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

On Time Synchronization Issues in Time-Sensitive Networks with Regulators and Nonideal Clocks

Flow reshaping is used in time-sensitive networks (as in the context of IEEE TSN and IETF Detnet) in order to reduce burstiness inside the network and to support the computation of guaranteed latency bounds. This is performed using per-flow regulators (such as the Token Bucket Filter) or interleaved regulators (as with IEEE TSN Asynchronous Traffic Shaping). Both types of regulators are beneficial as they cancel the increase of burstiness due to multiplexing inside the network. It was demonstrated, by using network calculus, that they do not increase the worst-case latency. However, the properties of regulators were established assuming that time is perfect in all network nodes. In reality, nodes use local, imperfect clocks. Time-sensitive networks exist in two flavours: (1) in non-synchronized networks, local clocks run independently at every node and their deviations are not controlled and (2) in synchronized networks, the deviations of local clocks are kept within very small bounds using for example a synchronization protocol (such as PTP) or a satellite based geo-positioning system (such as GPS). We revisit the properties of regulators in both cases. In non-synchronized networks, we show that ignoring the timing inaccuracies can lead to network instability due to unbounded delay in per-flow or interleaved regulators. We propose and analyze two methods (rate and burst cascade, and asynchronous dual arrival-curve method) for avoiding this problem. In synchronized networks, we show that there is no instability with per-flow regulators but, surprisingly, interleaved regulators can lead to instability. To establish these results, we develop a new framework that captures industrial requirements on clocks in both non-synchronized and synchronized networks, and we develop a toolbox that extends network calculus to account for clock imperfections.Comment: ACM SIGMETRICS 2020 Boston, Massachusetts, USA June 8-12, 202

Statistical Delay Bound for WirelessHART Networks

In this paper we provide a performance analysis framework for wireless industrial networks by deriving a service curve and a bound on the delay violation probability. For this purpose we use the (min,x) stochastic network calculus as well as a recently presented recursive formula for an end-to-end delay bound of wireless heterogeneous networks. The derived results are mapped to WirelessHART networks used in process automation and were validated via simulations. In addition to WirelessHART, our results can be applied to any wireless network whose physical layer conforms the IEEE 802.15.4 standard, while its MAC protocol incorporates TDMA and channel hopping, like e.g. ISA100.11a or TSCH-based networks. The provided delay analysis is especially useful during the network design phase, offering further research potential towards optimal routing and power management in QoS-constrained wireless industrial networks.Comment: Accepted at PE-WASUN 201

Theories and Models for Internet Quality of Service

We survey recent advances in theories and models for Internet Quality of Service (QoS). We start with the theory of network calculus, which lays the foundation for support of deterministic performance guarantees in networks, and illustrate its applications to integrated services, differentiated services, and streaming media playback delays. We also present mechanisms and architecture for scalable support of guaranteed services in the Internet, based on the concept of a stateless core. Methods for scalable control operations are also briefly discussed. We then turn our attention to statistical performance guarantees, and describe several new probabilistic results that can be used for a statistical dimensioning of differentiated services. Lastly, we review recent proposals and results in supporting performance guarantees in a best effort context. These include models for elastic throughput guarantees based on TCP performance modeling, techniques for some quality of service differentiation without access control, and methods that allow an application to control the performance it receives, in the absence of network support

Advances in Internet Quality of Service

We describe recent advances in theories and architecture that support performance guarantees needed for quality of service networks. We start with deterministic computations and give applications to integrated services, differentiated services, and playback delays. We review the methods used for obtaining a scalable integrated services support, based on the concept of a stateless core. New probabilistic results that can be used for a statistical dimensioning of differentiated services are explained; some are based on classical queuing theory, while others capitalize on the deterministic results. Then we discuss performance guarantees in a best effort context; we review: methods to provide some quality of service in a pure best effort environment; methods to provide some quality of service differentiation without access control, and methods that allow an application to control the performance it receives, in the absence of network support

Token bus LAN performance : modeling and simulation

A simulation model based on CSIM, a process oriented simulated language, to analyze the performance of the Token Bus protocol is developed. Performance measures such as throughput, average delay and maximum delay per packet are presented. System performance is analyzed for different loads, number of stations, network lengths, different physical and logical distribution of the stations with packet length as a parameter. Previous studies were based on the delay-throughput analysis with no discussion on the effect of variation of the logical and physical distribution of the stations on the performance of the model which is done in the present thesis. The load is offered to the network in the form of a stream of data packets with uniformly distributed inter-arrival times. A comparison of the Token Bus model with that of a CSNIA/CD model shows that the physical distribution of the stations has a minimum effect on the performance of the model in the case of the Token Bus model but has a considerable effect on that of the CSMA/CD model

Quasi-Deterministic Burstiness Bound for Aggregate of Independent, Periodic Flows

Time-sensitive networks require timely and accurate monitoring of the status of the network. To achieve this, many devices send packets periodically, which are then aggregated and forwarded to the controller. Bounding the aggregate burstiness of the traffic is then crucial for effective resource management. In this paper, we are interested in bounding this aggregate burstiness for independent and periodic flows. A deterministic bound is tight only when flows are perfectly synchronized, which is highly unlikely in practice and would be overly pessimistic. We compute the probability that the aggregate burstiness exceeds some value. When all flows have the same period and packet size, we obtain a closed-form bound using the Dvoretzky-Kiefer-Wolfowitz inequality. In the heterogeneous case, we group flows and combine the bounds obtained for each group using the convolution bound. Our bounds are numerically close to simulations and thus fairly tight. The resulting aggregate burstiness estimated for a non-zero violation probability is considerably smaller than the deterministic one: it grows in $\sqrt{n\log{n}}$, instead of $n$, where $n$ is the number of flows