Stability and Delay Bounds in Heterogeneous Networks of Aggregate Schedulers

Aggregate scheduling is one of the most promising solutions to the issue of scalability in networks, like DiffServ networks and high speed switches, where hard QoS guarantees are required. For networks of FIFO aggregate schedulers, the main existing sufficient conditions for stability (the possibility to derive bounds to delay and backlog at each node) are of little practical utility, as they are either relative to specific topologies, or based on strong ATM- like assumptions on the network (the so-called ”RIN” result), or they imply an extremely low node utilization. We use a deterministic approach to this problem. We identify a non linear operator on a vector space of finite (but large) dimension, and we derive a first sufficient condition for stability, based on the super-additive closure of this operator. Second, we use different upper bounds of this operator to obtain practical results. We find new sufficient conditions for stability, valid in an heterogeneous environment and without any of the restrictions of existing results. We present a polynomial time algorithm to test our sufficient conditions for stability. We show that with leaky-bucket constrained flows, the inner bound to the stability region derived with our algorithm is always larger than the one determined by all existing results. We prove that all the main existing results can be derived as special cases of our results. We also present a method to compute delay bounds in practical cases

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

Generalization of the RIN result to heterogeneous networks of aggregate schedulers and leaky bucket constrained flows

We consider networks of FIFO aggregate schedulers. Quite surprisingly, the natural condition (node utilization inferior to one) in general is not sufficient in these networks to ensure stability (boundedness of delay and backlog at each node). Deriving good sufficient conditions for stability and delay bounds for these networks is of fundamental importance if we want to offer quality of service guarantees in such networks as Diffserv networks, high speed switches and network-on-chips. The main existing sufficient conditions for stability in these networks are the "DiffServ bound" [1] and the Route Interference Number (RIN) result [2]. We use an algebraic approach. First, we develop a model of the network as a dynamical system, and we show how the problem can be reduced to properties of the state transition function. Second, we obtain new sufficient conditions for stability valid without any of the restrictions of the "RIN result". We show that in practical cases, when flows are leaky bucket constrained, the new sufficient conditions perform better than existing results. We also prove that the "RIN result" can be derived as a special case from our approach. We finally derive an expression for a bound to delay at all nodes

Generalization of the RIN Result to Heterogeneous Networks of Aggregate Schedulers and Leaky Bucket Constrained Flows

We consider networks of FIFO aggregate schedulers. Quite surprisingly, the natural condition (node utilization inferior to one) in general is not sufficient in these networks to ensure stability (boundedness of delay and backlog at each node). Deriving good sufficient conditions for stability and delay bounds for these networks is of fundamental importance if we want to offer quality of service guarantees in such networks as DiffServ networks, high speed switches and network-on-chips. The main existing sufficient conditions for stability in these networks are the “DiffServ bound” [1] and the Route Interference Number (RIN) result [2]. We use an algebraic approach. First, we develop a model of the network as a dynamical system, and we show how the problem can be reduced to properties of the state transition function. Second, we obtain new sufficient conditions for stability valid without any of the restrictions of the “RIN result”. We show that in practical cases, when flows are leaky bucket constrained, the new sufficient conditions perform better than existing results. We also prove that the “RIN result” can be derived as a special case from our approach. We finally derive an expression for a bound to delay at all nodes

Investigation of delay jitter of heterogeneous traffic in broadband networks

Scope and Methodology of Study: A critical challenge for both wired and wireless networking vendors and carrier companies is to be able to accurately estimate the quality of service (QoS) that will be provided based on the network architecture, router/switch topology, and protocol applied. As a result, this thesis focuses on the theoretical analysis of QoS parameters in term of inter-arrival jitter in differentiated services networks by deploying analytic/mathematical modeling technique and queueing theory, where the analytic model is expressed in terms of a set of equations that can be solved to yield the desired delay jitter parameter. In wireless networks with homogeneous traffic, the effects on the delay jitter in reference to the priority control scheme of the ARQ traffic for the two cases of: 1) the ARQ traffic has a priority over the original transmission traffic; and 2) the ARQ traffic has no priority over the original transmission traffic are evaluated. In wired broadband networks with heterogeneous traffic, the jitter analysis is conducted and the algorithm to control its effect is also developed.Findings and Conclusions: First, the results show that high priority packets always maintain the minimum inter-arrival jitter, which will not be affected even in heavy load situation. Second, the Gaussian traffic modeling is applied using the MVA approach to conduct the queue length analysis, and then the jitter analysis in heterogeneous broadband networks is investigated. While for wireless networks with homogeneous traffic, binomial distribution is used to conduct the queue length analysis, which is sufficient and relatively easy compared to heterogeneous traffic. Third, develop a service discipline called the tagged stream adaptive distortion-reducing peak output-rate enforcing to control and avoid the delay jitter increases without bound in heterogeneous broadband networks. Finally, through the analysis provided, the differential services, was proved not only viable, but also effective to control delay jitter. The analytic models that serve as guidelines to assist network system designers in controlling the QoS requested by customer in term of delay jitter

Statistical Service Guarantees for Traffic Scheduling in High-Speed Data Networks

School of Electrical and Computer Engineerin