The research on call centres has attracted many researchers from different disciplines recently. In this thesis, we focus on call centre modelling, analysis and design. In terms of modelling, traditionally call centres have been modelled as single-node queueing systems. Based on the Semiopen Queueing Network (SOQN) model proposed by Srinivasan et al. [42], we propose and study SOQN models with balking and abandonment (both exponential and general patience time distributions). In addition, we study the corresponding single-node queueing systems and obtain new results. For each model, we study the queue length distribution, waiting time distribution and the related performance measures. To facilitate the computation, we express the performance measures in terms of special functions. In terms of call centre design, we develop a design algorithm to determine the minimal number of CSRs (S) and trunk lines (N) to satisfy a given set of service level constraints.<p> The explicit expressions for performance measures obtained allow for theoretical analysis of the performance measures. For example we prove monotonicity and convexity properties of performance measures for the M/M/S/N and M/M/S/N + M models. We also study the comparison of different patience time distributions for the M/M/S/N+G model.<p> We provide numerical examples for each model and discuss numerical results such as monotonicity properties of performance measures. In particular, we illustrate the efficacy of our design algorithm for various models including patient, balking and abandonment models. The impact of model parameters on the design of call centres is also discussed based on the numerical examples. The results are computed using Matlab, where special functions are available.

The research on call centres has attracted many researchers from different disciplines recently. In this thesis, we focus on call centre modelling, analysis and design. In terms of modelling, traditionally call centres have been modelled as single-node queueing systems. Based on the Semiopen Queueing Network (SOQN) model proposed by Srinivasan et al. [42], we propose and study SOQN models with balking and abandonment (both exponential and general patience time distributions). In addition, we study the corresponding single-node queueing systems and obtain new results. For each model, we study the queue length distribution, waiting time distribution and the related performance measures. To facilitate the computation, we express the performance measures in terms of special functions. In terms of call centre design, we develop a design algorithm to determine the minimal number of CSRs (S) and trunk lines (N) to satisfy a given set of service level constraints.<p> The explicit expressions for performance measures obtained allow for theoretical analysis of the performance measures. For example we prove monotonicity and convexity properties of performance measures for the M/M/S/N and M/M/S/N + M models. We also study the comparison of different patience time distributions for the M/M/S/N+G model.<p> We provide numerical examples for each model and discuss numerical results such as monotonicity properties of performance measures. In particular, we illustrate the efficacy of our design algorithm for various models including patient, balking and abandonment models. The impact of model parameters on the design of call centres is also discussed based on the numerical examples. The results are computed using Matlab, where special functions are available.

This dissertation addresses the task of learning to rank, both in the supervised and unsupervised settings, by exploiting the interplay of convex functions, monotonic mappings and their fixed points. In the supervised setting of learning to rank, one wishes to learn from examples of correctly ordered items whereas in the unsupervised setting, one tries to maximize some quantitatively defined characteristic of a "good" ranking. A ranking method selects one permutation from among the combinatorially many permutations defined on the items to rank. Accomplishing this optimally in the supervised setting, with minimal loss in generality, if any, is challenging. In this dissertation this problem is addressed by optimizing, globally and efficiently, a statistically consistent loss functional over the class of compositions of a linear function by an arbitrary, strictly monotonic, separable mapping with large margins. This capability also enables learning the parameters of a generalized linear model with an unknown link function. The method can handle infinite dimensional feature spaces if the corresponding kernel function is known. In the unsupervised setting, a popular ranking approach is is link analysis over a graph of recommendations, as exemplified by pagerank. This dissertation shows that pagerank may be viewed as an instance of an unsupervised consensus optimization problem. The dissertation then solves a more general problem of unsupervised consensus over noisy, directed recommendation graphs that have uncertainty over the set of "out" edges that emanate from a vertex. The proposed consensus rank is essentially the pagerank over the expected edge-set, where the expectation is computed over the distribution that achieves the most agreeable consensus. This consensus is measured geometrically by a suitable Bregman divergence between the consensus rank and the ranks induced by item specific distributions Real world deployed ranking methods need to be resistant to spam, a particularly sophisticated type of which is link-spam. A popular class of countermeasures "de-spam" the corrupted webgraph by removing abusive pages identified by supervised learning. Since exhaustive detection and neutralization is infeasible, there is a need for ranking functions that can, on one hand, attenuate the effects of link-spam without supervision and on the other hand, counter spam more aggressively when supervision is available. A family of non-linear, iteratively defined monotonic functions is proposed that propagates "rank" and "trust" scores through the webgraph. It relies on non-linearity, monotonicity and Schurconvexity to provide the resistance against spam. / text

This thesis serves as an introduction and overview of the broad and closely related fields of mechanism design, contract theory, and information economics. Each chapter is intended to provide a self-contained guide to the particular area of application -- examples include adverse selection, moral hazard, and auctions. The reader should benefit from the thesis in two ways: by understanding the general notions of the revelation principle, incentive compatibility, and individual rationality from the mechanism design theory as well as by examining the particular information asymmetry models in the individual areas. Powered by TCPDF (www.tcpdf.org)

We analyze the notions of monotonicity and complete monotonicity for Markov Chains in continuous-time, taking values in a finite partially ordered set. Similarly to what happens in discrete-time, the two notions are not equivalent.<br> However, we show that there are partially ordered sets for which monotonicity and complete monotonicity coincide in continuous time but not in discrete-time. / Nous étudions les notions de monotonie et de monotonie complète pour les processus de Markov (ou chaînes de Markov à temps continu) prenant leurs valeurs dans un espace partiellement ordonné. Ces deux notions ne sont pas équivalentes, comme c'est le cas lorsque le temps est discret. Cependant, nous établissons que pour certains ensembles partiellement ordonnés, l'équivalence a lieu en temps continu bien que n'étant pas vraie en temps discret.

In this thesis,we report recent results on existence for variational inequalities in infinite-dimensional spaces under generalized monotonicity.

abstract: Borda's social choice method and Condorcet's social choice method are shown to satisfy different monotonicities and it is shown that it is impossible for any social choice method to satisfy them both. Results of a Monte Carlo simulation are presented which estimate the probability of each of the following social choice methods being manipulable: plurality (first past the post), Borda count, instant runoff, Kemeny-Young, Schulze, and majority Borda. The Kemeny-Young and Schulze methods exhibit the strongest resistance to random manipulability. Two variations of the majority judgment method, with different tie-breaking rules, are compared for continuity. A new variation is proposed which minimizes discontinuity. A framework for social choice methods based on grades is presented. It is based on the Balinski-Laraki framework, but doesn't require aggregation functions to be strictly monotone. By relaxing this restriction, strategy-proof aggregation functions can better handle a polarized electorate, can give a societal grade closer to the input grades, and can partially avoid certain voting paradoxes. A new cardinal voting method, called the linear median is presented, and is shown to have several very valuable properties. Range voting, the majority judgment, and the linear median are also simulated to compare their manipulability against that of the ordinal methods. / Dissertation/Thesis / Ph.D. Mathematics 2010

Iterative methods are extensively used to solve linear and nonlinear problems arising from both pure and applied sciences, and in particular, in fixed point theory and optimization. An iterative method which is used to find a fixed point of an operator or an optimal solution to an optimization problem generates a sequence in an iterative manner. We are in a hope that this sequence can converge to a solution of the problem under investigation. It is therefore quite naturally to require that the distance of this sequence to the solution set of the problem under investigation be decreasing from iteration to iteration. This is the idea of Fejer-monotonicity. In this paper, We consider quasi-Fejer monotone sequences; that is, we consider Fejer monotone sequences together with errors. Properties of quasi-Fejer monotone sequences are investigated, weak and strong convergence of quasi-Fejer monotone sequences are obtained, and an application to the convex feasibility problem is included.

Dans cette thèse, nous nous intéressons à la monotonie de la vitesse de la marche aléatoire excitée (MAE) avec biais $bein[0,1]$ dans la première direction $e_1$. Nous présentons une nouvelle preuve de la monotonie de la vitesse pour des grandes dimensions $dgeq d_0$ et pour le cas où le paramètre $be$ est petit quand $dgeq 8$. Ensuite, nous considérons les marches aléatoires avec plusieurs cookies aléatoires. La monotonie de la vitesse est ausi prouvée pour les cas particuliers par exemple des dimensions sont grandes, le paramètre de dérive $be$ est petit ou le nombre de cookies est grand. Ce sont les cas où la marche aléatoire est proche à la marche aléatoire simple. Pour l'existence de la vitesse, nous avons montré la loi des grands nombres pour un cas particulier du cookie aléatoire stationaire, mais nous n'arrivons pas encore pour le cas stationaire. Sur la monotonie, nous avons aussi vérifié que le nombre de points visités par la marche aléatoire simple avec biais $be$ est croissant.Finalement, une question très interessant: la monotonie de la vitesse, est-elle vraie pour la MAE pour les petites dimensions $2leq dleq 8.$ Pour cette motivation, nous avons prouvé que la vitesse est indéfiniment différentiable pour $be>0.$ Au point critique $0$, nous avons prouvé que la dérivée de la vitesse existe et égale $0$ pour $d=2$, existe et est positive pour $dgeq 4.$ Mais nous ne savons pas encore si la dérivée de l'ordre 2 en point $0$ existe ou au moin la dérivée est continue en $0$ pour prouver la monotonie de la vitesse au voisinage de $0$? / In this thesis, we are interested in the monotonicity of the speed of the excited random walk (ERW) with bias $bein[0,1]$ in the first direction $e_1.$ The speed is defined as the limit obtained by the law of large number for the horizontal component. The speed depend on the bias $be.$ We present a new proof of the monotonicity of the speed for the dimension $dgeq d_0$, where $d_0$ is large enough, or for the parameter $be$ is small when $dgeq 8$. After that, we consider the random walk with multi-random cookies. The monotonicity of the speed is also proved for some particular cas, for exemple when the dimension is high, or the parameter drift is small, or the number of cookies is large. These are the cas where the walk is near the simple random walk. For the existence of the speed, we also proved the law of large number for a particular cas of stationary cookie but we haven't yet gotten the cas stationary. On the monotonicity, we also proved the rang of the simple random walk with drift $be$ is increasing in the drift. Finally, a question very interesting: the monotonicity of the speed of ERW is true for the small dimension $2leq dleq 8$, isn't it? For this motivation, we proved the speed is infinitly differentiable for all $be>0.$ At the critical point $0,$ we also proved the derivative of the speed at $0$ exists and equals $0$ for $d=2$, exists and is positive for $dgeq 4.$ But we haven't yet known if the derivative of order $2$ at $0$ exists or at least the derivative is continuous at $0$ to prove the monotonicity of the speed in a neighbor of $0$.

A maioria dos textos na literatura de testes de hipóteses trata de critérios de otimalidade para um determinado problema de decisão. No entanto, existem, em menor quantidade, alguns textos sobre os problemas de se realizar testes de hipóteses simultâneos e sobre a concordância lógica de suas soluções ótimas. Algo que se espera de testes de hipóteses simultâneos e que, se uma hipótese H1 implica uma hipótese H0, então é desejável que a rejeição da hipótese H0 necessariamente implique na rejeição da hipótese H1, para uma mesma amostra observada. Essa propriedade é chamada aqui de monotonicidade. A fim de estudar essa propriedade sob um ponto de vista mais geral, neste trabalho é definida a nocão de classe de testes de hipóteses, que estende a funcão de teste para uma sigma-álgebra de possíveis hipóteses nulas, e introduzida uma definição de monotonicidade. Também é mostrado, por meio de alguns exemplos simples, que, para um nível de signicância fixado, a classe de testes Razão de Verossimilhanças Generalizada (RVG) não apresenta monotonicidade, ao contrário de testes formulados sob a perspectiva bayesiana, como o teste de Bayes baseado em probabilidades a posteriori, o teste de Lindley e o FBST. Porém, são verificadas, sob a teoria da decisão, quando possível, quais as condições suficientes para que uma classe de testes de hipóteses tenha monotonicidade. / Most of the texts in the literature of hypothesis testing deal with optimality criteria for a single decision problem. However, there are, to a lesser extent, texts on the problem of simultaneous hypothesis testing and the logical consistency of the optimal solutions of such procedures. For instance, the following property should be observed in simultaneous hypothesis testing: if a hypothesis H implies a hypothesis H0, then, on the basis of the same sample observation, the rejection of the hypothesis H0 necessarily should imply the rejection of the hypothesis H. Here, this property is called monotonicity. To investigate this property under a more general point of view, in this work, it is dened rst the notion of a class of hypothesis testing, which extends the test function to a sigma-eld of possible null hypotheses, and then the concept of monotonicity is introduced properly. It is also shown, through some simple examples, that for a xed signicance level, the class of Generalized Likelihood Ratio tests (GLR) does not meet monotonicity, as opposed to tests developed under the Bayesian perspective, such as Bayes tests based on posterior probabilities, Lindleys tests and Full Bayesian Signicance Tests (FBST). Finally, sucient conditions for a class of hypothesis testing to have monotonicity are determined, when possible, under a decision-theoretic approach.