A discrete-time queueing system with feedback and optional service

Queueing systems constitute a central tool in modeling and performance analysis. These types of systems are in our everyday life activities, and the theory of queueing systems was developed to provide models for forecasting behaviors of systems subject to random demand. The practical and useful applications of the discrete-time queues make the researchers to con- tinue making an e ort in analyzing this type of models. Thus the present contribution relates to a discrete-time Geo/G/1 queue in which some messages may need a second service time in addition to the rst essential service. In day-to-day life, there are numerous examples of queueing situations in general, for example, in manufacturing processes, telecommunication, home automation, etc, but in this paper a particular application is the use of video surveil- lance with intrusion recognition where all the arriving messages require the main service and only some may require the subsidiary service provided by the server with di erent types of strategies. We carry out a thorough study of the model, deriving analytical results for the stationary distribution. The generating functions of the number of messages in the queue and in the system are obtained. The generating functions of the busy period as well as the sojourn times of a message in the server, the queue and the system are also provided.

Queueuing system with failures and priorities

Queueing theory provides models, structural insights, problem solutions and algorithms to many application areas. Due to its practical applicability to production, manufacturing, home automation, communications technology, etc, more and more complex systems requires more elaborated models, tech- niques, algorithm, etc. need to be developed. Discrete-time models are very suitable in many situations and a feature that makes the analysis of discrete time systems technically more involved than its continuous time counterparts. In this paper we consider a discrete-time queueing system were failures in the server can occur as-well as priority messages. The possibility of failures of the server with general life time distribution is considered. We carry out an extensive study of the system by computing generating functions for the steady-state distribution of the number of messages in the queue and in the system. We also obtain generating functions for the stationary distribution of the busy period and sojourn times of a message in the server and in the system. Performance measures of the system are also provided.

Dynamic Multi-Objective Optimization With jMetal and Spark: a Case Study

Technologies for Big Data and Data Science are receiving increasing research interest nowadays. This paper introduces the prototyping architecture of a tool aimed to solve Big Data Optimization problems. Our tool combines the jMetal framework for multi-objective optimization with Apache Spark, a technology that is gaining momentum. In particular, we make use of the streaming facilities of Spark to feed an optimization problem with data from different sources. We demonstrate the use of our tool by solving a dynamic bi-objective instance of the Traveling Salesman Problem (TSP) based on near real-time traffic data from New York City, which is updated several times per minute. Our experiment shows that both jMetal and Spark can be integrated providing a software platform to deal with dynamic multi-optimization problems.