The Asymmetric Best-Effort Service

We present Asymmetric Best-Effort, a novel service to provide a ``throughput versus delay jitter'' differentiated service for IP packets. With this service, every best effort packet is marked as either green or blue. Green packets, typically sent by real-time applications such as interactive audio, receive more losses during bouts of congestion than blue ones. In return, they receive less delay jitter. Both green and blue services are best-effort. The incentive to choose one or other is based on the nature of one's traffic and on traffic conditions. If applications are TCP-friendly, an application sending blue packets will receive more throughput but also more delay jitter, than it would if it sent green packets for a given network state and path. Service provision at each cooperating router can achieved by Packet Admission Control (PAC) and scheduling. We develop and simulate an initial algorithm that supports this service. It uses a modified version of RED for packet drop differention while scheduling of blue and green packets is facilated using Earliest Deadline First (EDF). These first results show the feasiblity of the service

Branching processes, the max-plus algebra and network calculus

Branching processes can describe the dynamics of various queueing systems, peer-to-peer systems, delay tolerant networks, etc. In this paper we study the basic stochastic recursion of multitype branching processes, but in two non-standard contexts. First, we consider this recursion in the max-plus algebra where branching corresponds to finding the maximal offspring of the current generation. Secondly, we consider network-calculus-type deterministic bounds as introduced by Cruz, which we extend to handle branching-type processes. The paper provides both qualitative and quantitative results and introduces various applications of (max-plus) branching processes in queueing theory

Upconversion assisted self-pulsing in a high-concentration erbium doped fiber laser

We report results on experimental and theoretical characterisation of self-pulsing in high concentration erbium doped fibre laser which is free from erbium clusters. Unlike previous models of self-pulsing accounting for pair-induced quenching (PIQ) on the clustered erbium ions, new model has been developed with accounting for statistical nature of the excitation migration and upconversion and resonance-like pumpto-signal intensity noise transfer. The obtained results are in a good agreement with the experimental data

Mean-Field Limits Beyond Ordinary Differential Equations

16th International School on Formal Methods for the Design of Computer, Communication, and Software Systems, SFM 2016, Bertinoro, Italy, June 20-24, 2016, Advanced LecturesInternational audienceWe study the limiting behaviour of stochastic models of populations of interacting agents, as the number of agents goes to infinity. Classical mean-field results have established that this limiting behaviour is described by an ordinary differential equation (ODE) under two conditions: (1) that the dynamics is smooth; and (2) that the population is composed of a finite number of homogeneous sub-populations, each containing a large number of agents. This paper reviews recent work showing what happens if these conditions do not hold. In these cases, it is still possible to exhibit a limiting regime at the price of replacing the ODE by a more complex dynamical system. In the case of non-smooth or uncertain dynamics, the limiting regime is given by a differential inclusion. In the case of multiple population scales, the ODE is replaced by a stochastic hybrid automaton

A Domain-Specific Language for Incremental and Modular Design of Large-Scale Verifiably-Safe Flow Networks (Preliminary Report)

We define a domain-specific language (DSL) to inductively assemble flow networks from small networks or modules to produce arbitrarily large ones, with interchangeable functionally-equivalent parts. Our small networks or modules are "small" only as the building blocks in this inductive definition (there is no limit on their size). Associated with our DSL is a type theory, a system of formal annotations to express desirable properties of flow networks together with rules that enforce them as invariants across their interfaces, i.e, the rules guarantee the properties are preserved as we build larger networks from smaller ones. A prerequisite for a type theory is a formal semantics, i.e, a rigorous definition of the entities that qualify as feasible flows through the networks, possibly restricted to satisfy additional efficiency or safety requirements. This can be carried out in one of two ways, as a denotational semantics or as an operational (or reduction) semantics; we choose the first in preference to the second, partly to avoid exponential-growth rewriting in the operational approach. We set up a typing system and prove its soundness for our DSL.Comment: In Proceedings DSL 2011, arXiv:1109.032

Checking Individual Agent Behaviours in Markov Population Models by Fluid Approximation

In this chapter, we will describe, in a tutorial style, recent work on the use of fluid approximation techniques in the context of stochastic model checking. We will discuss the theoretical background and the algorithms working out an example. This approach is designed for population models, in which a (large) number of individual agents interact, which give rise to continuous time Markov chain (CTMC) models with a very large state space. We then focus on properties of individual agents in the system, specified by Continuous Stochastic Logic (CSL) formulae, and use fluid approximation techniques (specifically, the so called fast simulation) to check those properties. We will show that verification of such CSL formulae reduces to the computation of reachability probabilities in a special kind of time-inhomogeneous CTMC with a small state space, in which both the rates and the structure of the CTMC can change (discontinuously) with time. In this tutorial, we will discuss only briefly the theoretical issues behind the approach, like the decidability of the method and the consistency of the approximation scheme