  We consider the flow network model to solve the multiprocessor real-time task
scheduling problems. Using the flow network model or its generic form, linear
programming (LP) formulation, for the problems is not new. However, the
previous works have limitations, for example, that they are classified as
offline scheduling techniques since they establish a flow network model or an
LP problem considering a very long time interval. In this study, we propose how
to construct the flow network model for online scheduling periodic real-time
tasks on multiprocessors. Our key idea is to construct the flow network only
for the active instances of tasks at the current scheduling time, while
guaranteeing the existence of an optimal schedule for the future instances of
the tasks. The optimal scheduling is here defined to ensure that all real-time
tasks meet their deadlines when the total utilization demand of the given tasks
does not exceed the total processing capacity. We then propose the flow network
model-based polynomial-time scheduling algorithms. Advantageously, the flow
network model allows the task workload to be collected unfairly within a
certain time interval without losing the optimality. It thus leads us to
designing three unfair-but-optimal scheduling algorithms on both continuous and
discrete-time models. Especially, our unfair-but-optimal scheduling algorithm
on a discrete-time model is, to the best of our knowledge, the first in the
problem domain. We experimentally demonstrate that it significantly alleviates
the scheduling overheads, i.e., the reduced number of preemptions with the
comparable number of task migrations across processors.

Distributed, Parallel, and Cluster Computing