In modeling communication networks for simulation of survivability schemes, one goal is often to implement these schemes across varying degrees of nodal connectivity to get unbiased performance results. Abstractions of real networks, simple random networks, and families of networks are the most common categories of these sample networks. This paper looks at how using the network family concept provides a solid unbiased foundation to compare different network protection models. The network family provides an advantage over random networks by requiring one solution per average nodal degree, as opposed to having to solve many, which could take a significant amount of time. Also, because the network family looks at a protection scheme across a variety of average nodal connectivities, a clearer picture of the scheme’s performance is gained compared to just running the simulation on a single network or select few networks.
Communication technology is a fundamental component of modern societies, allowing rapid exchange of knowledge, collaboration, and much more. Underpinning this fundamental component of our society is a robust reliable network. As such, the need to drive reliability and availability in the core communication infrastructure is a constant concern. The focus of this work is on network survivability design where the most common failures occur in network spans. This is due to the highly uncontrolled environment in which these spans exist and the significant cost of redundancy and because fibre links comprising a span are generally quite lengthy (hundreds of kilometres in terrestrial long-haul networks and even longer in some undersea networks) and are often routed through remote locations that are difficult to fully secure. Even relatively small urban networks are subject to a high rate of cable cuts (one estimate claims 13 cuts per 1000 miles of fibre [
In the past two decades, many network survivability techniques have been developed to provision spare capacity on a network in such a way that it can withstand failure of one or more of its spans [
The most common network survivability techniques include 1+1
Implementing survivability schemes can take a number of approaches. Common design approaches include heuristic algorithms, including genetic algorithms, tabu search, and custom heuristics; however, to guarantee a certain level of optimality,
When designing or evaluating network survivability schemes, we must first select a set of test networks to evaluate those schemes. Common approaches for selecting these test networks include using topologies modeled after real networks and selecting topologies used elsewhere in literature or simulated random topologies. The difficulty in the selection of the test networks is with the ability to evaluate the survivability schemes’ performance across a variety of topologies and network connectivities. As will be shown later, network connectivity is a key dimension in evaluating schemes for providing a more complete picture of each scheme’s behaviour. Another approach that has been taken is to create what we call network families [
A network family is a set of networks varying only in the number of spans that each contains, where all nodes and a set of common spans keep a consistent configuration. These families are commonly designed by starting with a highly connected master network (Figure
An example for node network family.
The purpose of the study behind this paper is to evaluate the use of network families in comparison to two other methods of selecting test networks, stand-alone representations of real networks, and sets of randomly generated topologies.
A common method of evaluating an optimally (or near optimally) designed network is its redundancy, though various capacity measures can easily be used as a surrogate (total working plus spare capacity, total spare capacity, etc.). This redundancy metric is affected by a number of characteristics, five of which are of significance to the work herein. These characteristics include the demand matrix (traffic volume between each node pair in the network), the number of nodes in the network and their configuration, and the number of spans in the network and their configuration. It should be noted that, for full comparison across this range of factors influencing survivability scheme performance, each degree of freedom should be tested. It is the intention of this work to demonstrate a mechanism to isolate the number of spans (average nodal degree), as this can be a major differentiator in topology characteristics globally [
The demand matrix selected for a network topology obviously has a significant impact in the capacity and redundancy required. The impact of the demand matrix can come from a number of factors including overall volume and distribution, where distribution includes variability and locality. A demand matrix that is highly localized will require less capacity than the one that has a wide ranging demand pattern. Variability in demand patterns can also have a significant implication on overall capacity and redundancy as there would be a few large capacity demands that would dominate the requirements for redundant capacity and reduce the capability of the survivability scheme to share spare capacity. The effects and implications of demand patterns are difficult to predict, and, as such, keeping them consistent is an important consideration when comparing survivability schemes.
The nodal topology of a network also has a significant effect in the redundancy of a network, specifically in configuration and localized density. Consider the impact that modifying a single node in a network would have in path routing. This would impact path lengths and layouts and could introduce or remove trap topologies (Figure
The last two factors, network connectivity, and how that connectivity is arranged can also significantly affect redundancy in a network. The ability to diversely route traffic is directly related to the spatial diversity and number of spans in a network; we are able to more directly route survivable traffic and/or better share spare capacity in a richly connected network, reducing required redundancy. The configuration of the spans in the network also plays a role in network’s capacity requirements. If demand in a network is broadly distributed, but the connectivity is centered around relatively few clusters, the effect on route diversity and spare capacity sharing would increase redundancy and capacity requirements when compared to a network where average nodal degree was more consistent across nodes. This implies that although connectivity is a good descriptor of a network, the layout and configuration of the nodes and spans can have an impact on key metrics when evaluating a survivability scheme.
In summary, all of these characteristics are difficult to normalize, and each can have a significant effect on the redundancy or capacity cost of a survivable network design. The selection of test networks should account for these variables in order to evaluate the performance of the selected schemes across topologies and demands.
The above discussion is significant in that it frames the motivation to use network families. Network families are able to restrict the above dimensions to allow comparison of survivability schemes along one of the most important dimensions in a network, average connectivity.
Network families directly limit variability in demand matrices, nodal topology, and nodal density. Variability in span configuration and network connectivity are also tightly controlled. With each successive network varying only by the addition or removal of a single span, the effects of span configuration remain as consistent as possible, and the control variable becomes network connectivity. This control provides a greater level of confidence that changing levels of redundancy are due to characteristics of the survivability scheme and not an artifact of the differences between stand-alone test networks.
If random or unrelated networks were used in a comparative evaluation of a survivability scheme [
The purpose of this study is to investigate the use of network families in comparative evaluations of network survivability schemes or models across a range of network connectivities. Two common approaches also used in comparative analysis include using selected real world networks and using large sets of random networks. This study looks to quantitatively compare these approaches to test network selection in order to confirm that network families represent a valid selection method.
Our tests used three sets of networks; one set comprises a 15-node network family, a second set consists of 15-node stand-alone random networks, and a third set consists of a variety of actual networks. Our network family consisted of 15 related but distinct 15-node networks ranging in average nodal degree from
15-node master network in our test case family.
The set of random networks consists of 300 pseudorandomly generated networks, with 20 completely unrelated networks for each nodal degree in the network family. These networks were considered to be pseudorandom as they were derived to have characteristics that could be conceivably implemented in reality (with respect to node density and degree). Effort was made to keep the scale of the networks consistent (i.e., the point-to-point distances between the most distant nodes); however, there were variations that had to be accounted for in the analysis (Section
The actual networks used in this study were composed of data that is representative of networks that are currently implemented. We collected network maps of some service providers, regional networks, and international carriers from various online sources. Table
List of implemented networks used in this study.
Network | # Nodes | # Spans |
|
Notes |
---|---|---|---|---|
BNDCN | 21 | 29 | 2.76 | Bandcon International Network [ |
NG | 17 | 24 | 2.82 | Nobel-Germany National Network [ |
IN | 11 | 16 | 2.91 | ITC Deltacom Regional Network [ |
DELTA | 59 | 89 | 3.01 | ITC Deltacom Regional Network [ |
C&W | 24 | 38 | 3.16 | Cable & Wireless USA IP Backbone [ |
COX | 21 | 38 | 3.61 | Cox National IP Backbone Network [ |
BLCR | 15 | 28 | 3.73 | Bellcore Network [ |
NOR | 27 | 52 | 3.85 | Norway National Network [ |
BTNA | 35 | 72 | 4.11 | British Telecom North American Network [ |
NYC | 16 | 42 | 5.25 | New York Regional Network [ |
Three of the real networks (BLCR, NOR, and NYC) were later selected and used as master networks for their respective network families with the average nodal degree ranging from
As already discussed above, design models corresponding to five common network survivability schemes were used; these schemes were 1+1 APS, span restoration, path restoration, SBPP, and
The path-restorable and SBPP design models each were provided with the five shortest eligible working routes and the ten shortest eligible restorations routes for each lightpath demand (i.e., node pair). The 1+1 APS designs routed all demands on the single shortest pair of routes between their end nodes (no formal optimization needed). The span-restorable design model was provided with the five shortest eligible working routes per lightpath demand and the ten shortest eligible restorations routes for each span failure scenario. The
In terms of the demand matrix, a full mesh was used (with each node pair assigned some demand), with each node pair exchanging a randomly generated number of demands between 1 and 10 (using a uniform distribution). The network families and random networks used the exact same demand matrix, ensuring consistent demand volumes across the networks. The real networks used distinct, randomly generated demand matrices using the same parameters mentioned above.
All ILP formulations were implemented using AMP, and were solved using CPLEX 10.1 on a Sun 1.6 GHz quad CPU machine with 16 GB of RAM. The results are based on full CPLEX terminations with
Comparing network families with random networks was done using a normalized mean and maximum and minimum of the random networks with the normalized results of the network family, as shown in Figure
Normalized
Normalized span restoration JCA total capacity costs.
Normalized SBPP JCA total capacity costs.
Normalized path restoration JCA total capacity costs.
Normalized 1+1 APS JCA total capacity costs.
In order to compare the capacity costs of designs on different topologies, the results had to be normalized. This normalization removed the effects of slight variations in network scale. The network family capacity costs were normalized to the cost of the network corresponding to a nodal degree of 4.0 for each survivability scheme. The pseudorandom networks had to be normalized in a slightly different manner. The result for each random network was divided by the total unit cost (the cost of one unit of capacity allocated to each span) for all of the spans in the network and then normalized to the lowest cost network in the set of networks with
All curves shown follow a similar general behaviour, and the network family results were quite similar to the average of the pseudorandom networks. It is also obvious that there is a large gap between the maximum and minimum results for each average nodal degree. The mean difference for
As demonstrated in Figure
Normalized SBPP total costs of random networks with average and network family.
To account for the high level of variability in pseudorandom networks, a large number of test networks are required for each connectivity level (we used 20 and were able to produce a reasonably smooth average curve). Of significance, however, is that one network family of 15 networks produced similar results to the average of 300 networks. To more closely examine how closely a network family could reproduce the behaviour of the average of the pseudorandom networks, the first derivative (or slope) of the normalized total costs was compared. Figures
Slope of normalized
Slope of normalized span restoration JCA total capacity costs.
Slope of normalized SBPP JCA total capacity costs.
The comparison of the slopes of the pseudorandom network averages and the network family highlight how well one network family represents the behaviour of many random networks when compared across a range of network connectivities. This implies that using a network family to observe the behaviour of a survivability scheme and/or network design model over varying connectivities produces a result that is similar to the average of a large number of networks. When dealing with models that may take days, weeks, or months to find a solution, this provides significant time savings; one could use a single network family rather than many stand-alone (i.e., random) networks.
Next, we compare
Normalized
Slope of the normalized
Using a straightforward statistical analysis of the
The results obtained for SCA and JCA for path restoration mechanism are shown in Figures
Normalized path restoration SCA spare capacity costs.
Normalized path restoration JCA total capacity costs.
Similarly, for path restoration JCA, in Figure
We can also look at the slopes of the SCA and JCA capacity cost curves, as a metric for the reduction in total cost on a network as the average nodal degree increases; we plot those slopes in Figures
Slope of path restoration SCA normalized spare capacity cost.
Slope of path restoration JCA normalized total capacity cost.
We can use the same representation for data plotted in Figures
Normalized
Normalized
Normalized SBPP SCA spare capacity costs.
Normalized SBPP JCA total capacity costs.
Normalized span restoration SCA spare capacity costs.
Normalized span restoration JCA total capacity costs.
In the next part of our analysis, we generated network families from the 16-node NYC and the 27-node NOR real networks. For each network, we successively added and/or removed individual spans one at a time to produce a series of related networks of average nodal degrees ranging from slightly above 2.0 (subject to maintaining biconnectivity) to 4.0. We plot the results of this analysis in Figures
Normalized
Normalized
Normalized SBPP restoration SCA costs for network families based on real network.
Normalized SBPP restoration JCA costs for network families based on real network.
Normalized span restoration SCA costs for network families based on real network.
Normalized span restoration JCA costs for network families based on real network.
As we can observe from these figures, the behaviour of the various curves provides a closer semblance to that of the 15-node network families than we had observed earlier with the original stand-alone real networks. Except for only a few abnormalities, particularly in the NOR-based network family, these new families permit a much better view of the behaviour of the various survivability schemes and design models. Upon closer inspection of the abnormalities, they appear to be due to peculiarities in the eligible routes and
In any case, the trend observed in these curves is as we expected; if network families are generated from real networks rather than just selecting stand-alone real networks randomly for testing, we are able to overcome the irregularities that would otherwise have arisen and potentially obscured the behaviour(s) we sought to characterize. We can therefore assert that a comparative evaluation of design models over varying connectivity (as achieved via network families) allows us to better understand how a model behaves irrespective of the actual scale of cost. As a result, we do not need to run ILP design models with potentially hundreds of stand-alone test case networks; rather, it can be run just a few times over one or two network families. Hence, we are able to reduce overall experimental runtime while obtaining results that are more meaningful.
Evaluating survivability schemes and network optimization and design models across a variety of network connectivities provides a method to generalize the behaviour and performance of the model, and proper selection of a set of test case networks is important. Network families provide a way to evaluate generalized behaviour across varying network connectivities without having to incur the potentially significant computational time required if a large set of random networks were used. It was shown that there was little bias between the average of many pseudorandom networks and a sample network family.
With regard to the use of network families over real network representations, rather than pseudorandom artificial network topologies, the results provide much more confidence when generalized. We observed that use of stand-alone real networks can include peculiarities that could show wildly varying capacity design costs as we sweep through their various connectivity levels. Use of network families prevents this by evaluating results over a consistent set of networks.
The authors declare that there is no conflict of interests regarding the publication of this paper.