We consider the problem of capacity expansion in telecommunication networks under uncertain economic conditions with various market structures. We assume that the demands for network capacity have constant price-elasticity, and demand functions are parameterized by an economic condition that is modeled by a discrete time Markov process. We apply dynamic programming to obtain a state-dependent capacity expansion strategy that maximizes expected total discounted cash flow. We incorporate partial reversibility of investment by differentiating the purchasing cost and the salvage value of the capacity. This partial reversibility makes the value function non-differentiable and divides the solution space into BUY, KEEP, and SELL regions. By identifying certain structural properties of the optimal solution, we perform sensitivity analyses on the optimal investment decisions with respect to market parameters. Under the condition that the level of cost depreciation is larger than that of the downside movement of the economic condition in each time period, we are able to obtain an analytical expression for the optimal capacity level and reduce the multi-period investment decision problem into a single-period myopic problem. As a result, optimal capacity increment depends only on the current economic condition. We study this problem under both monopolistic and oligopolistic market structures. In particular, we investigate investment decisions by two firms in a duopoly setting with Cournot competition. We prove the existence and the uniqueness of the Cournot equilibrium strategies in the duopolistic capacity investment problem. In addition, we show how competition between firms affects total available capacity in the market, capacity price, consumer surplus, expected time to a certain level of price reduction, and expected time to the first investment. We perform an empirical analysis to test a theoretical prediction obtained from our model through linear regression utilizing historical market data. By examining several alternative indices as a proxy to the economic condition considered in our model, we show that the Civilian Employment is the best proxy to use in validating the linear relationship between telecommunications capacity expansion and the economic indicator.

Made available in DSpace on 2016-03-15T19:38:03Z (GMT). No. of bitstreams: 1 RONALDO DE CASTRO CORREA.pdf: 1467426 bytes, checksum: a5e2b011297c7075c278d2dfd4502c98 (MD5) Previous issue date: 2015-11-23 / Cellular automata are discrete dynamic systems that by local action rules, even very simple, can present arbitrarily complex global processing. The reversibility is a property that a few rules have and guarantees the existence of an inverse rule capable of reversing the temporal evolution of the original rule. For a rule be reversible all possible configurations of lattices must have only one predecessor, i.e., only one pre-image. In this context, it had been proposed in the literature the concept of rules may be characterized by its relative partial reversibility, that is, rules can be more or less reversible than others. This notion is represented by the rule pre-image pattern, which is composed of the quantities ordered pre-images of all the possible configurations of lattices up to a maximum size. To sort the rules of the reversible for less reversible, or group them if they had the same reversibility was made lexicographical ordering patterns of pre-images. This paper reviewed the original definition, based on elementary cellular automata, although the results are applicable to any other one-dimensional family rules. Thus, proposed it was a measure of the reversibility level of a rule, also based on its default pre-image, but now from the probability of correctly reverse each possible configurations of lattices up to a given maximum size. This measure allows us to analyze the degree of reversibility of a rule in absolute terms and not relative to other rules. Thus, it becomes possible to individually analyze the reversibility levels of rules, making it possible to infer the degree of rules reversible for lattices arbitrarily larger than calculated, in particular, identifying rules that tend to be reversible when the size of the lattices tends to infinity. It was also possible to define an operation that, from their own state transitions rule, allows to obtain partially rules that have the same level of reversibility without the need of standard calculating preview image, which is extremely expensive computationally. / Autômatos celulares são sistemas dinâmicos discretos que, por meio de regras de ação local, até mesmo muito simples, podem apresentar processamento global arbitrariamente complexo. A reversibilidade é uma propriedade que poucas regras possuem e que garante a existência de uma regra inversa capaz de reverter a evolução temporal da regra original. Para uma regra ser reversível, todas as configurações possíveis de reticulado devem possuir somente uma única configuração antecessora, ou seja, uma única pré-imagem. Nesse contexto, havia sido proposto na literatura o conceito de regras poderem ser caracterizadas por sua reversibilidade parcial relativa, ou seja, regras poderem ser mais ou menos reversíveis que outras. Essa noção é representada por meio do padrão de pré-imagem da regra, que é composto pelas quantidades ordenadas de pré-imagens de todas as configurações possíveis de reticulado, até um tamanho máximo. Para classificar as regras das mais reversíveis para as menos reversíveis, ou agrupá-las caso possuíssem a mesma reversibilidade, era feita a ordenação lexicográfica dos padrões de pré-imagens. Este trabalho reavaliou a definição original, com base nos autômatos celulares elementares, apesar de os resultados serem aplicáveis a qualquer outra família unidimensional de regras. Assim, foi proposta uma grandeza que representa o nível de reversibilidade de uma regra, também baseada em seu padrão de pré-imagem, mas agora a partir da probabilidade de reverter corretamente cada configuração possível de reticulado, até um tamanho máximo dado. Tal medida permite analisar o nível de reversibilidade de uma regra em termos absolutos, e não mais relativamente a outras regras. Dessa forma, torna-se possível analisar individualmente os níveis de reversibilidade das regras, o que possibilitou inferir o nível de reversibilidade de regras para reticulados arbitrariamente maiores que os calculados, em particular, identificando regras que tendem a ser reversíveis conforme o tamanho do reticulado tende a infinito. Também foi possível definir uma operação que, a partir das próprias transições de estado de uma regra, permite obter parcialmente as regras que possuem o mesmo nível de reversibilidade, sem a necessidade do cálculo do padrão de pré-imagem, que é extremamente custoso computacionalmente.