Vol 40, No 1 (2016)

The problem of constructing a feasible preemptive multiprocessor schedule is considered for a case where directive intervals are assigned, processors can have arbitrary performance, and the amount of tasks depends linearly on the volume of additional resources allocated for them. In cases where a feasible schedule is not found with an allocated volume of additional resources, the problem of optimally correcting the directive intervals is considered. The solution is based on an analysis of the necessary and sufficient conditions of a feasible schedule’s existence.

Reaction–diffusion type replicator systems are investigated for the case of a bimatrix. An approach proposed earlier for formalizing and analyzing distributed replicator systems with one matrix is applied to asymmetric conflicts. A game theory interpretation of the problem is described and the relation between dynamic properties of systems and their game characteristics is determined. The stability of a spatially homogeneous solution for a distributed system is considered and a theorem on maintaining stability is proved. The results are illustrated with two-dimensional examples in the case of distribution.

A modification of the discrete multistage exchange trading model with risky securities is considered. At each stage of trading, the players place their integer bids. One of the players knows the real price, while the other knows only its probability distribution. The transaction price is defined as a convex combination of the proposed bids with some given coefficient. The solution to an infinitely long game is obtained.