EUROPEAN CONFERENCE ON QUEUEING THEORY 2016

International audienceThis booklet contains the proceedings of the second European Conference in Queueing Theory (ECQT) that was held from the 18th to the 20th of July 2016 at the engineering school ENSEEIHT, Toulouse, France. ECQT is a biannual event where scientists and technicians in queueing theory and related areas get together to promote research, encourage interaction and exchange ideas. The spirit of the conference is to be a queueing event organized from within Europe, but open to participants from all over the world. The technical program of the 2016 edition consisted of 112 presentations organized in 29 sessions covering all trends in queueing theory, including the development of the theory, methodology advances, computational aspects and applications. Another exciting feature of ECQT2016 was the institution of the Takács Award for outstanding PhD thesis on "Queueing Theory and its Applications"

A Note on an M/M/s Queueing System with two Reconnect and two Redial Orbits

A queueing system with two reconnect orbits, two redial (retrial) orbits, s servers and two independent Poisson streams of customers is considered. An arriving customer of type i, i = 1, 2 is handled by an available server, if there is any; otherwise, he waits in an infinite buffer queue. A waiting customer of type i who did not get connected to a server will lose his patience and abandon after an exponentially distributed amount of time, the abandoned one may leave the system (lost customer) or move into one of the redial orbits, from which he makes a new attempt to reach the primary queue, and when a customer finishes his conversation with a server, he may comeback to the system, to one of the reconnect orbits where he will wait for another service. In this paper, a fluid model is used to derive a first order approximation for the number of customers in the redial and reconnect orbits in the heavy traffic. The fluid limit of such a model is a unique solution to a system of three differential equations

MSF-Model: Modeling Metastable Failures in Replicated Storage Systems

Metastable failure is a recent abstraction of a pattern of failures that occurs frequently in real-world distributed storage systems. In this paper, we propose a formal analysis and modeling of metastable failures in replicated storage systems. We focus on a foundational problem in distributed systems -- the problem of consensus -- to have an impact on a large class of systems. Our main contribution is the development of a queuing-based analytical model, MSF-Model, that can be used to characterize and predict metastable failures. MSF-Model integrates novel modeling concepts that allow modeling metastable failures which was interactable to model prior to our work. We also perform real experiments to reproduce and validate our model. Our real experiments show that MSF-Model predicts metastable failures with high accuracy by comparing the real experiment with the predictions from the queuing-based model

Optimal Pricing Strategies in Cognitive Radio Networks with Heterogeneous Secondary Users and Retrials

In a cognitive radio (CR) system, excessive access services for secondary users (SUs) lead to a substantial increase in congestion and the retrial phenomenon, both of which degrade the performance of CR networks, especially in overload conditions. This paper investigates the price-based spectrum access control policy that characterizes the network operator\u27s provision to heterogeneous and delay-sensitive SUs through pricing strategies. Based on shared-use dynamic spectrum access (DSA), the SUs can occupy the dedicated spectrum without degrading the operations of primary users (PUs). The service to transmission of SUs can be interrupted by an arriving PU, while the interrupted SUs join a retrial pool called an orbit, later trying to use the spectrum to complete the service. In the retrial orbit, the interrupted SU competes fairly with other SUs in the orbit. Such a DSA mechanism is formulated as a retrial queue with service interruptions and general service times. Regarding the heterogeneity of delay-sensitive SUs, we consider two cases: the delay-sensitive parameter follows a discrete distribution and a continuous distribution, respectively. In equilibrium, we find that the revenue-optimal price is unique, while there may exist a continuum of equilibria for the socially optimal price. In addition, the socially optimal price is always not greater than the revenue-optimal price, and thus the socially optimal arrival rate is not less than the revenue-optimal one, which is contrary with the conclusion, i.e., the socially optimal and revenue-optimal arrival rates are consistent, drawn in the literature for homogeneous SUs. Finally, we present numerical examples to show the effect of various parameters on the operator\u27s pricing strategies and SUs\u27 behavior

Stability Problems for Stochastic Models: Theory and Applications II

Most papers published in this Special Issue of Mathematics are written by the participants of the XXXVI International Seminar on Stability Problems for Stochastic Models, 21­25 June, 2021, Petrozavodsk, Russia. The scope of the seminar embraces the following topics: Limit theorems and stability problems; Asymptotic theory of stochastic processes; Stable distributions and processes; Asymptotic statistics; Discrete probability models; Characterization of probability distributions; Insurance and financial mathematics; Applied statistics; Queueing theory; and other fields. This Special Issue contains 12 papers by specialists who represent 6 countries: Belarus, France, Hungary, India, Italy, and Russia