  Scheduling is an important task allowing parallel systems to perform
efficiently and reliably. For modern computation systems, divisible load is a
special type of data which can be divided into arbitrary sizes and
independently processed in parallel. Such loads are commonly encountered in
applications which are processing a great amount of similar data units. For a
multi-task processor, the processor's speed may be time-varying due to the
arrival and departure of other background jobs. This paper studies an optimal
divisible loads scheduling problem on a single level tree network, whose
processing speeds and channel speeds are time-varying. Two recursive algorithms
are provided to solve this problem when the arrival and departure times of the
background jobs are known a priori and an iterative algorithm is provided to
solve the case where such times are not known. Numerical tests and evaluations
are performed for these three algorithms under different numbers of background
jobs and processors.
