### Article

## Algorithms for locomotives maintenance schedule

This paper is devoted to the problem of scheduling maintenance of locomotives in a depot. The problem based on the operation Eastern polygon of Russian Railways. A heuristic algorithm and a constraint programming model are presented. Numerical experiments on real data for real depot configurations were carried out to compare the performance of the heuristic algorithm and constraint programming model solved with IBM ILOG CPLEX Optimizer.

In this paper presented slot selection algorithms in economic model for independent job batch scheduling in a distributed computing with non-dedicated resources. Exiting approaches towards resource co-allocation and multiprocessor job scheduling in economic models of distributed computing are based on search of time-slots in resource occupancy schedules. The sought time-slots must match requirements of necessary span, computational resource properties, and cost. Usually such scheduling methods consider only one suited variant of time-slot set. This paper discloses a scheduling scheme that features multi-variant search. Two algorithms of linear complexity for search of alternative variants are compared. Having several optional resource configurations for each job makes an opportunity to perform an optimization of execution of the whole bath of jobs and to increase overall efficiency of scheduling.

This is the first book on the U.S. presidential election system to analyze the basic principles underlying the design of the existing system and those at the heart of competing proposals for improving the system. The book discusses how the use of some election rules embedded in the U.S. Constitution and in the Presidential Succession Act may cause skewed or weird election outcomes and election stalemates. The book argues that the act may not cover some rare though possible situations which the Twentieth Amendment authorizes Congress to address. Also, the book questions the constitutionality of the National Popular Vote Plan to introduce a direct popular presidential election de facto, without amending the Constitution, and addresses the plan’s “Achilles’ Heel.” In particular, the book shows that the plan may violate the Equal Protection Clause from the Fourteenth Amendment of the Constitution. Numerical examples are provided to show that the counterintuitive claims of the NPV originators and proponents that the plan will encourage presidential candidates to “chase” every vote in every state do not have any grounds. Finally, the book proposes a plan for improving the election system by combining at the national level the “one state, one vote” principle – embedded in the Constitution – and the “one person, one vote” principle. Under this plan no state loses its current Electoral College benefits while all the states gain more attention of presidential candidates.

The article outlines new contracts, regulating social relations on railway transport in the light of the current structural reform of this mode of transport. The aim of this reform is to provide a smooth economically sound transition of the natural monopolist - the railway service - to the market economy environment. However, the implementation of the reform has been downplayed. This can be explained by the fact that Russian Railways (RZD) have been maintaining their functions as the carrier while simultaneously handling the infrastructure facilities as the proprietor of both the infrastructure per se and the rolling stock. In the current laws these functions are to be executed by different subjects on a contractual basis, what has been shown in the paper. New contracts mentioned in the article must get legal framework in relation to other modes of transport.

This chapter describes an economic model for independent job flow management in distributed computing environments with non-dedicated resources. The model is based on the concept of fair resource distribution between users and owners of computational nodes by means of economic mechanisms in a virtual organization. Scheduling is performed in cycles in accordance with dynamically updated schedules on local processor nodes. Schedule optimization is performed using dynamic programming methods using the set of criteria in accordance with the economic policy of the virtual organization.

This chapter describes an economic model for independent job flow management in distributed computing environments with non-dedicated resources. The model is based on the concept of fair resource distribution between users and owners of computational nodes by means of economic mechanisms in a virtual organization. Scheduling is performed in cycles in accordance with dynamically updated schedules on local processor nodes. Schedule optimization is performed using dynamic programming methods using the set of criteria in accordance with the economic policy of the virtual organization.

This work presents slot selection algorithms in economic models for independent job batch scheduling in distributed computing with non-dedicated resources. Existing approaches towards resource co-allocation and multiprocessor job scheduling in economic models of distributed computing are based on search of time-slots in resource occupancy schedules. The sought time-slots must match requirements of necessary span, computational resource properties, and cost. Usually such scheduling methods consider only suited variant of time-slot set. This work discloses a scheduling scheme that features multi-variant search. Two algorithms of linear complexity for search of alternative variants are proposed and compared. Having several optional resource configurations for each job makes an opportunity to perform an optimization of execution of the whole batch of jobs and to increase overall efficiency of scheduling.

In this work, we present slot selection algorithms for job batch scheduling in distributed computing with non-dedicated resources. Jobs are parallel applications and these applications are independent. Existing approaches towards resource co-allocation and parallel job scheduling in economic models of distributed computing are based on search of time-slots in resource occupancy schedules. The sought time-slots must match requirements of necessary span, computational resource properties, and cost. Usually such scheduling methods consider only one suited variant of time-slot set. This work discloses a scheduling scheme that features multi-variant search. Two algorithms of linear complexity for search of alternative variants are proposed. Having several optional resource configurations for each job makes an opportunity to perform an optimization of execution of the whole batch of jobs and to increase overall efficiency of scheduling.

A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.