Jörg Liebeherr

New strategies for assigning real-time tasks to multiprocessor systems

Optimal scheduling of real-time tasks on multiprocessor systems is known to be computationally intractable for large task sets. Any practical scheduling algorithm for assigning real-time tasks to a multiprocessor system presents a trade-off between its computational complexity and its performance. In this study, new schedulability conditions are presented for homogeneous multiprocessor systems where individual processors execute the rate-monotonic scheduling algorithm. The conditions are used to develop new strategies for assigning real-time tasks to processors. The performance of the new strategies is shown to be significantly better than suggested by the existing literature. Under the realistic assumption that the load of each real-time task is small compared to the processing speed of each processor, it is shown that the processors can be almost fully utilized.

Application-layer multicasting with Delaunay triangulation overlays

Application-layer multicast supports group applications without the need for a network-layer multicast protocol. Here, applications arrange themselves in a logical overlay network and transfer data within the overlay. We present an application-layer multicast solution that uses a Delaunay triangulation as an overlay network topology. An advantage of using a Delaunay triangulation is that it allows each application to locally derive next-hop routing information without requiring a routing protocol in the overlay. A disadvantage of using a Delaunay triangulation is that the mapping of the overlay to the network topology at the network and data link layer may be suboptimal. We present a protocol, called Delaunay triangulation (DT protocol), which constructs Delaunay triangulation overlay networks. We present measurement experiments of the DT protocol for overlay networks with up to 10 000 members, that are running on a local PC cluster with 100 Linux PCs. The results show that the protocol stabilizes quickly, e.g., an overlay network with 10 000 nodes can be built in just over 30 s. The traffic measurements indicate that the average overhead of a node is only a few kilobits per second if the overlay network is in a steady state. Results of throughput experiments of multicast transmissions (using TCP unicast connections between neighbors in the overlay network) show an achievable throughput of approximately 15 Mb/s in an overlay with 100 nodes and 2 Mb/s in an overlay with 1000 nodes.

Deterministic delay bounds for VBR video in packet-switching networks: fundamental limits and practical trade-offs

Compressed digital video is one of the most important traffic types in future integrated services networks. However, a network service that supports delay-sensitive video imposes many problems since compressed video sources are variable bit rate (VBR) with a high degree of burstiness. In this paper, we consider a network service that can provide deterministic guarantees on the minimum throughput and the maximum delay of VBR video traffic. A common belief is that due to the burstiness of VBR traffic, such a service will not be efficient and will necessarily result in low network utilization. We investigate the fundamental limits and trade-offs in providing deterministic performance guarantees to video and use a set of 10 to 30 min. long MPEG-compressed video traces for evaluation. Contrary to conventional wisdom, we are able to show that, in many cases, a deterministic service can be provided to video traffic while maintaining a reasonable level of network utilization. We first consider an ideal network environment that employs the most accurate deterministic, time-invariant video traffic characterizations, the optimal earliest-deadline-first packet schedulers, and exact admission control conditions. The utilization achievable in this situation provides the fundamental limits of a deterministic service. We then investigate the utilization limits in a network environment that takes into account practical constraints, such as the need for simple and efficient policing mechanisms, packet scheduling algorithms, and admission control tests.

A network calculus with effective bandwidth

This paper establishes a link between two principal tools for the analysis of network traffic, namely, effective bandwidth and network calculus. It is shown that a general version of effective bandwidth can be expressed within the framework of a probabilistic version of the network calculus, where both arrivals and service are specified in terms of probabilistic bounds. By formulating well-known effective bandwidth expressions in terms of probabilistic envelope functions, the developed network calculus can be applied to a wide range of traffic types, including traffic that has self-similar characteristics. As applications, probabilistic lower bounds are presented on the service given by three different scheduling algorithms: static priority, earliest deadline first, and generalized processor sharing. Numerical examples show the impact of specific traffic models and scheduling algorithms on the multiplexing gain in a network.

Statistical service assurances for traffic scheduling algorithms

Network services for the most demanding advanced networked applications which require absolute, per-flow service assurances can be deterministic or statistical. By exploiting the statistical properties of traffic, statistical assurances can extract more capacity from a network than deterministic assurances. We consider statistical service assurances for traffic scheduling algorithms. We present functions, so-called effective envelopes, which are, with high certainty, upper bounds of multiplexed traffic. Effective envelopes can be used to obtain bounds on the amount of traffic on a link that can be provisioned with statistical service assurances. We show that our bounds can be applied to a variety of traffic scheduling algorithms. In fact, one can reuse existing admission control functions for scheduling algorithms with deterministic assurances. We present numerical examples which compare the number of flows with statistical assurances that can be admitted with our effective envelope approach to those achieved with existing methods.

Fundamental limits and tradeoffs of providing deterministic guarantees to VBR video traffic

Compressed digital video is one of the most important traffic types in future integrated services networks. However, a network service that supports delay-sensitive video imposes many problems since compressed video sources are variable bit rate (VBR) with a high degree of burstiness. In this paper, we consider a network service that can provide deterministic guarantees on the minimum throughput and the maximum delay of VBR video traffic. A common belief is that due to the burstiness of VBR traffic, such a service will not be efficient and will necessarily result in low network utilization. We investigate the fundamental limits and tradeoffs in providing deterministic performance guarantees to video and use a set of 10 to 90 minute long MPEG-compressed video traces for evaluation. Contrary to conventional wisdom, we are able to show that, in many cases, a deterministic service can be provided to video traffic while maintaining a reasonable level of network utilization. We first consider an ideal network environment that employs the most accurate deterministic, time-invariant video traffic characterizations, Earliest-Deadline-First packet schedulers, and exact admission control conditions. The utilization achievable in this situation provides the fundamental limits of a deterministic service. We then investigate the utilization limits in a network environment that takes into account practical constraints, such as the need for fast policing mechanisms, simple packet scheduling algorithms, and efficient admission control tests.

A network service curve approach for the stochastic analysis of networks

The stochastic network calculus is an evolving new methodology for backlog and delay analysis of networks that can account for statistical multiplexing gain. This paper advances the stochastic network calculus by deriving a network service curve, which expresses the service given to a flow by the network as a whole in terms of a probabilistic bound. The presented network service curve permits the calculation of statistical end-to-end delay and backlog bounds for broad classes of arrival and service distributions. The benefits of the derived service curve are illustrated for the exponentially bounded burstiness (EBB) traffic model. It is shown that end-to-end performance measures computed with a network service curve are bounded by O(Hlog H), where H is the number of nodes traversed by a flow. Using currently available techniques that compute end-to-end bounds by adding single node results, the corresponding performance measures are bounded by O(H3).

A Min-Plus Calculus for End-to-End Statistical Service Guarantees

The network calculus offers an elegant framework for determining worst-case bounds on delay and backlog in a network. This paper extends the network calculus to a probabilistic framework with statistical service guarantees. The notion of a statistical service curve is presented as a probabilistic bound on the service received by an individual flow or an aggregate of flows. The problem of concatenating per-node statistical service curves to form an end-to-end (network) statistical service curve is explored. Two solution approaches are presented that can each yield statistical network service curves. The first approach requires the availability of time scale bounds at which arrivals and departures at each node are correlated. The second approach considers a service curve that describes service over time intervals. Although the latter description of service is less general, it is argued that many practically relevant service curves may be compliant to this description

Scaling properties of statistical end-to-end bounds in the network calculus

The stochastic network calculus is an evolving new methodology for backlog and delay analysis of networks that can account for statistical multiplexing gain. This paper advances the stochastic network calculus by deriving a network service curve, which expresses the service given to a flow by the network as a whole in terms of a probabilistic bound. The presented network service curve permits the calculation of statistical end-to-end delay and backlog bounds for broad classes of arrival and service distributions. The benefits of the derived service curve are illustrated for the exponentially bounded burstiness (EBB) traffic model. It is shown that end-to-end performance measures computed with a network service curve are bounded by /spl Oscr/(H log H), where H is the number of nodes traversed by a flow. Using currently available techniques, which compute end-to-end bounds by adding single node results, the corresponding performance measures are bounded by /spl Oscr/(H/sup 3/).

A Quantitative Assured Forwarding service

The Assured Forwarding (AF) service of the IETF DiffServ architecture provides a qualitative service differentiation between classes of traffic, in the sense that a low-priority class experiences higher loss rates and higher delays than a high-priority class. However, the AF service does not quantify the difference in the service given to classes. In an effort to strengthen the service guarantees of the AF service, we propose a Quantitative Assured Forwarding service with absolute and proportional differentiation of loss, service rates, and packet delays. We present a feedback-based algorithm which enforces the desired class-level differentiation on a per-hop basis, without the need for admission control or signaling. Measurement results from a testbed of FreeBSD PC-routers on a 100 Mbit/s Ethernet network show the effectiveness of the proposed service, and indicate that our implementation is suitable for networks with high data rates.