On the Monotonicity of Process Number

International audienceGraph searching games involve a team of searchers that aims at capturing a fugitive in a graph. These games have been widely studied for their relationships with the tree-and the path-decomposition of graphs. In order to define de-compositions for directed graphs, similar games have been proposed in directed graphs. In this paper, we consider a game that has been defined and studied in the context of routing reconfiguration problems in WDM networks. Namely, in the processing game, the fugitive is invisible, arbitrarily fast, it moves in the opposite direction of the arcs of a digraph, but only as long as it can access to a strongly connected component free of searchers. We prove that the processing game is monotone which leads to its equivalence with a new digraph decomposition

Dynamic Service Rate Control for a Single Server Queue with Markov Modulated Arrivals

We consider the problem of service rate control of a single server queueing system with a finite-state Markov-modulated Poisson arrival process. We show that the optimal service rate is non-decreasing in the number of customers in the system; higher congestion rates warrant higher service rates. On the contrary, however, we show that the optimal service rate is not necessarily monotone in the current arrival rate. If the modulating process satisfies a stochastic monotonicity property the monotonicity is recovered. We examine several heuristics and show where heuristics are reasonable substitutes for the optimal control. None of the heuristics perform well in all the regimes. Secondly, we discuss when the Markov-modulated Poisson process with service rate control can act as a heuristic itself to approximate the control of a system with a periodic non-homogeneous Poisson arrival process. Not only is the current model of interest in the control of Internet or mobile networks with bursty traffic, but it is also useful in providing a tractable alternative for the control of service centers with non-stationary arrival rates.Comment: 32 Pages, 7 Figure

Application of Neural Networks to House Pricing and Bond Rating

Feed forward neural networks receive a growing attention as a data modelling tool in economic classification problems. It is well-known that controlling the design of a neural network can be cumbersome. Inaccuracies may lead to a manifold of problems in the application such as higher errors due to local optima, overfitting and ill-conditioning of the network, especially when the number of observations is small. In this paper we provide a method to overcome these difficulties by regulating the flexibility of the network and by rendering measures for validating the final network. In particular a method is proposed to equilibrate the number of hidden neurons and the value of the weight decay parameter based on 5 and 10-fold cross-validation. In the validation process the performance of the neural network is compared with a linear model with the same input variables. The degree of monotonicity with respect to each explanatory variable is calculated by numerical differentiation. The outcomes of this analysis is compared to what is expected from economic theory. Furthermore we propose a scheme for the application of monotonic neural networks to problems where monotonicity with respect to the explanatory variables is known a priori. The methods are illustrated in two case studies: predicting the price of housing in Boston metropolitan area and the classification of bond ratings.Classification;error estimation;monotonicity;finance;neural-network models

Queueing process with excluded-volume effect

We introduce an extension of the M/M/1 queueing process with a spatial structure and excluded- volume effect. The rule of particle hopping is the same as for the totally asymmetric simple exclusion process (TASEP). A stationary-state solution is constructed in a slightly arranged matrix product form of the open TASEP. We obtain the critical line that separates the parameter space depending on whether the model has the stationary state. We calculate the average length of the model and the number of particles and show the monotonicity of the probability of the length in the stationary state. We also consider a generalization of the model with backward hopping of particles allowed and an alternate joined system of the M/M/1 queueing process and the open TASEP.Comment: 9 figure