Asymptotically optimal worksharing in HNOWs: how long is "sufficiently long?"

We proved in (Adler et al., 2002) that "FIFO" worksharing protocols provide asymptotically optimal solutions to the HNOW-Exploitation Problem. In this problem, one has a bag of tasks, and one seeks to accomplish as much work as possible on a heterogeneous network of workstations (HNOW) N during a prespecified fixed period. Our study proceeded within a model that characterizes N via parameters that measure workstations\´ computational and communication powers. A worksharing protocol observes a FIFO regimen if it has M\´s workstations finish their assigned work, and return their results, in the same order in which they are supplied with their work. The asymptotic optimality of FIFO protocols resides in their accomplishing at least as much work as any other protocol during sufficiently long worksharing periods. We perform a suite of simulation experiments that delimit the length of "sufficiently long." We show that, over a range of values of model parameters, the superiority of FIFO protocols is usually observed during quite short worksharing episodes, often in the range of a few minutes, and seldom more than a few hours.