On deciding stability of multiclass queueing networks under buffer priority scheduling policies

One of the basic properties of a queueing network is stability. Roughly speaking, it is the property that the total number of jobs in the network remains bounded as a function of time. One of the key questions related to the stability issue is how to determine the exact conditions under which a given queueing network operating under a given scheduling policy remains stable. While there was much initial progress in addressing this question, most of the results obtained were partial at best and so the complete characterization of stable queueing networks is still lacking. In this paper, we resolve this open problem, albeit in a somewhat unexpected way. We show that characterizing stable queueing networks is an algorithmically undecidable problem for the case of nonpreemptive static buffer priority scheduling policies and deterministic interarrival and service times. Thus, no constructive characterization of stable queueing networks operating under this class of policies is possible. The result is established for queueing networks with finite and infinite buffer sizes and possibly zero service times, although we conjecture that it also holds in the case of models with only infinite buffers and nonzero service times. Our approach extends an earlier related work [Math. Oper. Res. 27 (2002) 272--293] and uses the so-called counter machine device as a reduction tool.Comment: Published in at http://dx.doi.org/10.1214/09-AAP597 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Worst case burstiness increase due to FIFO multiplexing

We consider a FIFO multiplexer fed by flows that are individually constrained by arrival curves, and look for the best possible arrival curve for every output flow. This problem arises in scenarios where aggregate multiplexing is performed, such as differentiated services or front ends to optical switches. We obtain an exact result for a fluid model and for piecewise linear concave arrival curves, which are common in practice and correspond to combinations of leaky buckets

Delay Jitter Bounds and Packet Scale Rate Guarantee for Expedited Forwarding

We consider the definition of the Expedited Forwarding Per-Hop Behaviour (EF PHB) as given in RFC 2598, and its impact on worst case end-to-end delay jitter. On one hand, the definition in RFC 2598 can be used to predict extremely low end-to-end delay jitter, independent of the network scale. On the other hand, we find that the worst case delay jitter can be made arbitrarily large, while each flow traverses at most a specified number of hops, if we allow networks to become arbitrarily large, this is in contradiction with the previous statement. We analyze where the contradiction originates, and find the explanation. It resides in the fact that the definition in RFC 2598 is not easily implementable in schedulers we know of, mainly because it is not formal enough, and also because it does not contain an error term. We propose a new definition for the EF PHB, called ``Packet Scale Rate Guarante

On Cyclic Dependencies and Regulators in Time-Sensitive Networks

For time-sensitive networks, as in the context of IEEE TSN and IETF Detnet, cyclic dependencies are associated with certain fundamental properties such as improving availability and decreasing reconfiguration effort. Nevertheless, the existence of cyclic dependencies can cause very large latency bounds or even global instability, thus making the proof of the timing predictability of such networks a much more challenging issue. Cyclic dependencies can be removed by reshaping flows inside the network, by means of regulators. We consider FIFO-per-class networks with two types of regulators: perflow regulators and interleaved regulators (the latter reshape entire flow aggregates). Such regulators come with a hardware cost that is less for an interleaved regulator than for a perflow regulator; both can affect the latency bounds in different ways. We analyze the benefits of both types of regulators in partial and full deployments in terms of latency. First, we propose Low-Cost Acyclic Network (LCAN), a new algorithm for finding the optimum number of regulators for breaking all cyclic dependencies. Then, we provide another algorithm, Fixed- Point Total Flow Analysis (FP-TFA), for computing end-to-end delay bounds for general topologies, i.e., with and without cyclic dependencies. An extensive analysis of these proposed algorithms was conducted on generic grid topologies. For these test networks, we find that FP-TFA computes small latency bounds; but, at a medium to high utilization, the benefit of regulators becomes apparent. At high utilization or for high line transmission-rates, a small number of per-flow regulators has an effect on the latency bound larger than a small number of interleaved regulators. Moreover, interleaved regulators need to be placed everywhere in the network to provide noticeable improvements. We validate the applicability of our approaches on a realistic industrial timesensitive network

Network level performance of differentiated services (diffserv) networks

The Differentiated Services (DiffServ) architecture is a promising means of providing Quality of Service (QoS) in Internet. In DiffServ networks, three service classes, or Per-hop Behaviors (PHBs), have been defined: Expedited Forwarding (EF), Assured Forwarding (AF) and Best Effort (BE). In this dissertation, the performance of DiffServ networks at the network level, such as end-to-end QoS, network stability, and fairness of bandwidth allocation over the entire network have been extensively investigated. It has been shown in literature that the end-to-end delay of EF traffic can go to infinity even in an over-provisioned network. In this dissertation, a simple scalable aggregate scheduling scheme, called Youngest Serve First (YSF) algorithm is proposed. YSF is not only able to guarantee finite end-to-end delay, but also to keep a low scheduling complexity. With respect to the Best Effort traffic, Random Exponential Marking (REM), an existing AQM scheme is studied under a new continuous time model, and its local stable condition is presented. Next, a novel virtual queue and rate based AQM scheme (VQR) is proposed, and its local stability condition has been presented. Then, a new AQM framework, Edge-based AQM (EAQM) is proposed. EAQM is easier to implement, and it achieves similar or better performance than traditional AQM schemes. With respect to the Assured Forwarding, a network-assist packet marking (NPM) scheme has been proposed. It has been demonstrated that NPM can fairly distribute bandwidth among AF aggregates based on their Committed Information Rates (CIRs) in both single and multiple bottleneck link networks

MANETs: Internet Connectivity and Transport Protocols

A Mobile Ad hoc Network (MANET) is a collection of mobile nodes connected together over a wireless medium, which self-organize into an autonomous multi-hop wireless network. This kind of networks allows people and devices to seamlessly internetwork in areas with no pre-existing communication infrastructure, e.g., disaster recovery environments. Ad hoc networking is not a new concept, having been around in various forms for over 20 years. However, in the past only tactical networks followed the ad hoc networking paradigm. Recently, the introduction of new technologies such as IEEE 802.11, are moved the application field of MANETs to a more commercial field. These evolutions have been generating a renewed and growing interest in the research and development of MANETs. It is widely recognized that a prerequisite for the commercial penetration of the ad hoc networking technologies is the integration with existing wired/wireless infrastructure-based networks to provide an easy and transparent access to the Internet and its services. However, most of the existing solutions for enabling the interconnection between MANETs and the Internet are based on complex and inefficient mechanisms, as Mobile-IP and IP tunnelling. This thesis describes an alternative approach to build multi-hop and heterogeneous proactive ad hoc networks, which can be used as flexible and low-cost extensions of traditional wired LANs. The proposed architecture provides transparent global Internet connectivity and address autocofiguration capabilities to mobile nodes without requiring configuration changes in the pre-existing wired LAN, and relying on basic layer-2 functionalities. This thesis also includes an experimental evaluation of the proposed architecture and a comparison between this architecture with a well-known alternative NAT-based solution. The experimental outcomes confirm that the proposed technique ensures higher per-connection throughputs than the NAT-based solution. This thesis also examines the problems encountered by TCP over multi-hop ad hoc networks. Research on efficient transport protocols for ad hoc networks is one of the most active topics in the MANET community. Such a great interest is basically motivated by numerous observations showing that, in general, TCP is not able to efficiently deal with the unstable and very dynamic environment provided by multi-hop ad hoc networks. This is because some assumptions, in TCP design, are clearly inspired by the characteristics of wired networks dominant at the time when it was conceived. More specifically, TCP implicitly assumes that packet loss is almost always due to congestion phenomena causing buffer overflows at intermediate routers. Furthermore, it also assumes that nodes are static (i.e., they do not change their position over time). Unfortunately, these assumptions do not hold in MANETs, since in this kind of networks packet losses due to interference and link-layer contentions are largely predominant, and nodes may be mobile. The typical approach to solve these problems is patching TCP to fix its inefficiencies while preserving compatibility with the original protocol. This thesis explores a different approach. Specifically, this thesis presents a new transport protocol (TPA) designed from scratch, and address TCP interoperability at a late design stage. In this way, TPA can include all desired features in a neat and coherent way. This thesis also includes an experimental, as well as, a simulative evaluation of TPA, and a comparison between TCP and TPA performance (in terms of throughput, number of unnecessary transmissions and fairness). The presented analysis considers several of possible configurations of the protocols parameters, different routing protocols, and various networking scenarios. In all the cases taken into consideration TPA significantly outperforms TCP

Improving Large-Scale Network Traffic Simulation with Multi-Resolution Models

Simulating a large-scale network like the Internet is a challenging undertaking because of the sheer volume of its traffic. Packet-oriented representation provides high-fidelity details but is computationally expensive; fluid-oriented representation offers high simulation efficiency at the price of losing packet-level details. Multi-resolution modeling techniques exploit the advantages of both representations by integrating them in the same simulation framework. This dissertation presents solutions to the problems regarding the efficiency, accuracy, and scalability of the traffic simulation models in this framework. The ``ripple effect\u27\u27 is a well-known problem inherent in event-driven fluid-oriented traffic simulation, causing explosion of fluid rate changes. Integrating multi-resolution traffic representations requires estimating arrival rates of packet-oriented traffic, calculating the queueing delay upon a packet arrival, and computing packet loss rate under buffer overflow. Real time simulation of a large or ultra-large network demands efficient background traffic simulation. The dissertation includes a rate smoothing technique that provably mitigates the ``ripple effect\u27\u27, an accurate and efficient approach that integrates traffic models at multiple abstraction levels, a sequential algorithm that achieves real time simulation of the coarse-grained traffic in a network with 3 tier-1 ISP (Internet Service Provider) backbones using an ordinary PC, and a highly scalable parallel algorithm that simulates network traffic at coarse time scales