DARPA ULTRALOG Final Report - Industrial and Manufacturing ...

Manuscript for IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS 14
distributing the computations and communications to multiple entities in the system. There are
two popular methods of decentralizing structured programming models: decomposition methods
and auction/bidding algorithms. Considering the compatible structure of the programming
model, we decentralize it through a non-iterative auction mechanism, so called multiple-unit
auction with variable supply [21]. In this auction a seller may be able and willing to adjust the
supply as a function of bidding.
4.1 Auction market design
In the programming model we have built, all nodes and components are coupled with each
other. However, it has a typical structure, where objective function and constraints are separable
to each node if one variable T is fixed. This characteristic makes it possible to solve the model
through an auctioning process for T. The completion time T is an unbounded resource and the
supply can be adjusted as a function of bidding.
To design the auction market we define two different types of participants in addition to the
components: Seller and Resource Manager. There is one seller in the system which determines
T * based on the bids from resource managers. A resource manager of each node manages the
resource of the node and arbitrates between its components and the seller.
We define T i as available resource of component i which is required minimally to the amount
of T i(min) as in (16) and maximally T i(max) as in (17).
T
T
= [ R ( t ) L ( t ) f ( v )]
(16)
i (min) i +
i
i
i(min)
= [ R ( t ) L ( t ) f ( v )]
(17)
i (max) i +
i
i
i(max)
A component i bids to its resource manager with maximal value as a function of T i as in (18).
The resource manager bids to the seller with maximal total value of its components as a function
of T based on the bids from its components as in (19). The seller decides T * based on the bids