate depends on how messages are distributed among the channels, and only indirectly on the total number of messages in the system. In this paper, we contrast the buffer requirements of shared and non-shared buffer schemes, when both types of schemes provide head-of-the-line processor-sharing service among channels. We formulate the problem as a system of functions representing the cumulative input and cumulative lost (potential) output to parts of the queueing system and model the vector of input functions as a multi-dimensional Brownian motion. The resulting heavy-traffic approximations predict much larger benefits from sharing buffers than those predicted by pure processor sharing.