reserved for constant bitrate (CBR) connections and VPs gain for CBR tra c. Within the VP classes the tra c mix may be arbitrary. VPs are also allowed to have ca ...
Network Engineering for ATM with Virtual Paths Thomas Bauschert Jochen Frings Rainer Siebenhaar Lehrstuhl fur Kommunikationsnetze Technische Universitat Munchen 80290 Munchen, Germany Summary
is accessed by ATM switches which terminate the VPs. The di erent VPs may span over several crossconnects and supply a logical direct connection between two access switches with a certain amount of bandwidth.
The asynchronous transfer mode is designed to supply virtual paths (VP). Using these VPs, fully meshed virtual networks can be build on top of the physical backbone network. In this paper we discuss several issues related to the cost optimal dimensioning of VP networks. The dimensioning problem is formulated as a mathematical optimization problem and a solution method is proposed. Results for a 23 node example network will be shown.
VP virtual path layer
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Introduction
Future public ATM networks will have a layered structure consisting of local networks, access networks and a long distance backbone network [1]. Network engineering will be done separately for these subnetworks in order to reduce complexity and to consider speci c demands for each layer. Only backbone facility network engineering problems will be regarded here. Two features of ATM have a substantial impact on these engineering problems: the cell based transmission allowing statistical multiplexing and the possibility to supply virtual paths. In this paper we consider only VPs with deterministic bandwidths that are not subject to statistical cell multiplexing with cells from di erent VPs. Therefore the sum of VP bandwidths on a physical link must not be greater than the link capacity (see gure 1).
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Figure 2: Virtual path and physical network layer
Aspects of network engineering
The rst stage in network engineering is the design of the topological structure of the network i.e. where to place the nodes and how to interconnect them. In most cases the location of the nodes is given for political or historical reasons. So only the structure of the interconnection graph has to be determined. This can be done through methods of topological optimization and graph theory. By performing this step connectivity and reliability constraints and link costs have to be regarded. The link cost information is simply a xed node interconnection cost per unit lenght, depending on the used technology. For ATM in most cases the result of the topological design phase will lead to a partly meshed backbone network structure. Given the topology of the facility backbone network and the end to end o ered trac values for each service class, the optimal size of the components and links must be calculated. These are subject to grade of service constraints on network performance. In case of an existing physical network the component sizes and available link capacities are already given and one can buy bandwidth in order to build up an appropriate VP network. Then the goal is to nd the least costly virtual network, which satis es the grade of service requirements. This subproblem of the general network dimensioning problem is considered in our paper. During network operation one normally has to cope
virtual paths with capacities N1, N2 , N3
virtual channels
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Figure 1: Virtual path concept The virtual path concept has been proposed to give maximum exibility to ATM networks. It provides the possibility to design an arbitrary VP network which is decoupled from the physical network and can be dynamically recon gured in case of trac uctuations or failures (see gure 2). The backbone network is supposed to consist of several ATM crossconnects, which are connected through high speed optical transmission links. It 1
ferent from the design load assumed in the dimensioning step. This could be due to inaccurate forecasting and transient or temporal load variations. The network should be operated so, that these e ects result in a minimum quality of service degradation for all service classes (graceful degradation). In classical circuit switched networks this requires the dynamic adaption of the routing strategy. Several methods have been developed for nonhierarchical networks all leading to a substantial gain in network performance. In the context of VP operated ATM networks the preferred mechanism for network adaption is the dynamic recon guration of the underlying VP network independent of the call routing strategy [2]. The separation of routing and bandwidth management is another important advantage of the VP concept. We have developed an optimization procedure which is able to calculate the optimal VP capacities in a quasistatic manner for practical ATM networks in a few minutes [3]. In case of link failures a VP recon guration mechanism is not fast enough to avoid the serious degradation of connection service quality. Therefore special failure protection mechanisms (link restoration, path restoration) have to be provided, which are able to guarantee a restoration up to 100 per cent. For correct operation of these mechanisms one naturally has to spend some extra capacity in the network dimensioning phase.
sumption makes sense because there is no multiplexing gain for CBR trac. Within the VP classes the trac mix may be arbitrary. VPs are also allowed to have capacity zero. Depending on the size and the topology of the physical network there may exist a large number of possible VP routes. In practice it is reasonable to restrict the number of VPs of each demand pair to some upper bound (e.g. the ve shortest routes). Regarding the call level we introduce service classes which are characterized through two trac description parameters: mean bitrate rm and peak bitrate rp. Note that for CBR services mean bitrate and peak bitrate are identical. We further assume, that call arrival and holding times are independent and negative exponentially distributed, i.e. we have Poisson trac. Only point to point connections between end to end node pairs are allowed. All connections are bidirectional with the same bandwidth requirements in both directions. ATM GoS requirements
The grade of service of ATM networks is characterized both by cell and call level measures. On the cell level these are mainly the cell loss probability, cell delay and delay jitter. On the call level like in classical circuit switched networks the call loss probability is a suitable service quality indicator. In case of VBR sources substantial bandwidth savings can be achieved through statistical multiplexing. This has led to the development of various connection acceptance algorithms, which may use information about the statistical properties of the call (given through the trac description parameters), the link status and the required cell level GoS. Unfortunately the evaluation of both cell and call level GoS during the dimensioning process would lead to very complex models, which can not be solved for realistic network sizes due to calculation time limitations. We therefore suggest to carry out investigations only on the call level regarding the end to end call blocking probability (EEB) as unique GoS measure. This is possible through introduction of the "equivalent bandwidth concept" by which each VBR call can be considered as requiring an equivalent bandwidth depending on the service parameter values, the required cell level GoS and the link status [8]. Connection acceptance then is only based on equivalent bandwidth values. With this approach all calculations can be performed like in the multi bitrate circuit switched case. In our model the e ective bandwidth connection acceptance algorithm proposed by Lindberger [9] is incorporated. According to [9] the e ective bitrate re is a function of rm, rp and the resource capacity N:
Cost optimal VP network dimensioning
The general network dimensioning problem can be seen as a cost minimization problem with several constraints. Depending on the goals of the network optimization, different cost functions can be envisaged, see e.g. [4], [5], [6], [7]. We deal with the problem of determining the least cost VP network where the objective function is represented by the weighted sum of used link capacities. The weighting factors could be di erent from link to link, taking into account di erent link bandwidth charges. The optimization constraints are due to physical restrictions on the link capacities and due to various requirements regarding grade of service (GoS), fairness and reliability. The following subsections describe the basic modeling assumptions in our work as well as further aspects which also have to be considered in the dimensioning model. Afterwards the dimensioning problem is stated as a mathematical optimization problem and a solution method is proposed. Finally the optimizationalgorithm is evaluated using an example network consisting of 23 ATM crossconnects. Basic modeling assumptions
At the network level we assume that the locations and connectivity of the crossconnects and access switches are given and may not be changed. All links of the physical transport network are assumed to be bidirectional. Concerning the VP level more than one VP per end to end node pair shall be allowed. An end to end node pair in our notation normally describes a pair of access switches and is also called demand pair (DP). Due to reliability requirements the VPs of a demand pair should have as few as possible (ideally no) links in common. We further assume that there exist two classes of VPs: VPs reserved for constant bitrate (CBR) connections and VPs
re = re(rm; rp; N) VC routing algorithm and equivalent single path model
As there is more than one VP per demand pair (at least for VPs carrying CBR calls) a virtual channel (VC) routing algorithm is necessary in order to select the VP on which an arriving call should be directed. Unfortunately the exact calculation of the end to end call blocking probability is very complicated or impossible for most practical routing algorithms. Therefore a simpli ed model, called the equivalent single path (ESP) model has been
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imate calculation of the multiservice call blocking probability for various routing strategies with a suciently small error if the VP bandwidths are large. In this model all VPs which belong to a demand pair and carry CBR trac are transformed into one equivalent VP whose bandwidth is simply the sum of them. This allows the application of a suitable one link blocking model for end to end blocking evaluation.
general blocking probability adjustment is much more complicated because a nonlinear optimization problem with a dimension equal to the number of trunk reservation parameters has to be solved. Network reliability
Network reliability means that in case of a link or node failure bandwidth still remains for the incurred demand pairs. A reliability degree is the amount of the remaining bandwidth and the way it is distributed. Network reliability can result from several schemes of bandwidth distibution to paths [17]. As we have presumed multiple disjoint VPs per demand pair, one way to achieve reliability is to limit the bandwidth of each VP to a certain percentage of the total bandwidth spent for this demand pair. Then at most % of the demand pairs capacity is lost if a single link failure occurs. According to this scheme the highest reliability can be achieved through the setting 1 = ( numberofV P ) 100%. The value 100% means that there is no reliability at all because the total bandwidth assigned to the demand pair can be allocated to only one VP. Naturally the value could be the same for all demand pairs or could be xed according to the degree of reliability that one wants to ensure for each demand pair individually. In order to achieve full reliability i.e. no loss of calls in case of an arbitrary single link or node failure a failure restoration mechanism has to be implemented. This needs some extra link capacity for redundancy. The required redundant link capacities can be calculated (and added to the former calculated link capacities) by solving an additional (linear) minimization problem after the network has been dimensioned without taking into account a failure restoration mechanism.
Multiservice call blocking evaluation and fairness
Several authors have studied systems in which several classes of trac with di erent bandwidth requirements try to access a common resource. In the simplest case of complete bandwidth sharing the blocking probabilities for each class of trac can be easily computed through a one dimensional recursive algorithm [11], [12]. However for optimization purposes and especially in the context of ATM (with large bandwidths and many service classes) this recursive algorithm is not well suited. We therefore investigated some published approximations and found that of Labourdette [13] the best one. The great advantage of Labourdettes approximation is that the computational evaluation is much faster than with the recursive algorithm and that derivatives can be deduced. Applying this approximation, the blocking probability B s of class s calls having access to a resource with capacity N is a continuous nonlinear function depending on N, the o ered trac values A1,..., AS and the (e ective) bitrates re1 ,..., reS of all service classes:
B s = f s (N; A1; :::; AS ; re1; :::; reS ) Applying the complete sharing policy to multiservice networks has the disadvantage that the blocking probabilities of the di erent service classes depend strongly on their bandwidth requirement and can di er in the order of several magnitudes. To avoid this, some kind of bandwidth sharing policy could be introduced. We compared two well known policies - the restricted access (RA) coordinate convex policy [14] and the trunk reservation policy of Roberts [15]. As a result the trunk reservation policy performs better in terms of eciency, easier parameter setting and blocking probability evaluation. The blocking probabilities can be calculated approximately dependent on the trunk reservation parameters through a one dimensional recursive algorithm similar to the one used in case of complete sharing. The blocking probability B s in general is a noncontinuous function of the resource capacity N, all trunk reservation parameters t1 ,..., tS , the o ered trac values A1 ,..., AS and the (e ective) bitrates re1 ,..., reS of all service classes:
Mathematical formulation of the optimization problem
The following notation is used throughout the rest of the paper. Remember that links and o ered trac are bidirectional and that the values correspond to only one direction: L number of links E number of equivalent single paths Se number of service classes on ESP e P number of paths Pe set of paths summarized to ESP e Pl set of paths which contain link l Np capacity assigned to path p Ne capacity assigned to ESP e wl costs per unit bandwidth on link l Cl upper bound for capacity on link l rese e . bitrate for class s calls on ESP e Bes call block. prob. of service class s on ESP e GoS desired grade of service (EEB design value) tse trunk res. param. acc. to class s on ESP e vs blocking prob. relation factor for class s e reliability degree for ESP e l link index e equivalent single path index s service class index p path index
B s = hs (N; t1 ; :::; tS; A1; :::; AS ; re1; :::; reS ) In the special case of equal call blocking probabilities for each service (complete fairness) the trunk reservation parameter setting can be done without complex calculations. Moreover a continuous approximation and related derivatives deduced from Labourdettes approximation can be found, too [16], [10]. The equal blocking probability B depends on the resource capacity N, the o ered trac values A1 ,..., AS and the (e ective) bitrates re1 ,..., reS of all service classes: B = g(N; A1 ; :::; AS ; re1; :::; reS )
The linear objective function of the optimization prob3
widths:
1 0 P L X X J= B A @ Npwl C l=1
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the trac descriptors rp , rm for all services, the offered trac values for all services and demand pairs, the link capacity upper bound Cl for all links and the reliability factors e for all ESP. The decision variables are the VP bandwidths Np for all possible paths, the bandwidths of the equivalent single paths Ne for all demand pairs and possibly the trunk reservation parameters tse . The interesting values of used link bandwidths can be easily obtained through summation over all VP capacities according to each link.
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The linear and nonlinear constraints of the optimization problem are: the sum of path capacities on a link must be less than the link bandwidth upper bound:
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the equivalent single path capacities must be positive: Ne 0 e (6) blocking constraints in case of complete bandwidth sharing: the blocking probability of the service class with the highest e ective bitrate must be less than the desired grade of service GoS (all other services su er a lower blocking anyway): Besmax = f smax (Ne ) = GoS e (7)
The direct solution of the above optimization problem is dicult for larger problems due to the nonlinear blocking constraints (7), (8), (9). It is possible however to eliminate the blocking constraints by solving them according to Ne or Ne and tse respectively. This way the optimization problem is transformed into a linear one with a reduced set of optimization variables Np . In the case of (7) and (8) Ne can be simply obtained through a numerical zero search, whereas for (9) E nonlinear optimization problems of the order Se + 1 (for the variables Ne and tse) have to be solved. The solution of the large scale LP can be obtained using standard methods. We used the FORTRAN based MINOS system developed at Stanford University [18]. MINOS is especially designed to solve large sparse linear and nonlinear optimization problems. For the nonlinear subproblems we recommend the use of a SQP algorithm implemented e.g. in the NAG library.
the sum of path capacities is equal to the bandwidth of the corresponding equivalent single path: P X
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reliability constraints (only valid if the number of VPs belonging to ESP e is greater than 1): Np e N e p (4)
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Solution method
Example
The dimensioning method is applied to a 23 node partly meshed example network, which could form the ATM backbone network for the wide area trac in Germany. The capacities of the access links are assumed to be no bottleneck and so, for simplicity, we only consider the links between the crossconnects. We have 253 demand pairs, which are logically fully meshed with virtual paths. Each demand pair is connected with up to 6 virtual paths, one of them reserved for VBR trac. The other paths of each demand pair have disjoint routes. The total number of virtual paths is 960 which is also the size of the linear program. The optimization is carried out for reliability degree 50% and complete fairness requirement (i.e. constraints (8) are valid). We assume 5 di erent service classes, three for CBR trac and two for VBR trac. The link cost weighting factors wi are all set to 1.0 for simplicity. Figure 3 shows the network topology and the required link capacities for the cost optimal scenario.
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blocking constraints in case of fair trunk reservation: the equal blocking probability must be less than the desired grade of service GoS: Be = g(Ne ) = GoS e (8) 8
blocking constraints in case of trunk reservation with arbitrary blocking probability relations: the blocking probability relations must be satis ed and additionally the highest blocking must be less than the desired grade of service: Be1 : Be2 : ::: : BeSe = v1 : v2 : ::: : vSe e (9) and (B s ) = GoS e Besmax = max s2Se e where Bes = hs(Ne ; tse ) These constraints can be reformulated as follows: e; s = smax (10) Bes ( v vs ) Besmax smax Besmax = GoS e; s = smax
Conclusions
In this paper an overview about various aspects of ATM network engineering is given and the cost optimal VP network dimensioning problem is adressed further. We show how important issues like statistical multiplexing or reliability requirements can be included into the modeling. The nonlinear dimensioning model is transformed into a linear one which can be solved much easier and the optimization is carried out for a 23 node example network. It should be noted however that in our model the linear transformation is not possible if one wants to supply multiple VBR paths per demand pair. This is due to the fact that the e ective bandwidth depends on the path's ca-
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Figure 3: Required link bandwidths for cost optimal scenario
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pacity value. Therefore the equivalent path concept cannot be applied and each VP must be treated separately. Thus the call routing strategy has to be considered, too. A possible solution to this problem is to perform the dimensioning for a routing strategy which is analytically tractable and represents some upper bound on the required capacity, e.g. load sharing routing. One fallback is that the optimization problem then gets far more complicated because of the unavoidable nonlinear constraints. We currently extend our work in these directions.
[12] [13]
References
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