Les fondements mathématiques pour une aide à la décision du réseau de transport aérien : cas de la République Démocratique du Congo.

DRC geopolitical situation was conceived by the colonizer in terms of his own interests based on the facility of the exporting means of our wealth towards the metropolis. During the second republic, the building of some airports had as unique criterion of selection, the interests of president. That situation is far from the economic, social and environmental preoccupations of our populations. The objective is to go from the situation existing in DRC and try an extension of the area in order to bring closer the capital of DRC to the contry. For this research there exist two combinatorial optimization problems wich are: localization problem and he one of cover. For better apprehending the reality we have used the multicriteria paradigm. For the case, two criteria related to the economic and social aspects have oriented the process help to the decision of extension

Analysis of the Performance Measures of a Non-Markovian Fuzzy Queue via Fuzzy Laplace Transforms Method

Laplace transforms play an essential role in the analysis of classical non-Markovian queueing systems. The problem addressed here is whether the Laplace transform approach is still valid for determining the characteristics of such a system in a fuzzy environment. In this paper, fuzzy Laplace transforms are applied to analyze the performance measures of a non-Markovian fuzzy queueing system FM/ FG/1. Starting from the fuzzy Laplace transform of the service time distribution, we define the fuzzy Laplace transform of the distribution of the dwell time of a customer in the system. By applying the properties of the moments of this distribution, the derivative of this fuzzy transform makes it possible to obtain a fuzzy expression of the average duration of stay of a customer in the system. This expression is the fuzzy formula of the same performance measure that can be obtained from its classical formula by the Zadeh extension principle. The fuzzy queue FM/ FE_k /1 is particularly treated in this text as a concrete case through its service time distribution. In addition to the fuzzy arithmetic of L-R type fuzzy numbers, based on the secant approximation, the properties of the moments of a random variable and Little's formula are used to compute the different performance measures of the system. A numerical example was successfully processed to validate this approach. The results obtained show that the modal values of the performance measures of a non-Markovian fuzzy queueing system are equal to the performance measures of the corresponding classical model computable by the Pollaczeck-Khintchine method. The fuzzy Laplace transforms approach is therefore applicable in the analysis of a fuzzy FM/FG/1 queueing system in the same way as the classical M/G/1 model

Les fondements mathématiques pour une aide à la décision du réseau de transport aérien : cas de la République Démocratique du Congo.

DRC geopolitical situation was conceived by the colonizer in terms of his own interests based on the facility of the exporting means of our wealth towards the metropolis. During the second republic, the building of some airports had as unique criterion of selection, the interests of president. That situation is far from the economic, social and environmental preoccupations of our populations. The objective is to go from the situation existing in DRC and try an extension of the area in order to bring closer the capital of DRC to the contry. For this research there exist two combinatorial optimization problems wich are: localization problem and he one of cover. For better apprehending the reality we have used the multicriteria paradigm. For the case, two criteria related to the economic and social aspects have oriented the process help to the decision of extension

Computing the Performance Parameters of the Markovian Queueing System FM/FM/1 In Transient State

In this chapter, we utilize L–R method to calculate the parameters of performance of fuzzy Markovian queueing system FM/FM/1 in transient regime. The technique of calculating used is the arithmetic of L–R fuzzy numbers restricted to secant approximations. The membership function has helped us to represent graphically the curves of fuzzy parameters of performance into the space in three dimensions in transient regime in fuzzy environment. An illustrative example is given in the medical field to show the relevance of this study in operational research and in particular in queueing systems

Simultaneous optimization: sectorization and congolese air traffic assignment by the method of preferential reference of dominance.

Air controllers encounter aeronautical problems everyday. Those problems complexity is growing as the latter problems emerge in aerial navigations sectors at the time of the air traffic assignment. As a long time as the number of aircraft in a sector is high, the controller-related load will increase in a nonlinear way. Currently, one counts, on the congolese territory, and especially in the vicinity of areas with wars, many planes movements. This would represent in a near future a difficult bulk of control for controllers. In order to avoid saturation in sectors, the congolese airspace must be divided in increasingly small sectors while distributing the workloads. To clarify the analysis, one is interested in the multicriteria optimization which deals with the case of the simultaneous presence of several objectives by the preferential reference of dominance method proposed by Joseph Okitonyumbe and Berthold Ulungu (2014). The latter method is based on a new characterization of the efficient solutions by building the probable assignments in order to minimize the load of control in the sector

Analysis of the Performance Measures of a Non-Markovian Fuzzy Queue via Fuzzy Laplace Transforms Method

Laplace transforms play an essential role in the analysis of classical non-Markovian queueing systems. The problem addressed here is whether the Laplace transform approach is still valid for determining the characteristics of such a system in a fuzzy environment. In this paper, fuzzy Laplace transforms are applied to analyze the performance measures of a non-Markovian fuzzy queueing system FM/ FG/1. Starting from the fuzzy Laplace transform of the service time distribution, we define the fuzzy Laplace transform of the distribution of the dwell time of a customer in the system. By applying the properties of the moments of this distribution, the derivative of this fuzzy transform makes it possible to obtain a fuzzy expression of the average duration of stay of a customer in the system. This expression is the fuzzy formula of the same performance measure that can be obtained from its classical formula by the Zadeh extension principle. The fuzzy queue FM/ FE_k /1 is particularly treated in this text as a concrete case through its service time distribution. In addition to the fuzzy arithmetic of L-R type fuzzy numbers, based on the secant approximation, the properties of the moments of a random variable and Little's formula are used to compute the different performance measures of the system. A numerical example was successfully processed to validate this approach. The results obtained show that the modal values of the performance measures of a non-Markovian fuzzy queueing system are equal to the performance measures of the corresponding classical model computable by the Pollaczeck-Khintchine method. The fuzzy Laplace transforms approach is therefore applicable in the analysis of a fuzzy FM/FG/1 queueing system in the same way as the classical M/G/1 model

Computing The Performance Parameters of A Fuzzy Markovian Queueing System Fm/Fm/1 In Transient Regime By The Flexible Alpha-Cuts Method

This scientific article sets out to solve the following fundamental problem to calculate the performance parameters of the FM/FM/1 queuing system in transient state. To resolve this problem the fuzzy arithmetic of  cuts and intervals was used in transient state (TS). To achieve the expected results of our work, we used the analytical method with its different stages which are : selecting textual or visual documents ( books, articles, conferences, seminars,... with or without internet); read and analyze the content of these documents; record selected documents related to our research topic; interpret during the reading and the classification, the data obtained. This method helped us to identify the appropriate mathematical approach to evolve the performance of the queuing system under study. This is precisely the relaxed a-cuts and intervals. To illustrate this approach, a numerical example is given in the sixth section. The membership function enabled us to represent the graphs of the performance parameters of the FM/FM/1 queuing system in the three-dimensional space in the transient regime in a fuzzy environment

Computing The Performance Parameters of A Fuzzy Markovian Queueing System Fm/Fm/1 In Transient Regime By The Flexible Alpha-Cuts Method

This scientific article sets out to solve the following fundamental problem to calculate the performance parameters of the FM/FM/1 queuing system in transient state. To resolve this problem the fuzzy arithmetic of  cuts and intervals was used in transient state (TS). To achieve the expected results of our work, we used the analytical method with its different stages which are : selecting textual or visual documents ( books, articles, conferences, seminars,... with or without internet); read and analyze the content of these documents; record selected documents related to our research topic; interpret during the reading and the classification, the data obtained. This method helped us to identify the appropriate mathematical approach to evolve the performance of the queuing system under study. This is precisely the relaxed a-cuts and intervals. To illustrate this approach, a numerical example is given in the sixth section. The membership function enabled us to represent the graphs of the performance parameters of the FM/FM/1 queuing system in the three-dimensional space in the transient regime in a fuzzy environment