Equilibrium resource distribution in a network model

A network is modeled by a weighted undirected graph G. Some certain time invariable resource is assigned to each node and is distributed among the incident edges at each time (time is assumed to be discrete). A state of the network corresponds to a distribution of resources of all nodes among the edges of G. At each time a vertex i evaluates its relationship with an adjacent vertex j according to a given function c _ij (x _ij , x _ji ) of the resources x _ij and x _ji provided by the nodes i and j to the edge (i, j). Since resources of the nodes are redistributed at every time, the state of the system varies in time. Some sufficient conditions are found for the existence of the limit and equilibrium states of the model; and precise formulas are given to compute these states in the case of a special function c _ij for an arbitrary graph G.     

Defence resource distribution between protection and decoys for constant resource stockpiling pace

The paper considers the optimal resource distribution between increasing protection of genuine elements and deploying decoys (false targets) in a situation when the attacker's and defender's resources are stockpiling and the resource increment rate is constant. It is assumed that the system must perform within an exogenously given time horizon and the attack time probability is uniformly distributed over this horizon. Series and parallel systems are considered. The defender optimizes the resource distribution in order to minimize the system vulnerability. The attacker cannot distinguish genuine and false elements and can attack a randomly chosen subset of the elements.     

Equilibrium and Pareto-optimality in noisy discrete duels with an arbitrary number of actions

We study a nonzero-sum game of two players that is a generalization of the antagonistic noisy duel of discrete type. The game is considered from the point of view of various criteria of optimality. We prove the existence of ε-equilibrium situations and show that the ε-equilibrium strategies that we found are ε-maxmin. Conditions under which the equilibrium plays are Pareto-optimal are given. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 2, pp. 147–155, 2007.     

Reinforcement learning versus heuristics for order acceptance on a single resource

Order Acceptance (OA) is one of the main functions in business control. Accepting an order when capacity is available could disable the system to accept more profitable orders in the future with opportunity losses as a consequence. Uncertain information is also an important issue here. We use Markov decision models and learning methods from Artificial Intelligence to find decision policies under uncertainty. Reinforcement Learning (RL) is quite a new approach in OA. It is shown here that RL works well compared with heuristics. It is demonstrated that employing an RL trained agent is a robust, flexible approach that in addition can be used to support the detection of good heuristics.     

Investigation of one-dimensional problem of resource distribution on an infinite time interval

Two controlled nonlinear dynamic models of resource distribution are considered in the case of an infinite horizon. Both of the models are studied on the basis of a known theoretical result that can only be applied without any constraints to the first problem. For both of the models, optimal solutions are found and their optimality is proved.     

Optimal resource distribution program in a two-sector economic model with a Cobb-Douglas production function with distinct amortization factors

We consider a resource distribution problem on a finite time interval with a terminal functional for a two-sector economic model with a two-factor Cobb-Douglas production function with distinct amortization factors. The problem can be reduced to a canonical form by scaling the state variables and time. We prove the optimality of an extremal solution constructed with the use of the maximum principle. For the case in which the initial state of the plant lies above the singular ray, the solution of the boundary value problem of the maximum principle is presented in closed form.     

Optimal resource allocation in survey designs

Resource allocation is a relatively new research area in survey designs and has not been fully addressed in the literature. Recently, the declining participation rates and increasing survey costs have steered research interests towards resource planning. Survey organizations across the world are considering the development of new mathematical models in order to improve the quality of survey results while taking into account optimal resource planning. In this paper, we address the problem of resource allocation in survey designs and we discuss its impact on the quality of the survey results. We propose a novel method in which the optimal allocation of survey resources is determined such that the quality of survey results, i.e., the survey response rate, is maximized. We demonstrate the effectiveness of our method by extensive numerical experiments.     

Optimal resource allocation in presidential primaries

A model for the optimal allocation of resources in presidential primaries is described, under the assumption that two candidates seek to maximize their expected delegate vote in a sequential game that allows for momentum transfer from earlier to later contests. Specifically, the model assumes that the probability that a voter in a primary state votes for a particular candidate is a function of both the resources that candidate and his opponent allocate to that primary and their performances in the immediately preceding primary - and indirectly on all earlier primaries. Given that the candidates make equal (optimal) allocations to each primary, a local maximum, which heavily emphasizes the earlier primaries, is found. Several modifications in the basic model are discussed. Preliminary financial expenditure data are used to test the basic model for the 1976 primaries, and some cursory comparisons with 1980 are made. Possible normative implications of changes in the primary rules are briefly considered, particularly with respect to inequities the present rules seem to engender.     

Robust resource allocations in temporal networks

Temporal networks describe workflows of time-consuming tasks whose processing order is constrained by precedence relations. In many cases, the durations of the network tasks can be influenced by the assignment of resources. This leads to the problem of selecting an ‘optimal’ resource allocation, where optimality is measured by network characteristics such as the makespan (i.e., the time required to complete all tasks). In this paper we study a robust resource allocation problem where the task durations are uncertain, and the goal is to minimise the worst-case makespan. We show that this problem is generically ${\mathcal{NP}}$ -hard. We then develop convergent bounds on the optimal objective value, as well as feasible allocations whose objective values are bracketed by these bounds. Numerical results provide empirical support for the proposed method.     

Stabilizing employment in a fluctuating resource economy

We consider a resource management problem in which the management objective is to minimize fluctuations in resource economics. Stabilizing management policies consist of memoryless state feedback control strategies for a class of discrete-time resource models which contain unknown but bounded fluctuations. The underlying theory is based on conditions developed for Lyapunov-type stability of sets. The design of the stabilizing policies is illustrated by a simulation example from resource economics. Specifically, employment of fishermen is stabilized by using a subsidizing and taxing policy in an open-access common-property fishery in which the value of the resource and the resource level fluctuate, and where entry and exit dynamics are determined by fluctuating revenues obtained from the fishery.This work was supported by NSF and AFOSR under Grant No. ECS-86-02524.The support by the Yrjö Jahnsson Foundation is greatly acknowledged.     

On swarm-level resource allocation in BitTorrent communities

BitTorrent is a peer-to-peer computer network protocol for sharing content in an efficient and scalable way. Modeling and analysis of the popular private BitTorrent communities has become an active area of research. In these communities users are strongly incentivized to contribute their resources, i.e., to share their files. In BitTorrent terminology, users who have finished downloading files and stay online to share these files with others in the network are called seeders. The combination of seeders and downloaders of a file is called a swarm. In this paper we examine and evaluate the efficiency of the resource allocation of seeders in multiple swarms. This is formulated as an integer linear fractional programming problem. The evaluation is done on traces representing two existing BitTorrent communities. We find that in communities, particularly with low users-to-files ratio (which is typically the case), there is room for improvement.     

Optimality conditions in a resource allocation problem

Translated from Vychislitel'nye Kompleksy i Modelirovanie Slozhnykh Sistem, pp. 138–141, Moscow State University, 1989.     

Inverse complementarity in a resource deficit model

The concept of inverse complementarity for a parametric family of optimization problems is introduced. This concept is an effective tool for solving complicated applied problems arising in socioeconomic systems. As an example, a nonlinear resource deficit model is constructed in which the equilibrium is characterized by an external market value of resources coinciding with internal objectively determined resource estimates. An extraproximal method is proposed for computing an equilibrium solution. The convergence of the method is proved. Original Russian Text. A.V. Zykina, 2008, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2008, Vol. 48, No. 11, pp. 1968–1978.     

具有随机参数的盾构管片弹性密封垫防水性能优化分析

盾构管片接缝弹性密封垫断面的几何尺寸极易受生产工艺的影响而呈现出随机性,从而对盾构管片弹性密封垫的防水性能产生影响.该文选取密封垫的孔洞圆心坐标、孔径、断面宽度、断面高度等参数作为随机输入变量,运用ANSYS-PDS模块得出了各随机参数对密封垫防水性能的灵敏度数值,结果显示圆孔孔径对闭合压力及接触应力的影响较其他几何尺寸更大;圆孔垂向位置改变对闭合压力及接触应力的影响较横向位置更大.在此基础上,应用ANSYS优化设计模块,选取密封垫闭合压力和下表面平均接触应力作为状态变量,以在闭合压力不超过某一定值的条件下接触应力最大为目标函数,对密封垫进行几何参数优化分析,得出了某盾构隧道弹性密封垫优化断面,试验结果很好地验证了优化计算结果的可靠性.     

Mathematical cognition: individual differences in resource allocation

Individuals scoring higher in tests of general cognitive abilities tend to perform better on novel and familiar mathematical tasks. It has been scarcely investigated how this superior mathematical performance relates to the amount of cognitive resources that is invested to solve a given task. In this study we propose that, on novel tasks, individuals with high cognitive abilities outperform less able individuals, because they allocate a higher amount of resources. On familiar tasks, however, individuals with higher abilities profit from more efficient processes compared to individuals of lower cognitive abilities. We tested this hypothesis by administering to 11th graders a geometric analogy task not practiced at school and an algebraic transformation task comprising operations that are routinely required during mathematical courses. General cognitive abilities were measured with Ravens Advanced Progressive matrices (fluid intelligence), the d2 (focused attention) and KAI-N (working memory capacity). Resource allocation was measured by assessing pupil diameter during the problem-solving process. Performance on both the analogy and the algebra task was correlated with general cognitive abilities, especially fluid intelligence. In line with our assumptions, a positive correlation between fluid intelligence and resource allocation was observed in the novel geometric analogy task, whereas the correlation was not significant in the more familiar algebra task.     

Optimal resource allocation in a complex queueing system

This paper studies the optimal allocation of service rates in a three-stage complex queueing system with total finite waiting space. The word ‘optimal’ is being used in the seitse minimising sum of costs of servers and holding subject to relevant constraints. The problem has been solved through geometric programming.     

Habit formation and resource dependence in dynastic economies

This paper studies the consequences of habit formation in dynastic economies that exploit exhaustible resources. If the strength of habits is below a critical level, positive bequests generate Ramsey-Stiglitz equilibria: the altruism factor determines long-run growth and habits increase output levels by increasing capital accumulation and smoothing resource extraction during the transition. If the strength of habits is above the threshold, zero bequests induce Diamond-Mourmouras equilibria: the transitional effects become permanent and habits increase long-run growth. Results differ from those of capital-labor models because resource dependence implies that long-run growth is determined by the intergenerational distribution of wealth.     

Equilibrium path in oligopolistic market of nonrenewable resource

In this paper we study the oligopoly model of nonrenewable resource in which the unit production cost is variable and depends on the resource reserve level. We consider both the open-loop strategy and the closed-loop strategy of this dynamical differential game. For the case of linear cost function we have observed that the open-loop equilibrium and the self-feedback equilibrium satisfy the same equilibrium conditions, which can be described as a dynamical system. The analysis shows that the equilibrium path of the model is the stable orbit of this system, and this result leads to further studies of the properties of the total extraction and reserve and the individual ones of each producer. For the total extraction rate and reserve, some of the properties are similar to those of most oligopoly models with fixed unit production cost. For the individual behaviors, we have found out the solution expressions of the individual extraction rate and resource reserve and got the main result that the producer with larger initial stock has a larger but declining market share and the share of each producer converges toward the average one when time approaches to infinite.