Fabrice Guillemin

This paper considers an M/G/1 queue with finite capacity and phase type (PH) distributed services. The goal of the paper is to study the sensitivity of the stationary distribution of the number of customers in the queue on a given parameter, namely t...

A large proportion of jobs submitted to modern computing clusters and data centers are parallelizable and capable of running on a flexible number of computing cores or servers. Although allocating more servers to such a job results in a higher speed-up in the job’s execution, it reduces the number of servers available to other jobs, which in the worst case, can result in an incoming job not finding any available server to run immediately upon arrival. Hence, a key question to address is: how to optimally allocate servers to jobs such that (i) the average execution time across jobs is minimized and (ii) almost all jobs find at least one server immediately upon arrival. To address this question, we consider a system with n servers, where jobs are parallelizable up to $d^{(n)}$ servers and the speed-up function of jobs is concave and increasing. Jobs not finding any available servers upon entry are blocked and lost. We propose a simple server allocation scheme that achieves the minimum average execution time of accepted jobs while ensuring that the blocking probability of jobs vanishes as the system becomes large ( $n \to \infty $ ). This result is established for various traffic conditions as well as for heterogeneous workloads. To prove our result, we employ Stein’s method which also yields non-asymptotic bounds on the blocking probability and the mean execution time. Furthermore, our simulations show that the performance of the scheme is insensitive to the distribution of job execution times.

A large proportion of jobs submitted to modern computing clusters and data centers are parallelizable and capable of running on a flexible number of computing cores or servers. Although allocating more servers to such a job results in a higher speed-up in the job's execution, it reduces the number of servers available to other jobs, which in the worst case, can result in an incoming job not finding any available server to run immediately upon arrival. Hence, a key question to address is: how to optimally allocate servers to jobs such that (i) the average execution time across jobs is minimized and (ii) almost all jobs find at least one server immediately upon arrival. To address this question, we consider a system with n servers, where jobs are parallelizable up to d⁽ⁿ⁾ servers and the speed-up function of jobs is concave and increasing. Jobs not finding any available servers upon entry are blocked and lost. We propose a simple server allocation scheme that achieves the minimum average execution time of accepted jobs while ensuring that the blocking probability of jobs vanishes as the system becomes large (n → ∞). This result is established for various traffic conditions as well as for heterogeneous workloads. To prove our result, we employ Stein's method which also yields non-asymptotic bounds on the blocking probability and the mean execution time. Furthermore, our simulations show that the performance of the scheme is insensitive to the distribution of job execution times.

Summary: The last decade has witnessed important development of network softwarization that has revolutionized the practice of networks. Virtualized networks bring novel and specific requirements for the control and orchestration of containerized network functions that are scattered across the network. In this regard, the migration of virtualized network functions plays a pivotal role to best meet the requirements of optimal resource utilization, load balancing and fault tolerance. The purpose of this survey is to offer a detailed overview of the progress on container migration so as to provide a better understanding of the trade‐off between the benefits associated with the migration and the practical challenges. The paper includes a classification of the placement algorithms that map the containerized network functions on the virtualized infrastructure. Following, a taxonomy of the migration techniques that perform the transfer of the containerized microservices is proposed.

Network Slice placement with the problem of allocation of resources from a virtualized substrate network is an optimization problem which can be formulated as a multi-objective Integer Linear Programming (ILP) problem. However, to cope with the complexity of such a continuous task and seeking for optimality and automation, the use of Machine Learning (ML) techniques appear as a promising approach. We introduce a hybrid placement solution based on Deep Reinforcement Learning (DRL) and a dedicated optimization heuristic based on the "Power of Two Choices" principle. The DRL algorithm uses the so-called Asynchronous Advantage Actor Critic (A3C) algorithm for fast learning, and Graph Convolutional Networks (GCN) to automate feature extraction from the physical substrate network. The proposed Heuristically-Assisted DRL (HA-DRL) allows for the acceleration of the learning process and substantial gain in resource usage when compared against other state-of-the-art approaches, as evidenced by evaluation results.