Differentiable Programming & Network Calculus: Configuration Synthesis under Delay Constraints

With the advent of standards for deterministic network behavior, synthesizing network designs under delay constraints becomes the natural next task to tackle. Network Calculus (NC) has become a key method for validating industrial networks, as it computes formally verified end-to-end delay bounds. However, analyses from the NC framework have been designed to bound the delay of one flow at a time. Attempts to use classical analyses to derive a network configuration have shown that this approach is poorly suited to practical use cases. Consider finding a delay-optimal routing configuration: one model had to be created for each routing alternative, then each flow delay had to be bounded, and then the bounds had to be compared to the given constraints. To overcome this three-step process, we introduce Differential Network Calculus. We extend NC to allow the differentiation of delay bounds w.r.t. to a wide range of network parameters - such as flow paths or priority. This opens up NC to a class of efficient nonlinear optimization techniques that exploit the gradient of the delay bound. Our numerical evaluation on the routing and priority assignment problem shows that our novel method can synthesize flow paths and priorities in a matter of seconds, outperforming existing methods by several orders of magnitude

Improving Resource Efficiency in Cloud Computing

Customers inside the cloud computing market are heterogeneous in several aspects, e.g., willingness to pay and performance requirement. By taking advantage of trade-offs created by these heterogeneities, the service provider can realize a more efficient system. This thesis is concerned with methods to improve the utilization of cloud infrastructure resources, and with the role of pricing in realizing those improvements and leveraging heterogeneity. Towards improving utilization, we explore methods to optimize network usage through traffic engineering. Particularly, we introduce a novel optimization framework to decrease the bandwidth required by inter-data center networks through traffic scheduling and shaping, and then propose algorithms to improve network utilization based on the analytical results derived from the optimization. When considering pricing, we focus on elucidating conditions under which providing a mix of services can increase a service provider\u27s revenue. Specifically, we characterize the conditions under which providing a ``delayed\u27\u27 service can result in a higher revenue for the service provider, and then offer guidelines for both users and providers

Algorithms and efficiency of Network calculus

This document presents some results obtained in the field of network calculus, a theory based on the (min,plus) algebra and whose aim is to compute worst-case performance bounds in communication networks. This theory models flows circulating in a network and the service offeredby the network elements by cumulative functions and those functions are abstracted by enveloped on which the computations are performed.Several aspects are addressed. A first part is devoted to the clarification and the improvements of the performance bounds computed using this theory: the different typesof service curves and the relation between them are clarified; a new operator of packet curves introduced, in order to describe the packetsizes the same way as the flows; and we improve the way of computing worst-case performance bounds, that is classically based on the(min,plus) operators, by introducing linear programs that compute the exact worst-case performances in some cases and improve the bounds inthe other cases.The second part presents some examples other application of the results first developed for networks calculus: algorithms of convolution of (min,plus) functions have received a lot of attention by the network calculus community in order to compute bounds efficiently. We show here an example of use for approximating the numerical solution of the Hamilton-Jacobi equation. Another example is to use the concept of arrival curve to supervise a flow. This is done with simple algorithm that can follow the evolution of the behavior of a flow