RISK MANAGEMENT IN MAQISTRAL GAS AND OIL PIPELINE SYSTEMS WITH POTENTIAL COST CONSTRAINTS

The problem of managing technical and technological risks in main gas and oil pipeline systems, subject to the possibility of limited funds allocated for the prevention and elimination of the consequences of accidents, is considered in the form of a semi-Markov decision-making model for a controlled Markov process in continuous time with the criterion of the maximum average discounted income. To find the optimal nonrandomized Markov stationary strategy, a procedure is proposed based on reducing the formulated fuzzy problem to an equivalent Boolean programming problem with deterministic constraints. To solve the resulting system of inequality constraints, an algorithm has been developed for finding basic solutions for an arbitrary number of accidents and measures to eliminate them. The numerical implementation of the proposed approach is implemented for the real problem of risk management in the main gas pipeline with unclear cost constraints. Keywords: semi-Markov decision-making process, Markov stationary strategy, feasibility optimization, basic solutions to inequalities.

Discrete stop-or-go games

Dubins and Savage (How to gamble if you must: inequalities for stochastic processes, McGraw-Hill, New York, 1965) found an optimal strategy for limsup gambling problems in which a player has at most two choices at every state x at most one of which could differ from the point mass $$\delta (x)$$ δ ( x ) . Their result is extended here to a family of two-person, zero-sum stochastic games in which each player is similarly restricted. For these games we show that player 1 always has a pure optimal stationary strategy and that player 2 has a pure $$\epsilon $$ ϵ -optimal stationary strategy for every $$\epsilon > 0$$ ϵ > 0 . However, player 2 has no optimal strategy in general. A generalization to n-person games is formulated and $$\epsilon $$ ϵ -equilibria are constructed.

Linear Programming and Zero-Sum Two-Person Undiscounted Semi-Markov Games

In this paper, zero-sum two-person finite undiscounted (limiting average) semi-Markov games (SMGs) are considered. We prove that the solutions of the game when both players are restricted to semi-Markov strategies are solutions for the original game. In addition, we show that if one player fixes a stationary strategy, then the other player can restrict himself in solving an undiscounted semi-Markov decision process associated with that stationary strategy. The undiscounted SMGs are also studied when the transition probabilities and the transition times are controlled by a fixed player in all states. If such games are unichain, we prove that the value and optimal stationary strategies of the players can be obtained from an optimal solution of a linear programming algorithm. We propose a realistic and generalized traveling inspection model that suitably fits into the class of one player control undiscounted unichain semi-Markov games.

Borel and Hausdorff hierarchies in topological spaces of Choquet games and their effectivization

What parts of the classical descriptive set theory done in Polish spaces still hold for more general topological spaces, possibly T0 or T1, but not T2 (i.e. not Hausdorff)? This question has been addressed by Selivanov in a series of papers centred on algebraic domains. And recently it has been considered by de Brecht for quasi-Polish spaces, a framework that contains both countably based continuous domains and Polish spaces. In this paper, we present alternative unifying topological spaces, that we call approximation spaces. They are exactly the spaces for which player Nonempty has a stationary strategy in the Choquet game. A natural proper subclass of approximation spaces coincides with the class of quasi-Polish spaces. We study the Borel and Hausdorff difference hierarchies in approximation spaces, revisiting the work done for the other topological spaces. We also consider the problem of effectivization of these results.

Two-person red-and-black stochastic games

We define a leavable stochastic game which is a possible two-person generalization of the classical red-and-black gambling problem. We show that there are three basic possibilities for a two-person red-and-black game which, by analogy with gambling theory, we call the subfair, the fair and the superfair cases. A suitable generalization of what in gambling theory is called bold play is proved to be a uniformly ε-optimal stationary strategy for player I in the fair and the subfair cases whereas a generalization of timid play is shown to be ε-optimal for player I in the superfair possibility.

Two-person red-and-black stochastic games

We define a leavable stochastic game which is a possible two-person generalization of the classical red-and-black gambling problem. We show that there are three basic possibilities for a two-person red-and-black game which, by analogy with gambling theory, we call the subfair, the fair and the superfair cases. A suitable generalization of what in gambling theory is called bold play is proved to be a uniformly ε-optimal stationary strategy for player I in the fair and the subfair cases whereas a generalization of timid play is shown to be ε-optimal for player I in the superfair possibility.