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"

Achieving Optimal Throughput and Near-Optimal Asymptotic Delay Performance in Multi-Channel Wireless Networks with Low Complexity: A Practical Greedy Scheduling Policy

In this paper, we focus on the scheduling problem in multi-channel wireless networks, e.g., the downlink of a single cell in fourth generation (4G) OFDM-based cellular networks. Our goal is to design practical scheduling policies that can achieve provably good performance in terms of both throughput and delay, at a low complexity. While a class of $O(n^{2.5} \log n)$-complexity hybrid scheduling policies are recently developed to guarantee both rate-function delay optimality (in the many-channel many-user asymptotic regime) and throughput optimality (in the general non-asymptotic setting), their practical complexity is typically high. To address this issue, we develop a simple greedy policy called Delay-based Server-Side-Greedy (D-SSG) with a \lower complexity $2n^2+2n$, and rigorously prove that D-SSG not only achieves throughput optimality, but also guarantees near-optimal asymptotic delay performance. Specifically, we show that the rate-function attained by D-SSG for any delay-violation threshold $b$, is no smaller than the maximum achievable rate-function by any scheduling policy for threshold $b-1$. Thus, we are able to achieve a reduction in complexity (from $O(n^{2.5} \log n)$ of the hybrid policies to $2n^2 + 2n$) with a minimal drop in the delay performance. More importantly, in practice, D-SSG generally has a substantially lower complexity than the hybrid policies that typically have a large constant factor hidden in the $O(\cdot)$ notation. Finally, we conduct numerical simulations to validate our theoretical results in various scenarios. The simulation results show that D-SSG not only guarantees a near-optimal rate-function, but also empirically is virtually indistinguishable from delay-optimal policies.Comment: Accepted for publication by the IEEE/ACM Transactions on Networking, February 2014. A preliminary version of this work was presented at IEEE INFOCOM 2013, Turin, Italy, April 201

Join-Idle-Queue with Service Elasticity: Large-Scale Asymptotics of a Non-monotone System

We consider the model of a token-based joint auto-scaling and load balancing strategy, proposed in a recent paper by Mukherjee, Dhara, Borst, and van Leeuwaarden (SIGMETRICS '17, arXiv:1703.08373), which offers an efficient scalable implementation and yet achieves asymptotically optimal steady-state delay performance and energy consumption as the number of servers $N\to\infty$. In the above work, the asymptotic results are obtained under the assumption that the queues have fixed-size finite buffers, and therefore the fundamental question of stability of the proposed scheme with infinite buffers was left open. In this paper, we address this fundamental stability question. The system stability under the usual subcritical load assumption is not automatic. Moreover, the stability may not even hold for all $N$. The key challenge stems from the fact that the process lacks monotonicity, which has been the powerful primary tool for establishing stability in load balancing models. We develop a novel method to prove that the subcritically loaded system is stable for large enough $N$, and establish convergence of steady-state distributions to the optimal one, as $N \to \infty$. The method goes beyond the state of the art techniques -- it uses an induction-based idea and a "weak monotonicity" property of the model; this technique is of independent interest and may have broader applicability.Comment: 30 page

Performance and reliability modelling of computing systems using spectral expansion

PhD ThesisThis thesis is concerned with the analytical modelling of computing and other discrete event systems, for steady state performance and dependability. That is carried out using a novel solution technique, known as the spectral expansion method. The type of problems considered, and the systems analysed, are represented by certain two-dimensional Markov-processes on finite or semi-infinite lattice strips. A sub set of these Markov processes are the Quasi-Birth-and-Death processes. These models are important because they have wide ranging applications in the design and analysis of modern communications, advanced computing systems, flexible manufacturing systems and in dependability modelling. Though the matrixgeometric method is the presently most popular method, in this area, it suffers from certain drawbacks, as illustrated in one of the chapters. Spectral expansion clearly rises above those limitations. This also, is shown with the aid of examples. The contributions of this thesis can be divided into two categories. They are, • The theoretical foundation of the spectral expansion method is laid. Stability analysis of these Markov processes is carried out. Efficient numerical solution algorithms are developed. A comparative study is performed to show that the spectral expansion algorithm has an edge over the matrix-geometric method, in computational efficiency, accuracy and ease of use. • The method is applied to several non-trivial and complicated modelling problems, occuring in computer and communication systems. Performance measures are evaluated and optimisation issues are addressed