WCFS: a new framework for analyzing multiserver systems

Isaac Grosof, Mor Harchol-Balter, Alan Scheller-Wolf

Abstract: Multiserver queueing systems are found at the core of a wide variety of practical systems. Many important multiserver models have a previously-unexplained similarity: identical mean response time behavior is empirically observed in the heavy traffic limit. We explain this similarity for the first time. We do so by introducing the work-conserving finite-skip (WCFS) framework, which encompasses a broad class of important models. This class includes the heterogeneous M/G/k, the Limited Processor Sharing policy for the M/G/1, the Threshold Parallelism model and the Multiserver-Job model under a novel scheduling algorithm. We prove that for all WCFS models, scaled mean response time $$E[T](1-\rho )$$ E [ T ] ( 1 - ρ ) converges to the same value, $$E[S^2]/(2E[S])$$ E [ S 2 ] / ( 2 E [ S ] ) , in the heavy-traffic limit, which is also the heavy traffic limit for the M/G/1/FCFS. Moreover, we prove additively tight bounds on mean response time for the WCFS class, which hold for all load $$\rho $$ ρ . For each of the four models mentioned above, our bounds are the first known bounds on mean response time.