Søren Blaabjerg

A new degree of freedom in ATM network dimensioning: optimizing the logical configuration

A mathematical model is presented that provides a well-defined formulation of the logical configuration problem of ATM networks (the carriers of future B-ISDN) with the objective of maximizing the total expected network revenue, given the physical network parameters and the traffic requirements of each virtual subnetwork. A two-phase solution procedure is developed in which the decision variables are the logical link capacities that specify the logical decomposition into virtual subnetworks, and the load sharing parameters. The first phase of the solution finds a global optimum in a rougher model. The second phase uses this as an initial point for a gradient-based hill climbing that applies the partial derivatives of the network revenue function obtained in a more refined model. >

Modeling and Simulation of Mixed Queueing and Loss Systems

In this paper, we investigate a multi-rate network in which wide-band calls are allowed to wait if insufficient resources are available at the time of the call arrival. On the link level, an analytical model is presented and simulations have been carried out on the network level. The results indicate that allowing a few wide-band calls to queue can give a significant improvement in performance in terms of network revenue , as well as a means to level out the blocking probabilities of the different traffic classes. This improvement becomes significant when the service discipline of the waiting calls (of different bandwidth requirements) is adaptive in the sense that longer queues get served first. This observation motivates the investigation of the impact of various buffer space assignment and queueing disciplines on network revenue and call blocking probabilities. The study of such mixed delay and queueing networks is motivated by its possible applications to traffic problems in future Broadband Integrated Services Digital Networks as well as in multi-rate cellular radio networks.

A Partially-Blocking Queueing System with CBR/VBR and ABR/UBR Arrival Streams

In this paper we consider an ATM transmission link, to which CBR or VBR and ABR or UBR calls arrive according to independent Poisson processes. CBR/VBR calls (characterized by their equivalent bandwidth) are blocked and leave the system if the available link capacity is less than required at the time of arrival. ABR/UBR calls, however, accept partial blocking, meaning that they may enter service even if the available capacity is less than the specified required peak bandwidth, but greater than the so called minimal accepted bandwidth. Partially blocked ABR/UBR calls instead experience longer service time, since smaller given bandwidth entails proportionally longer time spent in the system, as first suggested in [3] and analyzed in details herein. Throughout the life time of an ABR/UBR connection, its bandwidth consumption fluctuates in accordance with the current load on the link but always at the highest possible value up to their peak bandwidth (greedy sources). Additionally, if this minimal accepted bandwidth is unavailable at the time of arrival, ABR/UBR calls are allowed to wait in a finite queue. This system is modeled by a Continuous Time Markov Chain (CTMC) and the CBR/VBR and ABR/UBR blocking probabilities and the mean ABR/UBR waiting- and service times are derived.

Models for setting ATM parameter values

In ATM networks, a user should negotiate at connection set-up a traffic contract which includes traffic characteristics and requested QoS. The traffic characteristics currently considered are the Peak Cell Rate, the Sustainable Cell Rate, the Intrinsic Burst Tolerance and the Cell Delay Variation (CDV) tolerance(s). The values taken by these traffic parameters characterize the so-called “Worst Case Traffic” that is used by CAC procedures for accepting a new connection and allocating resources to it. Conformance to the negotiated traffic characteristics is defined, at the ingress User to Network Interface (UNI) and at subsequent Inter Carrier Interfaces (ICIs), by algorithmic rules based on the Generic Cell Rate Algorithm (GCRA) formalism. Conformance rules are implemented by policing mechanisms that control the traffic submitted by the user and discard excess traffic. It is therefore essential to set traffic characteristic values that are relevant to the considered cell stream, and that ensure that the amount of non-conforming traffic is small. Using a queueing model representation for the GCRA formalism, several methods are available for choosing the traffic characteristics. This paper presents approximate methods and discusses their applicability. We then discuss the problem of obtaining traffic characteristic values for a connection that has crossed a series of switching nodes. This problem is particularly relevant for the traffic contract components corresponding to ICIs that are distant from the original source.

Admission control of CBR/VBR and ABR/UBR call arrival streams: a Markov decision approach

This paper evaluates a Markov decision approach to connection admission control of guaranteed services and best effort services. Two different schemes that support integration of guaranteed services and best effort services are evaluated: a preemptive scheme and a partial blocking scheme. The Markov decision approach finds policies that are optimal in terms of long-term reward. The Markov decision policy performs intelligent blocking which implements bandwidth reservation for wide-band traffic. Numerical results with three traffic classes, a narrow-band and a wide-band guaranteed class and a narrow-band best effort class, show that the Markov decision method, applied to both the preemptive and the partial blocking scheme, yields higher long-term reward than the complete sharing method when the amount of wide-band guaranteed traffic is large. The results also show that the preemptive scheme and the partial blocking scheme are efficient for different types of traffic mixes.

Blocking Probability Approximations and Revenue Optimization in Multirate Loss Networks

For the end-to-end (Originator-Destination pair) call blocking probability computation in multirate loss networks the so-called reduced load approximation under link independence assumption is often used, because it allows the derivation of analytical and numerical results. Its accuracy and extendibility to multirouting or multicasting networks (like me B-ISDN), however, is seldom studied. This paper attempts to generalize this assumption and to assess the usefulness of this generalization by comparing simulation and approximation results on link, route, and end-to-end blocking probability evaluation for these kinds of networks. The accuracy of the approximation is examined by a simulation tool called Flexible Simulation Platform for ATM Networks. An important application example of this generalized link-, route- and Originator-Destination pair blocking measure is the formulation of an optimization model for multirate loss networks, which optimizes carried traffic and network revenue.

Enhancing ATM Network Performance by Optimizing the Virtual Network Configuration

Virtual or logical subnetworks are expected to play an important role in large B-ISDN configurations. This gives an additional degree of freedom to ATM network architectures, since even for a fixed physical network the logical configuration can still vary depending on particular demands and conditions. This new degree of freedom calls for new solutions to utilize the opportunity for the potential enhancement of network performance by optimizing the logical configuration, as part of optimizing the distributed network architecture. In this paper a framework and model, along with efficient solution algorithms, are presented to dimension virtual ATM networks on top of the same physical infrastructure network, such that the virtual networks share the infrastructure, while the total network revenue is optimized. The algorithms are tried on various network scenarios and a trade-off between the quality of the result and running time is exhibited.

On the superposition of a number of CDV affected cell streams

This paper considers the superposition of a number of Constant Bit Rate (CBR) cell streams which have been exposed to Cell Delay Variation (CDV). The case in which the CBR cell streams are affected by CDV in a single multiplexer is characterized by a diffusion model. Another and simpler model is used to characterize the effect of CDV after a number of multiplexing stages.

Cell delay variation in an ATM multiplexer

In this paper Cell Delay Variation (CDV) in an ATM multiplexer is investigated in the case where a Constant Bit Rate (CBR) traffic stream is mixed with a background traffic stream that arrives in the form of independent and identically distributed batches with general batch size distribution (Batch Bemoulli process). An exact Markovian solution approach is presented which gives the entries in the underlying transition matrix in closed form. In addition an approximate diffusion approach that is both computational simple and provides insight into the point process properties of the CBR stream after passing through the multiplexer is presented. It is demonstrated that the diffusion approximation has nice properties: it is second order exact in the heavy traffic case, and it provides fast and reasonable accuracy results over a wide range of system parameters.