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"

Performance Modelling and Optimisation of Multi-hop Networks

A major challenge in the design of large-scale networks is to predict and optimise the total time and energy consumption required to deliver a packet from a source node to a destination node. Examples of such complex networks include wireless ad hoc and sensor networks which need to deal with the effects of node mobility, routing inaccuracies, higher packet loss rates, limited or time-varying effective bandwidth, energy constraints, and the computational limitations of the nodes. They also include more reliable communication environments, such as wired networks, that are susceptible to random failures, security threats and malicious behaviours which compromise their quality of service (QoS) guarantees. In such networks, packets traverse a number of hops that cannot be determined in advance and encounter non-homogeneous network conditions that have been largely ignored in the literature. This thesis examines analytical properties of packet travel in large networks and investigates the implications of some packet coding techniques on both QoS and resource utilisation. Specifically, we use a mixed jump and diffusion model to represent packet traversal through large networks. The model accounts for network non-homogeneity regarding routing and the loss rate that a packet experiences as it passes successive segments of a source to destination route. A mixed analytical-numerical method is developed to compute the average packet travel time and the energy it consumes. The model is able to capture the effects of increased loss rate in areas remote from the source and destination, variable rate of advancement towards destination over the route, as well as of defending against malicious packets within a certain distance from the destination. We then consider sending multiple coded packets that follow independent paths to the destination node so as to mitigate the effects of losses and routing inaccuracies. We study a homogeneous medium and obtain the time-dependent properties of the packet’s travel process, allowing us to compare the merits and limitations of coding, both in terms of delivery times and energy efficiency. Finally, we propose models that can assist in the analysis and optimisation of the performance of inter-flow network coding (NC). We analyse two queueing models for a router that carries out NC, in addition to its standard packet routing function. The approach is extended to the study of multiple hops, which leads to an optimisation problem that characterises the optimal time that packets should be held back in a router, waiting for coding opportunities to arise, so that the total packet end-to-end delay is minimised

Separation of timescales in a two-layered network

We investigate a computer network consisting of two layers occurring in, for example, application servers. The first layer incorporates the arrival of jobs at a network of multi-server nodes, which we model as a many-server Jackson network. At the second layer, active servers at these nodes act now as customers who are served by a common CPU. Our main result shows a separation of time scales in heavy traffic: the main source of randomness occurs at the (aggregate) CPU layer; the interactions between different types of nodes at the other layer is shown to converge to a fixed point at a faster time scale; this also yields a state-space collapse property. Apart from these fundamental insights, we also obtain an explicit approximation for the joint law of the number of jobs in the system, which is provably accurate for heavily loaded systems and performs numerically well for moderately loaded systems. The obtained results for the model under consideration can be applied to thread-pool dimensioning in application servers, while the technique seems applicable to other layered systems too.Comment: 8 pages, 2 figures, 1 table, ITC 24 (2012

Dynamical Modeling of Cloud Applications for Runtime Performance Management

Cloud computing has quickly grown to become an essential component in many modern-day software applications. It allows consumers, such as a provider of some web service, to quickly and on demand obtain the necessary computational resources to run their applications. It is desirable for these service providers to keep the running cost of their cloud application low while adhering to various performance constraints. This is made difficult due to the dynamics imposed by, e.g., resource contentions or changing arrival rate of users, and the fact that there exist multiple ways of influencing the performance of a running cloud application. To facilitate decision making in this environment, performance models can be introduced that relate the workload and different actions to important performance metrics.In this thesis, such performance models of cloud applications are studied. In particular, we focus on modeling using queueing theory and on the fluid model for approximating the often intractable dynamics of the queue lengths. First, existing results on how the fluid model can be obtained from the mean-field approximation of a closed queueing network are simplified and extended to allow for mixed networks. The queues are allowed to follow the processor sharing or delay disciplines, and can have multiple classes with phase-type service times. An improvement to this fluid model is then presented to increase accuracy when the \emph{system size}, i.e., number of servers, initial population, and arrival rate, is small. Furthermore, a closed-form approximation of the response time CDF is presented. The methods are tested in a series of simulation experiments and shown to be accurate. This mean-field fluid model is then used to derive a general fluid model for microservices with interservice delays. The model is shown to be completely extractable at runtime in a distributed fashion. It is further evaluated on a simple microservice application and found to accurately predict important performance metrics in most cases. Furthermore, a method is devised to reduce the cost of a running application by tuning load balancing parameters between replicas. The method is built on gradient stepping by applying automatic differentiation to the fluid model. This allows for arbitrarily defined cost functions and constraints, most notably including different response time percentiles. The method is tested on a simple application distributed over multiple computing clusters and is shown to reduce costs while adhering to percentile constraints. Finally, modeling of request cloning is studied using the novel concept of synchronized service. This allows certain forms of cloning over servers, each modeled with a single queue, to be equivalently expressed as one single queue. The concept is very general regarding the involved queueing discipline and distributions, but instead introduces new, less realistic assumptions. How the equivalent queue model is affected by relaxing these assumptions is studied considering the processor sharing discipline, and an extension to enable modeling of speculative execution is made. In a simulation campaign, it is shown that these relaxations only has a minor effect in certain cases

Queueing Systems with Heavy Tails

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Asymptotically optimal priority policies for indexable and non-indexable restless bandits

We study the asymptotic optimal control of multi-class restless bandits. A restless bandit is a controllable stochastic process whose state evolution depends on whether or not the bandit is made active. Since finding the optimal control is typically intractable, we propose a class of priority policies that are proved to be asymptotically optimal under a global attractor property and a technical condition. We consider both a fixed population of bandits as well as a dynamic population where bandits can depart and arrive. As an example of a dynamic population of bandits, we analyze a multi-class M/M/S+M queue for which we show asymptotic optimality of an index policy.We combine fluid-scaling techniques with linear programming results to prove that when bandits are indexable, Whittle's index policy is included in our class of priority policies. We thereby generalize a result of Weber and Weiss (1990) about asymptotic optimality of Whittle's index policy to settings with (i) several classes of bandits, (ii) arrivals of new bandits, and (iii) multiple actions. Indexability of the bandits is not required for our results to hold. For non-indexable bandits we describe how to select priority policies from the class of asymptotically optimal policies and present numerical evidence that, outside the asymptotic regime, the performance of our proposed priority policies is nearly optimal