Novel Methods for Divisible Load Distribution with Start-Up Costs on a Complete b-Ary Tree

This work investigates divisible load distribution using multi-installment processing on complete
b
-ary tree networks. Classic methods of distributing a divisible load divide the computation and communication processes into multiple time intervals in a pipelined fashion. The algorithm
$\mathbb {M}$
(
m
ulti-installment) herein uses multi-installment processing with pipelined communication to reduce the initial distribution time and to improve the performance. Closed-form expressions for the parallel processing time and speed-up are derived. This work reveals that the asymptotic speed-up of the proposed algorithm is
$b\beta +1$
where
$\beta$
is the computation-to-communication ratio of a node in the system. Algorithm
$\mathbb {M}$
outperforms the classic algorithm in all cases. The algorithm
$\mathbb {S}$
(
s
tart-up cost) that is developed herein includes the computation and communication start-up costs. Finally, two algorithms
$\mathbb {M}$
and
$\mathbb {S}$
are combined to form algorithm
$\mathbb {MS}$
with even better performance than each.