DARPA ULTRALOG Final Report - Industrial and Manufacturing ...

Manuscript for IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS 7
system performance can depend on its resource allocation to these two components. There are
several CPU scheduling algorithms for allocating a CPU resource amongst multiple threads.
Among the scheduling algorithms, proportional CPU share (PS) scheduling is known for its
simplicity, flexibility, and fairness [14]. In PS scheduling threads are assigned weights and
resource shares are determined proportional to the weights [15]. Excess CPU time from some
threads is allocated fairly to other threads. There are many PS scheduling algorithms such as
Weighted Round-Robin scheduling, Lottery scheduling, and Stride scheduling [16]-[18]. We
adopt PS scheduling as resource allocation scheme because of its generality in addition to the
benefits mentioned above. We define resource allocation variable set w = {w i (t): i∈A, t≥0} in
which w i (t) is a non-negative weight of component i at time t. If total managed weight of a node
n is ω n , the boundary condition for assigning weights over time can be described as:
∑
i∈K
n
wi
( t)
= ωn
where wi
( t)
≥ 0 . (1)
2.3 Problem definition
The service provided by the network is to produce a global solution to a given problem, which
is an aggregate of partial solutions of individual tasks. QoS of the network is determined by the
value of global solution and the cost of completion time. The value of global solution is the
summation of partial solution values, and the cost of completion time is determined by a cost
function CCT(T) which is a monotonically increasing function with completion time T. We
assume that the solution values and cost are represented in a common unit 2 . Consider v d i as the
value mode used to process d th task by component i and e i the number of tasks processed by
component i to the completion. Then, the control objective is to maximize QoS by utilizing
2 Relative importance can be considered by scaling the functions and it results in the same function structures.