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The information technologies have evolved in such a way that communication between computers or hosts has become common, so much that the worldwide organization (governments and corporations) depends on it; what could happen if these computers stop working for a long time is catastrophic. Unfortunately, networks are attacked by malware such as viruses and worms that could collapse the system. This has served as motivation for the formal study of computer worms and epidemics to develop strategies for prevention and protection; this is why in this paper, before analyzing epidemiological models, a set of formal definitions based on set theory and functions is proposed for describing 21 concepts used in the study of worms. These definitions provide a basis for future qualitative research on the behavior of computer worms, and quantitative for the study of their epidemiological models.

In the biological environment, there has been created epidemiological models that attempt to explain the spread dynamics of an epidemic in a population to predict the behavior of possible epidemics that can affect humanity. Based on that, this paper focused on the study of epidem­ics worms because they can spread by themselves from one infected host to the entire network of susceptible hosts. In this paper we analyzed the susceptible-infected (SI) model which assumes that in a community with n individuals, the num­ber of individuals in the susceptible state S(t) are in direct contact with the number of individuals that are in infected state I(t). These last individuals can spread the infection or switch to an infectious state with the factor B as a speed of infection. This model is based on differential equations so it can­not be implemented directly on a computer. Due to the complexity of this model, it is proposed an approximate model based on finite different equa­tions to achieve a simulation of the epidemic us­ing a set theory and cardinality obtaining an itera­tive numerical method which consists on basics arithmetic operations. Additionally, having in mind this is an approximate model, it will be pre­sented an error due to truncation or rounding. At the end of this paper it will be presented a case of study developed in Simulink of Matlab software, and the results of the model based on difference equations is compared with the finite-difference approximate model including the analysis of ap­proximation errors

Los sistemas en tiempo real (STR) procesan sus actividades a través de tareas que a su vez están formadas por un conjunto de instancias, las cuales tienen seis restricciones temporales: tiempo de arribo, tiempo de inicio, tiempo de ejecución, tiempo de finalizado, tiempo excedente y plazo. De estas seis restricciones, el tiempo de ejecución depende directamente del software y hardware de la computadora, originando que la variación de esta restricción temporal esté vinculada con diversos factores externos e internos, esta variación puede ocasionar que algunas instancias no cumplan su plazo; por este motivo es importante proponer un modelo para reconstruir el comportamiento de los tiempos de ejecución, con el fin de: dimensionar de manera correcta el sistema en tiempo real, proponer técnicas adecuadas de tolerancia a fallos y mejorar sus módulos de operación. Por lo cual en este trabajo, se propone un modelo para reconstruir los tiempos de ejecución obtenidos de la medición hecha a un algoritmo de programación elaborado en el sistema operativo en tiempo real QNX Neutrino 6.5. Dicha reconstrucción se hace a través de un modelo tipo autoregresivo de promedios móviles integrado con un estimador de parámetros construido con un procedimiento de filtrado digital difuso (FDD). Se usa el error cuadrático medio para validar la reconstrucción, el cual converge a una región cercana a cero y permite concluir que la reconstrucción es buena.

Un Sistema en Tiempo Real (STR) implantado en una computadora digital, interactúa con el mundo físico a través del acondicionamiento de variables (sensores, actuadores convertidores Analógico/Digital A/D y Digital/ Analógico D/A) y procesa sus peticiones mediante tareas en tiempo real (Ji: i¿Z+). Cada Ji está formada por un conjunto de instancias {ji,k: i, k¿Z+, i es el índice de la tarea, k es el índice de la instancia} con al menos tres restricciones temporales: tiempo de arribo, tiempo de ejecución y plazo (Li,k, Ci,k, Di,k). En este sentido, es importante proponer un modelo para reconstruir el comportamiento de los tiempos de ejecución Ci,k. El modelo propuesto es un ARMA con un estimador de parámetros basado en la variable instrumental. Los tiempos de ejecución fueron medidos experimentalmente en QNX Neutrino 6.5 utilizando un procesador Intel Core i7 de 2.66 GHz. Se presentan los antecedentes teóricos del modelado de tareas en tiempo real, las mediciones de tiempo de ejecución, el modelo de tiempos de ejecución, el estimador de parámetros con variable instrumental, la experimentación y los resultados.

Real-time systems (RTS) process their activities through tasks which in turn consist of a set of instances, each one of this real-time task (RTT) have six temporary constraints: arrival time, start time, execution time, end time, over time and deadline. Of these six constraints, the execution time depends directly on the software and hardware of the computer, because of that this temporary constraints varies due to external and internal factors, this variation may cause at least some instance does not satisfy the deadline, in this sense it is important to propose a model to reconstruct the behavior of the execution times for the purpose to determine the proportions of the Real-time System, propose appropriate techniques of fault tolerance and improve operating modules. Therefore in this paper, is proposed a model to reconstruct the execution times from measurements made at a program algorithm developed in the real-time operating system QNX Neutrino 6.5. This reconstruction is done by a model type autoregressive–moving-average integrated with parameter estimator constructed with a digital filtering procedure diffuse (FDD). To validate the reconstruction is used the mean square error which converges to a region close to zero and indicate that the reconstruction is good.

A Real-time System (RTS) implemented in a digital computer interacts with the physical world through knowledge variables (sensors, actuators, Analogical - Digital, and Digital-Analogical convertors) processing its requirements through real-time tasks (Ji: i∈Z+). Each Ji is formed by a set of instances {ji,k: i, k∈Z+, i is the task index, k is the instance index} with at least three time constraints: arrival, execution and, interval times (Li,k, Ci,k, Di,k). The execution time identification ˆCi ,k , is based on Instrumental Variable parameter estimation and the recursive state space ARMA model. The execution times were measured experimentally using a Real-time Operative System QNX 6.5 Neutrino in an Intel Core i7 processor with a speed of 2.66 GHz. This paper presents a state of the art real-time task model, execution time measurements, an Instrumental Variable parameter estimator on recursive state space identification, experimentation and, results.