Allocation rules on networks

When allocating a resource, geographical and infrastructural constraints have to be taken into account. We study the problem of distributing a resource through a network from sources endowed with the resource to citizens with claims. A link between a source and an agent depicts the possibility of a transfer from the source to the agent. Given the supplies at each source, the claims of citizens, and the network, the question is how to allocate the available resources among the citizens. We consider a simple allocation problem that is free of network constraints, where the total amount can be freely distributed. The simple allocation problem is a claims problem where the total amount of claims is greater than what is available. We focus on consistent and resource monotonic rules in claims problems that satisfy equal treatment of equals. We call these rules fairness principles and we extend fairness principles to allocation rules on networks. We require that for each pair of citizens in the network, the extension is robust with respect to the fairness principle. We call this condition pairwise robustness with respect to the fairness principle. We provide an algorithm and show that each fairness principle has a unique extension which is pairwise robust with respect to the fairness principle. We give applications of the algorithm for three fairness principles: egalitarianism, proportionality and equal sacrifice.

Cooperative Profit Sharing in Coalition-Based Resource Allocation in Wireless Networks

We consider a network in which several service providers offer wireless access to their respective subscribed customers through potentially multihop routes. If providers cooperate by jointly deploying and pooling their resources, such as spectrum and infrastructure (e.g., base stations) and agree to serve each others' customers, their aggregate payoffs, and individual shares, may substantially increase through opportunistic utilization of resources. The potential of such cooperation can, however, be realized only if each provider intelligently determines with whom it would cooperate, when it would cooperate, and how it would deploy and share its resources during such cooperation. Also, developing a rational basis for sharing the aggregate payoffs is imperative for the stability of the coalitions. We model such cooperation using the theory of transferable payoff coalitional games. We show that the optimum cooperation strategy, which involves the acquisition, deployment, and allocation of the channels and base stations (to customers), can be computed as the solution of a concave or an integer optimization. We next show that the grand coalition is stable in many different settings, i.e., if all providers cooperate, there is always an operating point that maximizes the providers' aggregate payoff, while offering each a share that removes any incentive to split from the coalition. The optimal cooperation strategy and the stabilizing payoff shares can be obtained in polynomial time by respectively solving the primals and the duals of the above optimizations, using distributed computations and limited exchange of confidential information among the providers. Numerical evaluations reveal that cooperation substantially enhances individual providers' payoffs under the optimal cooperation strategy and several different payoff sharing rules.

An algorithm for dynamic optimal bandwidth allocation in communication networks

We study the problem of optimal bandwidth allocation in communication networks. We consider a queueing model with two queues to which traffic from different competing flows arrive. The queue length at the buffers is observed every T instants of time, on the basis of which a decision on the amount of bandwidth to be allocated to each buffer for the next T instants is made. We consider a class of closed-loop feedback policies for the system and use a twotimescale simultaneous perturbation stochastic approximation(SPSA) algorithm to find an optimal policy within the prescribed class. We study the performance of the proposed algorithm on a numerical setting. Our algorithm is found to exhibit good performance.

Optimal Parameterized Policies for Resource Allocation in Communication Networks

The problem of finding optimal parameterized feedback policies for dynamic bandwidth allocation in communication networks is studied. We consider a queueing model with two queues to which traffic from different competing flows arrive. The queue length at the buffers is observed every T instants of time, on the basis of which a decision on the amount of bandwidth to be allocated to each buffer for the next T instants is made. We consider two different classes of multilevel closed-loop feedback policies for the system and use a two-timescale simultaneous perturbation stochastic approximation (SPSA) algorithm to find optimal policies within each prescribed class. We study the performance of the proposed algorithm on a numerical setting and show performance comparisons of the two optimal multilevel closedloop policies with optimal open loop policies. We observe that closed loop policies of Class B that tune parameters for both the queues and do not have the constraint that the entire bandwidth be used at each instant exhibit the best results overall as they offer greater flexibility in parameter tuning. Index Terms — Resource allocation, dynamic bandwidth allocation in communication networks, two-timescale SPSA algorithm, optimal parameterized policies. I.

Forward-looking Pairwise Stability in Networks with Externalities

We consider cooperation situations where players have network relations. Networks evolve according to a stationary transition probability matrix and at each moment in time players receive payoffs from a stationary allocation rule. Players discount the future by a common factor. The pair formed by an allocation rule and a transition probability matrix is called a forward-looking network formation scheme if, first, the probability that a link is created is positive if the discounted, expected gains to its two participants are positive, and if, second, the probability that a link is eliminated is positive if the discounted, expected gains to at least one of its two participants are positive. The main result is the existence, for all discount factors and all value functions, of a forward-looking network formation scheme. Furthermore, we can always nd a forward-looking network formation scheme such that (i) the allocation rule is component balanced and (ii) the transition probabilities increase in the di erence in payo s for the corresponding players responsible for the transition. We use this dynamic solution concept to explore the tension between e ciency and stability.

No-Holdback allocation rules for continuous-time assemble-to-order systems

This paper analyzes a class of common-component allocation rules, termed no-holdback (NHB) rules, in continuous-review assemble-to-order (ATO) systems with positive lead times. The inventory of each component is replenished following an independent base-stock policy. In contrast to the usually assumed first-come-first-served (FCFS) component allocation rule in the literature, an NHB rule allocates a component to a product demand only if it will yield immediate fulfillment of that demand. We identify metrics as well as cost and product structures under which NHB rules outperform all other component allocation rules. For systems with certain product structures, we obtain key performance expressions and compare them to those under FCFS. For general product structures, we present performance bounds and approximations. Finally, we discuss the applicability of these results to more general ATO systems. © 2010 INFORMS.

Comparison of algorithms for loss allocation in transmission networks considering power redispatch

An analysis of the performances of three important methods for generators and loads loss allocation is presented. The discussed methods are: based on pro-rata technique; based on the incremental technique; and based on matrices of circuit. The algorithms are tested considering different generation conditions, using a known electric power system: IEEE 14 bus. Presented and discussed results verify: the location and the magnitude of generators and loads; the possibility to have agents well or poorly located in each network configuration; the discriminatory behavior considering variations in the power flow in the transmission lines. © 2004 IEEE.

Minimal cross-subsidies approach for loss allocation in distribution networks with open access

Open access philosophy applied by regulatory agencies may lead to a scenario where captive consumers will solely face the responsibility on distribution network's losses even with Independent Energy Producers (also known as Distributed Generation) and Independent Energy Consumers connected to the system. This work proposes the utilization of a loss allocation method in distribution systems where open access is allowed, in which cross-subsidies, that appear due to the influence the generators have over the system losses, are minimized. Thus, guaranteeing to some extent the efficiency and transparency of the economic signals of the market. Results obtained through the Zbus loss allocation method adapted for distribution networks are processed in such a way that the corresponding allocation to the generation buses is divided among the consumer buses, while still considering consumers spatial characteristics. © 2007 IEEE.

Expected Fair Allocation in Farsighted Network Formation

I consider cooperation situations where players have network relations. Networks evolve according to a stationary transition probability matrix and at each moment in time players receive payoffs from a stationary allocation rule. Players discount the future by a common factor. The pair formed by an allocation rule and a transition probability matrix is called expected fair if for every link in the network both participants gain, marginally, and in discounted, expected terms, the same from it; and it is called a pairwise network formation procedure if the probability that a link is created (or eliminated) is positive if the discounted, expected gains to its two participants are positive too. The main result is the existence, for the discount factor small enough, of an expected fair and pairwise network formation procedure where the allocation rule is component balanced, meaning it distributes the total value of any maximal connected subnetwork among its participants. This existence result holds for all discount factors when the pairwise network formation procedure is restricted. I finally provide some comparison with previous models of farsighted network formation.

Portfolio size effect in retirement accounts : what does it imply for lifecycle asset allocation funds?

Lifecycle funds offered by retirement plan providers allocate aggressively to risky asset classes when the employee participants are young, gradually switching to more conservative asset classes as they grow older and approach retirement. This approach focuses on maximizing growth of the accumulation fund in the initial years and preserving its value in the later years. The authors simulate terminal wealth outcomes based on conventional lifecycle asset allocation rules as well as on contrarian strategies that reverse the direction of asset switching. The evidence suggests that the growth in portfolio size over time significantly impacts the asset allocation decision. Due to the portfolio size effect that is observed by the authors, the terminal value of accumulation in retirement accounts is influenced more by the asset allocation strategy adopted in later years relative to that adopted in early years. By mechanistically switching to conservative assets in the later years of a plan, lifecycle strategies sacrifice significant growth opportunity and prove counterproductive to the participant's wealth accumulation objective. The authors' conclude that this sacrifice does not seem to be compensated adequately in terms of reducing the risk of potentially adverse outcomes.

Gittins indices and constrained allocation in clinical trials

We explore the use of Gittins indices to search for near optimality in sequential clinical trials. Some adaptive allocation rules are proposed to achieve the following two objectives as far as possible: (i) to reduce the expected successes lost, (ii) to minimize the error probability at the end. Simulation results indicate the merits of the rules based on Gittins indices for small trial sizes. The rules are generalized to the case when neither of the response densities is known. Asymptotic optimality is derived for the constrained rules. A simple allocation rule is recommended for one-stage models. The simulation results indicate that it works better than both equal allocation and Bather's randomized allocation. We conclude with a discussion of possible further developments.

Roteamento e alocação de comprimento de onda em redes WDM segundo algoritmo baseado em regras da natureza.

O surgimento de novos serviços de telecomunicações tem provocado um enorme aumento no tráfego de dados nas redes de transmissão. Para atender a essa demanda crescente, novas tecnologias foram desenvolvidas e implementadas ao longo dos anos, sendo que um dos principais avanços está na área de transmissão óptica, devido à grande capacidade de transporte de informação da fibra óptica. A tecnologia que melhor explora a capacidade desse meio de transmissão atualmente é a multiplexação por divisão de comprimento de onda ou Wavelength Division Multiplexing (WDM) que permite a transmissão de diversos sinais utilizando apenas uma fibra óptica. Redes ópticas WDM se tornaram muito complexas, com enorme capacidade de transmissão de informação (terabits por segundo), para atender à explosão de necessidade por largura de banda. Nesse contexto, é de extrema importância que os recursos dessas redes sejam utilizados de forma inteligente e otimizada. Um dos maiores desafios em uma rede óptica é a escolha de uma rota e a seleção de um comprimento de onda disponível na rede para atender uma solicitação de conexão utilizando o menor número de recursos possível. Esse problema é bastante complexo e ficou conhecido como problema de roteamento e alocação de comprimento de onda ou, simplesmente, problema RWA (Routing and Wavelentgh Assignment problem). Muitos estudos foram realizados com o objetivo de encontrar uma solução eficiente para esse problema, mas nem sempre é possível aliar bom desempenho com baixo tempo de execução, requisito fundamental em redes de telecomunicações. A técnica de algoritmo genético (AG) tem sido utilizada para encontrar soluções de problemas de otimização, como é o caso do problema RWA, e tem obtido resultados superiores quando comparada com soluções heurísticas tradicionais encontradas na literatura. Esta dissertação apresenta, resumidamente, os conceitos de redes ópticas e de algoritmos genéticos, e descreve uma formulação do problema RWA adequada à solução por algoritmo genético.