Greedy geometric routing enables scalable, stateless communication in IoT and edge networks by relying solely on local coordinate information. However, this efficiency is underpinned by a structural backbone—the Hyperbolic Minimum Spanning Tree (HMST)—which introduces critical implications for performance and resilience. We analyze the HMST as a locally inferable routing scaffold emerging from hyperbolic embeddings, using Edge Load Centrality (ELC) to assess its importance. We show that HMST edges carry a disproportionate routing load and that removing them causes up to $50 \%$ failure in greedy routing—far exceeding the impact of random removals. While this reveals a vulnerability, the HMST’s local reconstructability also enables autonomous recovery of the network. We discuss the implications for resilient, self-organizing network management and coordinate-aware security.

Hyperbolically embedded networks have emerged as powerful structures for efficient routing and management in diverse fields, including internet infrastructure, edge computing, and IoT environments. Leveraging the rich geometric information inherent in hyperbolic coordinates-such as hierarchy, popularity, and node similarity-these networks achieve scalability and optimal performance. However, the detailed structural information encoded by these coordinates also exposes such networks to novel vulnerabilities. This study introduces a distributed, selforganizing attack model specifically designed to exploit hyperbolic embeddings through strategic link removals. Nodes independently identify inter-sector connections based solely on local geometric coordinates, progressively dismantling the network's global connectivity. Our comparative evaluation demonstrates that the proposed sector-based attack efficiently fragments the network while removing fewer links compared to traditional partitioning methods. Analysis of edge removal distribution reveals insights into node vulnerability patterns and network resilience. This work highlights the necessity of addressing such security threats proactively and discusses potential countermeasures, underscoring the inherent challenges due to the global nature of geometric embeddings.

The growing scale and complexity of Internet of Things (IoT) networks present critical challenges for maintaining and recovering connectivity, especially in dynamic environments or after large-scale fragmentation caused by disasters. Traditional centralized approaches often face scalability, resilience, and energy efficiency issues. Hyperbolic geometry, which has successfully modeled hierarchical and scale-free structures in large-scale systems such as the Internet's AS topology, offers a promising foundation for addressing these challenges. This paper introduces hyperbolic trees as a novel framework for IoT connectivity management. Nodes are embedded in a hyperbolic plane, and connectivity is maintained or restored through a simple local rule: each node connects to the nearest node with a smaller radial coordinate. This distributed, asynchronous approach allows nodes to autonomously reorganize and recover connectivity without centralized coordination, ensuring scalability and adaptability. We demonstrate that hyperbolic trees provide a robust, energy-efficient solution for both maintaining and recovering IoT network connectivity. Numerical results validate the framework's scalability and effectiveness, highlighting its applicability in scenarios ranging from routine management to disaster recovery. These findings establish hyperbolic trees as a practical and scalable tool for resilient IoT connectivity management in next-generation networks.

To evaluate the expected availability of a backbone network service, the administrator should consider all possible failure scenarios under the specific service availability model stipulated in the corresponding service-level agreement. Given the increase in natural disasters and malicious attacks with geographically extensive impact, considering only independent single component failures is often insufficient. This paper builds a stochastic model of geographically correlated link failures caused by disasters to estimate the hazards an optical backbone network may be prone to and to understand the complex correlation between possible link failures. We first consider link failures only and later extend our model also to capture node failures. With such a model, one can quickly extract essential information such as the probability of an arbitrary set of network resources to fail simultaneously, the probability of two nodes to be disconnected, the probability of a path to survive a disaster. Furthermore, we introduce standard data structures and a unified terminology on Probabilistic Shared Risk Link Groups (PSRLGs), along with a pre-computation process, which represents the failure probability of a set of resources succinctly. In particular, we generate a quasilinear-sized data structure in polynomial time, which allows the efficient computation of the cumulative failure probability of any set of network elements. Our evaluation is based on carefully pre-processed seismic hazard data matched to real-world optical backbone network topologies.

Routing in large-scale computer networks today is built on hop-by-hop routing: packet headers specify the destination address and routers use internal forwarding tables to map addresses to next-hop ports. In this paper we take a new look at the scalability of this paradigm. We define a new model that reduces forwarding tables to sequential strings, which then lend themselves readily to an information-theoretical analysis. Contrary to previous work, our analysis is not of worst-case nature, but gives verifiable and realizable memory requirement characterizations even when subjected to concrete topologies and routing policies. We formulate the optimal address space design problem as the task to set node addresses in order to minimize certain network-wide entropy-related measures. We derive tight space bounds for many well-known graph families and we propose a simple heuristic to find optimal address spaces for general graphs. Our evaluations suggest that in structured graphs, including most practically important network topologies, significant memory savings can be attained by forwarding table compression over our optimized address spaces. According to our knowledge, our work is the first to bridge the gap between computer network scalability and information-theory.

In order to evaluate the expected availability of a service, a network administrator should consider all possible failure scenarios under the specific service availability model stipulated in the corresponding service-level agreement. Given the increase in natural disasters and malicious attacks with geographically extensive impact, considering only independent single link failures is often insufficient. In this paper, we build a stochastic model of geographically correlated link failures caused by disasters, in order to estimate the hazards a network may be prone to, and to understand the complex correlation between possible link failures. With such a model, one can quickly extract information, such as the probability of an arbitrary set of links to fail simultaneously, the probability of two nodes to be disconnected, the probability of a path to survive a failure, etc. Furthermore, we introduce a pre-computation process, which enables us to succinctly represent the joint probability distribution of link failures. In particular, we generate, in polynomial time, a quasilinear-sized data structure, with which the joint failure probability of any set of links can be computed efficiently.

Market segmentation and technological heterogeneity are major obstacles along the way towards the realization of fast service creation expected to be part the fifth generation network feature set. In this paper we present our vision of creating a 5G Exchange that remove these obstacles by enabling the orchestration of networking and service resources in an automated way across technological and administrative domains, We describe the challenges and our motivation, the proposed networking architecture framework, showing and its relation to current standardization efforts. We present the next steps in terms of implementation and experimentation, and propose a sandbox environment where partners may experiment with life-size multidomain network orchestration.

Large-scale information dissemination in multicast communications has been increasingly attracting attention, be it through uptake in new services or through recent research efforts. In these, the core issues are supporting increased forwarding speed, avoiding state in the forwarding elements, and scaling in terms of the multicast tree size. This paper addresses all these challenges-which are crucial for any scalable multicast scheme to be successful-by revisiting the idea of in-packet Bloom filters and source routing. As opposed to the traditional in-packet Bloom filter concept, we build our Bloom filter by enclosing limited information about the structure of the tree. Analytical investigation is conducted and approximation formulas are provided for optimal-length Bloom filters, in which we got rid of typical Bloom filter illnesses such as false-positive forwarding. These filters can be used in several multicast implementations, which are demonstrated through a prototype. Thorough simulations are conducted to demonstrate the scalability of the proposed Bloom filters compared to its counterparts.

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.

The 4CaaSt project aims at developing a PaaS framework that enables flexible definition, marketing, deployment and management of Cloud-based services and applications. The major innovations proposed by 4CaaSt are the blueprint and its lifecycle management, a one stop shop for Cloud services and a PaaS level resource management featuring elasticity. 4CaaSt also provides a portfolio of ready to use Cloud native services and Cloud-aware immigrant technologies.

No abstract available.

This paper takes a first step towards generalizing compact routing to arbitrary routing policies that favor a broader set of path attributes beyond path length. Using the formalism of routing algebras we identify the algebraic requirements for a routing policy to be realizable with sublinear size routing tables and we show that a wealth of practical policies can be classified by our results. By generalizing the notion of stretch, we also discover the algebraic validity of compact routing schemes considered so far and we show that there are routing policies for which one cannot expect sublinear scaling even if permitting arbitrary constant stretch.

The problem of fair and feasible allocation of user throughputs in capacitated networks is investigated. The main contribution of the paper is an extension of network fairness, and in particular, max-min fairness from the traditional "fixed- path" model to a more versatile, routing-independent model. We show that the set of throughput configurations realizable in a capacitated network makes up a polyhedron, which gives rise to a max-min fair allocation completely analogous to the conventional case.

The problem of fair and feasible allocation of user throughputs in capacitated networks is investigated. The main contribution of the paper is a novel geometric approach, which facilitates to generalize several throughput allocation strategies, most importantly max-min fairness, from the traditional "fixed-path" model to a more versatile, routing-independent model. We show that the set of throughput configurations realizable in a capacitated network makes up a polyhedron, which gives rise to a max-min fair allocation completely analogous to the conventional one. An algorithm to compute this polyhedron is also presented, whose viability is demonstrated by comprehensive evaluation studies.

In this paper we shall establish a set of dimensioning rules for different VoIP networks using various measurement-based user behavior properties as input parameters. In order to solve the problem of dimensioning VoIP networks we focus on the aggregated VoIP links. These dimensioning procedures undoubtedly play an important role in efficiently operating extreme telephony networks like call centers and Small Businesses. Such special networks produce traffic characteristics significantly different from those of PSTN networks or general VoIP networks. Our purpose is to use simple input parameters in order to estimate the traffic characteristics of a certain link. By keeping the QoS parameters in sufficient range we present a solution to approximate link usage. The communication may be characterized with special properties such as few but very active subscribers, high internal call rate, very long-, or very short call durations, etc. In this way a simple and useful dimensioning method is achieved, utilizing the very properties of such networks, which may reduce the number of required voice channels operated.

This paper deals with bandwidth requirement estimates in buffered statistical multiplexers with the underlying many sources asymptotics modeling framework. Within this multiplexer model refined approximation for buffered workload loss ratio is considered. Based on this direct and computationally feasible equivalent bandwidth requirement estimator is presented in full accordance with the corresponding QoS constraint.

Network calculus is the result of recent developments in the area of network analysis, providing considerable insight into the behavior of (packet-based) communication networks. The classical approach uses deterministic bounds to describe systems having stochastic properties in nature, offering simple formulation to a set of-otherwise analytically hardly tractable-problems. Eliminating probabilistic nature, however, often leads to-practically hardly usable-loose bounds after quantification. In this paper, we address the problem of extending the network calculus theory to regain the advantage coming from the statistical multiplexing effect, preserving at the same time easy discussion that the original approach provides us. During the main part of the paper we introduce and discuss some important theorems about the novel effective w-arrival and w-service curves. As an example we show how to apply the results to the efficient computation of the workload loss ratio, as an important and widely used quality of service parameter while remaining in the framework and concept of the network calculus.

The estimation of resource usage in network nodes is a basic issue from the point of QoS (quality of service) provisioning. The estimation of the buffer overflow is considered in network elements represented by a service curve property. Existing results (Vojnovic, M. and Le Boudec, J.-Y., IEEE Trans. Commun., 2002; Gulya/spl acute/s, A. et al., IEEE GLOBECOM, 2004), define bounds on buffer overflow for such elements, multiplexing homogeneous and heterogeneous independent regulated inputs. The requirement of independence for the inputs can be reduced by setting up new bounds for the homogeneous case, using a bounding technique which relies only on the limited independence among the inputs (Siegel, A. et al., ACM-SIAM Symp. Discrete Algms, 1993). Beside the presentation of the new bounds, it is shown that they improve existing ones in all cases, and an investigation is given about the independence properties which are required from the input flows.

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.

The estimation of resource usage in network nodes is a basic issue from the point of QoS (quality of service) provisioning. This paper is about estimating the buffer overflow within network elements, which are represented by a service curve property. There are some previous investigations which define bounds on buffer overflow for such elements, multiplexing homogeneous and heterogeneous independent regulated inputs. The main topic of this paper is setting up new bounds for the heterogeneous case, by using a new PGF (probability generating function) approximation presented in (J. Biro et al, Proc. of 1st Int. Work. Conf. on Performance Modelling and Eval. of Heterogeneous Networks, 2003). We show, that the new bounds are also valid for the homogeneous case, so the results for the homogeneous and the heterogeneous case can be integrated into a single formula. It is also shown, that the new bounds improve the existing ones in most cases.

Dynamic traffic engineering requires the operation of load balanced routing. Load sharing, however, implies a thus far neglected, currently hidden problem: insufficient path integrity. Since load balancing requires changing the routes of traffic in order to achieve proper load distribution, path changes of ongoing communications go hand in hand with dynamic traffic engineering. Frequent path changes will not only degrade the performance of current TCP based applications but they will also dramatically influence the grade of service experienced by future QoS critical applications. To overcome this problem, we present a two level hashing based mechanism for route pinning under load balancing. We analytically formalise the path integrity and convergence time achievable for our routing model, and use these formulas for dimensioning path integrity aware load balancing.

In the widely studied and powerful bufferless fluid flow multiplexing model (bffm), important QoS measures are often considered such as saturation probability and workload loss ratio. When regulated traffic are multiplexed into a buffer, similar QoS measures can also be identified such as buffer overflow probability and buffer workload loss ratio. In this paper, we set up a family of closed-form bounds which can be applied for QoS measures arising in both multiplexing models. The bounds have been compared based on numerical investigations.

The paper is concerned with continuously operating optimization neural networks with lossy dynamics. As the main feature of the neural model time-varying nature of neuron activation functions is introduced. The model presented is general in the sense that it covers the cases of neural networks for combinatorial optimization (Hopfield-like networks) and neural models for optimization problems with continuous decision variables (i.e., Kennedy and Chua's neural network). Besides the rigorous stability analysis of the proposed neural network it is also highlighted the importance of the lossy dynamics, it is shown how to derive lossy versions of improved Hopfield neural models from it and explored the relations to other optimization neural systems.

The paper deals with analog neural networks which can be used for solving nonlinear constrained optimization tasks using the penalty function approach. The neural model developed can be regarded as asymptotically exact dynamic solver in a sense that the equilibrium state represents a solution which can be arbitrarily close to that of the original constrained optimization task. Although it is a quite natural requirement, generally it can be fulfilled only with infinitely large penalty multipliers. The neural network presented provides another way for generating solutions arbitrarily close to the exact one at finite penalty multipliers. The usefulness of the optimization neural network presented is also illustrated by numerical examples.

In this paper we set up a family of conservative upper bounds for QoS measures applicable in QoS guaranteed packet-based communication networks. The bounds are distribution free that is they depend only on the number of traffic sources, the peak rates of the flows and the mean arrival intensity of the aggregated traffic stream. No other information on the traffic distribution is required. The bounds have been developed under the well known bufferless fluid flow multiplexing (bffm) modeling framework, nevertheless, an important property is also discussed in the paper, namely they can also be applicable to the buffered statistical multiplexer case when the input flows are regulated. The performances of the bounds are analyzed and comparative numerical investigations are also presented in both multiplexing models.

The minimum cost multicommodity flow problem plays a central role in today's operations research theory with applications ranging from transportation and logistics to telecommunications network routing. In this paper, we introduce a novel Lagrangian-relaxation technique, which, given an initial feasible solution, can solve the minimum cost multicommodity flow problem as a sequence of single-commodity flow problems. Our methodology is best suited for OSPF traffic engineering, because it can rapidly improve a given path set towards approximate optimality while simultaneously provides the link weights, which implement the paths as shortest paths.

The paper is concerned with the approximation of equivalent capacity in the context of bufferless fluid flow multiplexing (BFFM) based on parsimonious characterization of traffic flows, i.e., only the number of flows, the peak arrival rates and the aggregate mean arrival rate are assumed to be known. In bufferless statistical multiplexing, a main stream of research investigates the phenomenon that the combined arrival rate of flows multiplexed on a transmission link exceeds the total link capacity. In the widely studied BFFM model, important QoS measures are often considered, such as saturation probability and workload loss ratio, and, based on these measures, the corresponding minimum transmission capacity required by the flow aggregate. New and direct estimators for the equivalent capacity are presented and compared to previously developed ones; their significance in call admission control is also highlighted. To that end we also perform different approximations of the probability generating functions of the rate distribution of the aggregate flow; they are often essential parts of QoS measure estimates.

This paper reviews the applicability of simplified bandwidth requirement estimators that need only the mean and the peak rates of traffic flows as input, instead of the full statistical description of the traffic required by their original form. The estimators approximate the effective bandwidth function, the key component of the bandwidth requirement estimate, with the logarithmic moment generating function of on-off source. It is demonstrated that this on-off type approximation has to be used with care as it results in a loss of information about the traffic streams. This is manifested in the reduction of the advanced bandwidth estimator method of the many sources asymptotics into the basic Chernoff-type technique. As a consequence bandwidth requirement estimator built on/off type approximation overlook the multiplexing gain occurring in the buffers, which results in overly conservative estimates close or equal to the peak rate when applied to traffic aggregates.

This paper proposes network level call admission control (CAC) algorithms for the most significant theoretical traffic scheduling algorithm, generalized processor sharing (GPS), and highlights important issues that arise when generalizing single node CAC results to the network level. The framework allows arbitrary network topology, in which competing leaky bucket controlled sessions are considered to be arbitrary weighted. This weighting relaxes bandwidth-delay coupling and extends the usable weight space of the admissible region, which make possible to build resource efficient CAC algorithms on the network level when combined with the tight delay bounds of [Barta, F. et al., 2001]. In order to keep end-to-end delay bounds under control, network nodes apply traffic shaping to eliminate the effects of complex traffic interactions.

This paper proposes several call admission control (CAC) algorithms for tandem networks that employ the generalized processor sharing (GPS) scheduling discipline, and also points out important network issues that are crucial in the design of network level CAC algorithms for GPS. Sessions are considered to be leaky bucket constrained and are regulated by traffic shapers at each network node. The end-to-end service curve approach of Barta et al. (2001) is used to carry out the analytical framework of our algorithms. Different CAC algorithms are developed to support different session treatment strategies and diverse server capacities. The proposed algorithms follow different end-to-end delay provisioning strategies whose performance is compared through numerical examples.

In end-to-end congestion control protocols, sources continuously obtain feedback from the network, detect the level of congestion along their network path and adjust their sending rate accordingly. The level of congestion can be represented by the loss rate in TCP Tahoe/Reno, queuing delay in TCP Vegas or marking probability in ECN-capable protocols. We call them the congestion measures. Our aim in this paper is to generalize the congestion measures and investigate their common properties, especially the so-called "population effect", where the total congestion level tends to increase with the number of active connections. This better understanding of the congestion measures promotes the use of ECN-like router mechanisms to avoid the negative impact of population effect. We also propose the use of congestion measures in available bandwidth estimation and dynamic path selection algorithms.

This paper identifies the requirements placed against a resource manager function for use in QoS-enabled IP networks. The structure of the Internet and the composition of the services motivate the development of on-line resource brokers that can make admission decisions in real time, based on the best up-to-date information available on the state of the network. The difficulties with traffic models and traffic characterisation stimulate the use of measurement-based techniques that bypass the modelling step and provide the resource requirements of the traffic directly. The paper introduces a novel method for the computation of the bandwidth requirement of Internet traffic flows using the many sources asymptotics. The estimator method significantly reduces the computational complexity of the calculations, allowing the real-time operation of the algorithm even in a measurement-based environment. The method delivers bandwidth-type quantity, the format preferred by Internet control applications. The savings arising from the reduced computational complexity compared to existing methods are demonstrated in a numerical example.

This paper concerns the fairness of TCP Vegas, a new version of TCP proposed by Brakmo et al., (1994). Firstly, we show some uncertainties in bandwidth allocation and buffer occupancy when the system is in the stable state. These uncertainties come from the using of two threshold values (/spl alpha/, /spl beta/) in the applied innovative congestion avoidance mechanism. We propose a modification in the existing implementations of TCP Vegas to reduce the uncertainties without losing the stability. Secondly, the notion of the ideal TCP Vegas, which has no uncertainties, is defined. We prove that the ideal TCP Vegas is exactly proportionally fair in bandwidth sharing. This property of the real TCP Vegas is tested by simulation. We also show how to implement weighted proportional fairness with TCP Vegas.

This work is motivated by the increasing need of end-to-end performance bound provisioning in multi-service networks. Providing performance bounds in a networking environment is a difficult problem as traffic is bursty and its dynamics is far more complex than in a single server environment. As end-to-end bounds are basically based on local switch guarantees, computation of local performance bounds requires the knowledge of traffic conditions at inputs of each switch. This paper investigates the problem of traffic characterization of arbitrary topology networks that employ the generalized processor sharing (GPS) scheduling discipline at each node. The study focuses on the derivation of internal (at inputs of switches) traffic descriptors of sessions which are originally leaky bucket constrained at the network edge. Allowing arbitrary weight assignment of sessions the analysis classifies GPS networks into different sets by means of various stability conditions. Methods are presented for the determination of internal traffic parameters in cyclic, acyclic networks with and without virtual feedback. Numerical examples are shown for the illustration of our algorithmic approach for the above mentioned scenarios as well as for end-to-end delay computation of sessions.

We propose a solution to the problem of calculating deterministic end-to-end delay bounds in arbitrary topology networks, which employ the generalized processor sharing (GPS) discipline at each node. We give a general framework under network calculus by extending the service curve model of GPS and constructing the end-to-end service curve for each session, from which exact values of delay and backlog bounds can be computed. Network internal traffic characterization and traffic shaping are applied to support local performance bound computation. Sessions are allowed to be arbitrary weighted and virtual feedback is handled by the iterative approach of Barta, Nemeth, Szabo and Bird (see ICC2001). Numerical examples are shown to illustrate our algorithmic approach for per-session end-to-end delay bound computation.

This paper is concerned with the saturation probability of aggregate traffic data arrival rate on a communication link. This performance metric also referred to as the tail distribution of aggregate traffic is essential in traffic control and management algorithms of high speed networks including future QoS Internet. In this paper, efficient closed form upper bounds have been derived for the saturation probability when very little information is available on the aggregate traffic. The performance of these estimators is also investigated via numerical examples.

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.

The paper is concerned with analyzing a time-division multiplexing method with two priority classes. A discrete-time model is established for analyzing the queuing behaviour of low priority traffic streams. The motivation came from dynamic transfer mode (DTM) networks which uses time-division multiplexing of channels, however the results might also be used for other fast circuit switched networks. The model to be investigated is based on the important observation that from the viewpoint of low priority traffic the system behaves as a queuing system subjected to periodic server interruption. The probability generating function (p.g.f.) of the system time and system content of low priority messages is expressed in closed forms from which the first two moments can be calculated in a straightforward manner. Tail probabilities of system content and system time are also derived by applying an efficient approximation technique. Finally, we also give numerical examples as simple illustrations.

In teletraffic theory an important and useful performance measure is the tail distribution of aggregate traffic. Generally it is very hard and computationally expensive to determine the exact distribution of the aggregate traffic, even if we know the exact distribution of each traffic source. therefore, efficient estimators should be developed. In the paper, we show simple estimators which are based on Hoeffding's (1963) statistical inequalities for tail distribution. The estimators to be presented are very simple, they use only limited information on the traffic characteristics. the properties of these bounds are performed and are also compared by the accuracy and the regions of parameters where they overperform each other. Finally, we present a possibly tighter upper bounds for the tail distribution using more accurate approximations.

This paper addresses the issue of how to solve convex programming problems by analog artificial neural networks (ANNs), with applications in asynchronous transfer mode (ATM) resource management. We first show that the essential and difficult optimization problem of dimensioning the system of virtual subnetworks in ATM networks can be modeled as a convex programming task. Here the transformation of the problem into a convex programming task is a nontrivial step. We also present and analyze an analog ANN architecture that is capable of solving such convex programming tasks with time-varying penalty multipliers. The latter property makes it possible to perform quick sensitivity analysis with respect to the constraints in order to identify the bottleneck capacities in the network or those which give the highest return if we invest in extending them.