DARPA ULTRALOG Final Report - Industrial and Manufacturing ...

Manuscript for IEEE Transactions on Automatic Control 17
decentralization will give a byproduct, information security. As we discussed earlier our effort is
to support survivability. If information is revealed to others directly information security will be
in question. In this section we decentralize the programming model through an auction market.
7.1 Two-tier auction market
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 [27]. In this auction a seller may be able and willing
to adjust the supply as a function of bidding. In the programming model we have built, all
components are coupled with each other. However, the objective function and constraints are
separable 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 a seller
which determines T * based on the bids from the components. We call this auction market as
Two-tier Auctioning Model.
We define T i as available resource of component i which is required minimally to the amount
of T i(min) as in (12) and maximally T i(max) as in (13).
T
T
= [ R ( t ) L ( t ) f ( v )] / MRA ( t )
(12)
i (min) i +
i
i
i(min)
= [ R ( t ) L ( t ) f ( v )] / MRA ( t )
(13)
i (max) i +
i
Each component bids to the seller with maximal value as a function of T as in (14). The seller
decides T * based on the bids by considering CCT(T) as in (15). After the seller broadcasts T * ,
each component selects its optimal value mode in the limits T * as in (16). Though this auctioning
i
i(max)
i
i