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.

All-regime Lagrangian-Remap numerical schemes for the gas dynamics equations. Applications to the large friction and low Mach coefficients

In this talk, we propose an all regime Lagrange-Projection like numerical scheme for the gas dynamics equations. By all regime, we mean that the numerical scheme is able to compute accurate approximate solutions with an under-resolved discretization with respect to the Mach number M, i.e. such that the ratio between the Mach number M and the mesh size or the time step is small with respect to 1. The key idea is to decouple acoustic and transport phenomenon and then alter the numerical flux in the acoustic approximation to obtain a uniform truncation error in term of M. This modified scheme is conservative and endowed with good stability properties with respect to the positivity of the density and the internal energy. A discrete entropy inequality under a condition on the modification is obtained thanks to a reinterpretation of the modified scheme in the Harten Lax and van Leer formalism. A natural extension to multi-dimensional problems discretized over unstructured mesh is proposed. Then a simple and efficient semi implicit scheme is also proposed. The resulting scheme is stable under a CFL condition driven by the (slow) material waves and not by the (fast) acoustic waves and so verifies the all regime property. Numerical evidences are proposed and show the ability of the scheme to deal with tests where the flow regime may vary from low to high Mach values.