Volume 31 - 2019 - CARI 2018

Special issue for CARI 2018

1. Dynamic resource allocations in virtual networks through a knapsack problem's dynamic programming solution

Vianney Kengne Tchendji ; Yannick Florian YANKAM.
The high-value Internet services that have been significantly enhanced with the integration of network virtualization and Software Defined Networking (SDN) technology are increasingly attracting the attention of end-users and major computer network companies (Google, Amazon, Yahoo, Cisco, ...). In order to cope with this high demand, network resource providers (bandwidth, storage space, throughput, etc.) must implement the right models to understand and hold the users' needs while maximizing profits reaped or the number of satisfied requests into the virtual networks. This need is even more urgent that users' requests can be linked, thereby imposing to the InP some constraints concerning the mutual satisfaction of requests, which further complicates the problem. From this perspective, we show that the problem of resource allocation to users based on their requests is a knapsack problem and can therefore be solved efficiently by using the best dynamic programming solutions for the knapsack problem. Our contribution takes the dynamic resources allocation as a multiple knapsack's problem instances on variable value requests.

2. ε-TPN: definition of a Time Petri Net formalism simulating the behaviour of the timed grafcets

Médésu Sogbohossou ; Medesu Sogbohossou ; Antoine Vianou ; Nabil Gmati ; Eric Badouel ; Bruce Watson.
To allow a formal verification of timed GRAFCET models, many authors proposed to translate them into formal and well-reputed languages such as timed automata or Time Petri nets (TPN). Thus, the work presented in [Sogbohossou, Vianou, Formal modeling of grafcets with Time Petri nets, IEEE Transactions on Control Systems Technology, 23(5)(2015)] concerns the TPN formalism: the resulting TPN of the translation, called here ε-TPN, integrates some infinitesimal delays (ε) to simulate the synchronous semantics of the grafcet. The first goal of this paper is to specify a formal operational semantics for an ε-TPN to amend the previous one: especially, priority is introduced here between two defined categories of the ε-TPN transitions, in order to respect strictly the synchronous hypothesis. The second goal is to provide how to build the finite state space abstraction resulting from the new definitions.

3. Operating diagram of a flocculation model in the chemostat

Radhouane Fekih-Salem ; Tewfik Sari.
The objective of this study is to analyze a model of the chemostat involving the attachment and detachment dynamics of planktonic and aggregated biomass in the presence of a single resource. Considering the mortality of species, we give a complete analysis for the existence and local stability of all steady states for general monotonic growth rates. The model exhibits a rich set of behaviors with a multiplicity of coexistence steady states, bi-stability, and occurrence of stable limit cycles. Moreover, we determine the operating diagram which depicts the asymptotic behavior of the system with respect to control parameters. It shows the emergence of a bi-stability region through a saddle-node bifurcation and the occurrence of coexistence region through a transcritical bifurcation. Finally, we illustrate the importance of the mortality on the destabilization of the microbial ecosystem by promoting the washout of species.

4. A Calculus of Interfaces for Distributed Collaborative Systems: The Guarded Attribute Grammar Approach

Eric Badouel ; Rodrigue Aimé Djeumen Djatcha.
We address the problem of component reuse in the context of service-oriented programming and more specifically for the design of user-centric distributed collaborative systems modelled by Guarded Attribute Grammars. Following the contract-based specification of components we devel-opp an approach to an interface theory for the components of a collaborative system in three stages: we define a composition of interfaces that specifies how the component behaves with respect to its environement, we introduce an implementation order on interfaces and finally a residual operation on interfaces characterizing the systems that, when composed with a given component, can complement it in order to realize a global specification.