József Bíró

On shortest path representation

Lately, it has been proposed to use shortest path first routing to implement Traffic Engineering in IP networks. The idea is to set the link weights so that the shortest paths, and the traffic thereof, follow the paths designated by the operator. Clearly, only certain shortest path representable path sets can be used in this setting, that is, paths which become shortest paths over some appropriately chosen positive, integer-valued link weights. Our main objective in this paper is to distill and unify the theory of shortest path representability under the umbrella of a novel flow-theoretic framework. In the first part of the paper, we introduce our framework and state a descriptive necessary and sufficient condition to characterize shortest path representable paths. Unfortunately, traditional methods to calculate the corresponding link weights usually produce a bunch of superfluous shortest paths, often leading to congestion along the unconsidered paths. Thus, the second part of the paper is devoted to reducing the number of paths in a representation to the bare minimum. To the best of our knowledge, this is the first time that an algorithm is proposed, which is not only able to find a minimal representation in polynomial time, but also assures link weight integrality. Moreover, we give a necessary and sufficient condition to the existence of a one-to-one mapping between a path set and its shortest path representation. However, as revealed by our simulation studies, this condition seems overly restrictive and instead, minimal representations prove much more beneficial.

Call admission control in generalized processor sharing (GPS) schedulers using non-rate proportional weighting of sessions

Generalized processor sharing (GPS) is an ideal fluid scheduling discipline that supports well defined delay and loss bounds on leaky-bucket constrained traffic. Its packetized versions (WFQ, WF2Q, PGPS etc.) are considered as the packet scheduler of choice in IP routers and ATM switches of the future. The currently accepted approach for the design of GPS schedulers is based on deterministic QoS guarantees, which is overly conservative due to the applied loose bounds and leads to limitations on capacity. We developed a framework for the computation of tighter delay bounds, bandwidth and delay de-coupling in GPS systems. In this paper, we propose several effective call admission control (CAC) algorithms that work in the bandwidth and delay de-coupled system while using the tighter delay bounds presented herein. One of the proposed CAC algorithms also handles the best-effort service class beside the QoS guaranteed service classes. Performance evaluation of several CAC algorithms are presented.

Nonrate-proportional weighting of generalized processor sharing schedulers

This paper is concerned with GPS-based packet schedulers which are very important elements of guaranteed QoS networks. After recalling the basic properties of generalized processor sharing we introduce a novel approach to calculate tighter delay bounds than given in the former works of Parekh et al. (1993, 1994). This not only allows better utilization of networks resources but supports basis for arbitrary weighting of sessions. An efficient and numerically inexpensive algorithm for computing these bounds is also presented herein. Further we relax the rate-proportional weighting constraint and show that our delay bound calculation is applicable for any arbitrary (nonrate-proportional) weighted GPS system. Numerical examples demonstrate the flexibility of our algorithm in terms of adjusting delay and bandwidth easily between theoretical bounds. This approach is a very important step towards avoiding bandwidth-delay coupling which is a well-known problem of GPS-based rate-proportional servers.

Stateless multi-stage dissemination of information: Source routing revisited

Large-scale information distribution has been increasingly attracting attention, be it through uptake in new services or through recent research efforts in fields like information-centric networking. The core issue to be addressed is the more efficient distribution of information to a large set of receivers. Avoiding state in the forwarding elements is crucial for any scheme to be successful. This paper addresses this challenge by revisiting the idea of in-packet Bloom filters and source routing. As opposed to the traditional in-packet Bloom filter concept which represent the trees flatly as sets, we build our filter by enclosing limited information about the structure of the tree, namely its stage decomposition, which helps to get rid of typical Bloom filter illnesses as infinite loops and false positive forwarding. Our analytical and simulation results show that by using this information we obtain more succinct tree representation while still maintaining forwarding efficiency.

Navigable networks as Nash equilibria of navigation games

Common sense suggests that networks are not random mazes of purposeless connections, but that these connections are organized so that networks can perform their functions well. One function common to many networks is targeted transport or navigation. Here, using game theory, we show that minimalistic networks designed to maximize the navigation efficiency at minimal cost share basic structural properties with real networks. These idealistic networks are Nash equilibria of a network construction game whose purpose is to find an optimal trade-off between the network cost and navigability. We show that these skeletons are present in the Internet, metabolic, English word, US airport, Hungarian road networks, and in a structural network of the human brain. The knowledge of these skeletons allows one to identify the minimal number of edges, by altering which one can efficiently improve or paralyse navigation in the network.

A precomputation scheme for minimum interference routing: the least-critical-path-first algorithm

This paper focuses on the selection of bandwidth-guaranteed channels for communication sessions that require it. The basic idea comes from minimum interference routing: select a feasible path that puts the least possible restriction on the available transmission capacity of other communicating parties. This is achieved by circumventing some critical bottleneck links. The main contribution of the paper is a novel characterization of link criticality, the criticality threshold, which can be readily precompiled for routing dozens of subsequent calls. Based on this finding we define a generic precomputation framework for minimum interference routing, the least-critical-path-first routing algorithm. We show by means of extensive simulations that efficient route precomputation is possible even in the case, when accurate resource availability information is not immediately available.

Call admission control in generalized processor sharing schedulers with tight deterministic delay bounds

Generalized processor sharing (GPS) is reported as the most important ideal fluid scheduling discipline, which many practical packet scheduling algorithms (WFQ, WF^2Q) are built on. However, all of them bear the bandwidth-delay coupling property due to the commonly used rate-proportional weighting of sessions and offer too loose deterministic delay bounds. These deficiencies lead to poor network utilization and preclude the development of efficient call admission control (CAC) schemes. In this paper we address these problems by proposing an algorithm for tight individual session delay bound computation and several CAC algorithms for session resource assignment in a bandwidth-delay decoupled GPS system. Besides the analytical framework numerical examples as well as the complexity analysis of different CAC algorithms are also presented.

Worst-Case Deterministic Delay Bounds for Arbitrary Weighted Generalized Processor Sharing Schedulers

Generalized Processor Sharing (GPS) is realized as the most important ideal fluid scheduling discipline in guaranteed QoS networks. The well-known problem of GPS-based rate-proportional servers is the bandwidth delay coupling which leads to inefficient resource utilization. In this paper we introduce the concept of non rate-proportional (or arbitrary) weighting of sessions in GPS systems. Such an approach in a GPS node of network constrained by leaky buckets can handle bandwidth and delay parameters independently, thus allowing better utilization of network resources. Moreover, we show that even under the traditional bandwidth delay coupled system (rate-proportional weighting) it is possible to determine tighter delay bounds of sessions than that of presented in earlier papers. A numerically inexpensive algorithm, which works in any arbitrary weighted GPS system is also presented for computing delay bounds. Besides the analytical work numerical examples are also shown.

On the Representability of Arbitrary Path Sets as Shortest Paths: Theory, Algorithms, and Complexity

The question, whether an optional set of routes can be represented as shortest paths, and if yes, then how, has been a rather scarcely investigated problem up until now. In turn, an algorithm that, given an arbitrary set of traffic engineered paths, can efficiently compute OSPF link weights as to map the given paths to shortest paths may be of huge importance in today’s IP networks, which still rely on legacy shortest-path-first routing protocols. This article establishes the fundamental theory and algorithms of shortest path representability, and concludes that in general it is much more difficult task to compute shortest path representable paths than to actually calculate link weights for such paths.

Efficient Chernoff-Based Resource Assessment Techniques in Multi-Service Networks

In this paper two main performance measures are discussed for stream traffic flows multiplexed on a communication link: the saturation probability, that is the probability of resource overload, and the equivalent capacity of aggregate traffic, which is the necessary bandwidth for a link to carry the traffic with a given overflow probability. The investigations have been made in the context of rate envelope (bufferless) multiplexing by the aid of the well-known Chernoff bounding method. After showing fundamental relations between the aforementioned measures, we shed considerable light on some important properties. Finally, some newly developed estimates are presented.