# On the selection of management/monitoring nodes in highly dynamic networks

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9 9 Estimated traffic/node Estimated traffic/node Number of nodes Number of nodes Fig. 3. Estimated traffic per node for various placement algorithms in simulation without (top) and with (bottom) preferential attachments the algorithm in the largest network tested without preferential attachment and 28% more in the preferential attachment scenario. B. Node lifetime estimation In order to be able to estimate a nodes lifespan the estimation algorithm must first have a few observations of nodes to work with. The more node deaths observed the closer the fit to the real distribution is achieved. The first, and simplest test is to work with the lognormal distribution (this is the distribution assumed by the tail fitting algorithm). Figure 4 shows the actual and estimated complimentary cumulative distribution function (CCDF) from the lifetime estimation algorithm after 20 observations, 100 observations and 1000 observations of lifetimes which have a lognormal distribution with µ = 7.0 and σ 2 = 1.5. The line Actual dist is the correct distribution, Estimated dist is the raw Kaplan Meier estimate and Tail fit dist is the estimate corrected with tail fitting. As mentioned in section III-B the Kaplan Meier estimator is a non-parametric estimate which cannot make estimates about lifespans not yet observed so the distribution finishes with the longest lifespan observed in the system and cannot estimate further. The tail-fitting algorithm corrects this by fitting a lognormal tail to the final 20% of K M points. When 20 observations have been made there is insufficient data for a tail fit and that line is omitted. The K M algorithm does a good job at distribution estimation for early parts of the CCDF P(S>X) CCDF P(S>X) CCDF P(S>X) Estimated dist Actual dist e X (seconds) Estimated dist Tail fit dist Actual dist e e-05 X (seconds) 1e-06 Estimated dist Tail fit dist Actual dist 1e e+06 1e+07 X (seconds) Fig. 4. Node lifespan distribution estimation for 20 lifespan observations (top), 100 (middle) and 1000 (bottom) curve but is very poor at the tail. Unfortunately it is the tail of the distribution which is often most important for lifespan estimation (while only a small percentage of nodes have lifespans over 100,000 seconds they contribute a great deal to the expected lifespan of an average node). At 100 observations the fit to the distribution with the tail fitting is good and at 1,000 observations nearly perfect. In a running system the controller would quickly get 1,000 observations of nodes and could then run using only its most recent estimations. The estimation procedure is computationally inexpensive. Figure 5 shows the lifespan estimation for the same experiment. As can be seen, after only 20 observations the estimation is quite wrong. At the tail the estimator cannot make an evaluation of lifespan from data and the program simply estimates that the node will live as long again as its current lifespan (the linear part of the estimate). By chance this

12 12 AP node longevity (seconds) Estimated traffic/node Time policy strength Time policy strength Fig. 8. Node lifespan (top) and estimated traffic per node (bottom) for one hour simulation with various time policies equation 3 and the β parameter. A manager could use high values of β when stability is the primary concern and traffic due to node placement is less of an issue. However, the very highest values did not seem to make too much difference in lifespan seen. Therefore, some degree of optimal node placement can be made with β = 10 (policy strength 3) without a penalty to the achieved stability. On the other hand, if traffic reduction is the priority then it can be seen that β = 0.1 (policy strength 1) produces an increase in node lifetime with little damage to the traffic reducing effects. VII. TESTBED RESULTS The testbed results, using the VLSP platform, were run on six physical machines. For repeatability the VLSP experiments were run with the same parameters as the simulation experiments wherever possible. The VLSP can handle fewer nodes than pure simulation, however, it has the advantage that the traffic measured is real traffic, in our case, generated by the monitoring software. This traffic differs considerably from the estimated traffic algorithm as the routing may be non-optimal (since real systems take time for routing to converge after a node or link vanishes) and packets may be dropped. Information sources may continue to send traffic to dead aggregation points (until they are informed of a new aggregation point) and by the nature of distance vector routing, transient routing loops may occur. The parameter settings were largely the same as for the simulation but the arrival rates were kept lower as, obviously, the VLSP could handle fewer routers than the simulation. The information sources send a small amount of monitoring information to the aggregation points every second. Aggregation points are recalculated (potentially added and potentially information sources are moved to new aggregation points) every ten seconds as with the simulation. A. Traffic minimisation Figure 9 shows the testbed results for the three node placement algorithms with and without preferential attachment. Because the network sizes are smaller than in simulation and the number of runs fewer, the error bars representing one standard deviation either side of the mean are relatively larger than in the simulation case. However, the pattern still remains clear with the algorithm out performing which in turn out performs. For the smallest network size tested there are only approximately four aggregation points and the error bars are very large. This indicates that in those settings the difference between runs with the same algorithm is much greater than the difference made by the algorithms themselves. That is to say, the statistical variation in the network topologies themselves had a greater effect on traffic than the node placement algorithms. This is not surprising when such nodes would only have three or four aggregation points (and also the difference between a node with 39 nodes and hence 3 aggregation points and 40 notes and 4 aggregation points would be extremely large). It should also be noted that the routing system responded well to the highly dynamic nature of the network. Even though in the most extreme scenario tested one virtual router would die on average every three seconds the number of lost packets in the network remained small (three runs averaged 0.75, 0.32 and 0.36 packets dropped per second for the last ten minutes of simulation less than 0.5% of the traffic). B. Lifespan maximisation Figure 10 shows the results of the lifespan maximisation policies run on the testbed. The testbed runs have fewer nodes than simulation runs. The arrival rate is set to a mean value of one node every two seconds which means that in equilibrium there are around 250 nodes but the mean churn rate simulates around 1,500 nodes in the full hour of testbed time. These figures are for a non preferential attachment model with the same time policies as for the simulation results shown in figure 7. Ten runs are done for each policy and a data point is the mean and standard deviation of these points for a given placement policy and time policy as described in the table in section VI-C. Because of the smaller number of nodes these graphs are harder to interpret than the ones for the simulation and the error bars are larger Figure 10 (bottom) shows that for the and policies the trend appears to be what we would expect. The node maximising policies increase lifespan. However, with fewer nodes (and fewer node deaths from which to create estimates) the lifespan extension is not as great. The figure

13 13 Data Traffic/node (bytes/unit time) Number of nodes Data Traffic/node (bytes/unit time) Time policy strength Data Traffic/node (bytes/unit time) Number of nodes AP mean lifetime Time policy strength Fig. 9. Data traffic per node for various placement algorithms in the testbed without Preferential attachment (top) and with (bottom) Fig. 10. Data traffic per node (top) and IAP lifespan (bottom) for one hour on the testbed with various time policies also shows the effects of the various time policies. As expected the stronger (higher numbered) policies favouring longer lived nodes are producing a higher mean lifespan for nodes. Again, however, the size of the error bars makes interpreting too much from the graphs difficult. It seems loosely to show that the lifespan estimation does produce a benefit (particularly in the random case). The fact that the benefit is smaller is to be expected as the algorithm has fewer nodes to learn the distribution from in this system. Figure 10 (top) shows the same run from the point of view of network traffic. The results are what would be expected from simulation (see figure 7) for the and algorithms. The algorithm does not seem to suffer increased traffic as the time penalty increases. However, this may be a product of the large error bars. While these figures are consistent with the simulation results (with that single exception) the large error bars make it hard to interpret further. VIII. SUMMARY AND CONCLUSIONS This paper has investigated the selection of management/monitoring nodes in a highly dynamic network environment. In a rapidly changing network environment, monitoring and management are both extremely critical and difficult to achieve tasks. The management algorithms presented are computationally cheap and can be implemented in a decentralised way. They can select nodes to reduce resulting traffic or to choose stable nodes (that is, those most likely to be long-lived). A new, locally optimal algorithm () was proposed. It selects the best node to reduce current management and monitoring traffic on the network. Following the problem of selecting nodes by lifespan (that is the time remaining until the node exits the network) is investigated. A simple estimator for remaining lifespan is given, together with an improved estimator with tail fitting. The combined algorithm which tackles node placement and node-lifetime maximisation is known as Time. The algorithms were tested both in simulation and on a new testbed environment, the VLSP testbed. The simulation environment tests networks with up to 5,000 nodes and with a churn of 36,000 nodes (36,000 nodes in total created of which approximately 5,000 are in use simultaneously) over the simulation period. The testbed environment used virtual routers running on Java virtual machines and emulated around 220 nodes with a churn of around 6,000 nodes over the simulation period. The algorithm proved successful in reducing the traffic generated by the monitoring nodes when compared with and algorithms. In addition, the Time algorithm combines node placement with lifespan maximisation in a tunable way. To some extent, selecting optimally placed nodes and selecting nodes with the longest lifespan are potentially competing problems (although in the case of the preferential attachment system it was shown that sometimes long-lived nodes were also well-placed). It

15 the University of York was gained in His research interests include network topologies, network traffic statistics and overlay network. Stuart Clayman received his PhD in Computer Science from University College London in He has worked as a Research Lecturer at Kingston University and is now a Senior Research Fellow at UCL. He co-authored 30 conference and journal papers. His research interests and expertise lie in the areas of software engineering and programming paradigms; distributed systems; cloud systems, systems management; networked media; and knowledge-based systems. He also has previous extensive experience in the commercial arena undertaking architecture and development for software engineering and networking systems. George Pavlou holds the Chair of Communication Networks at the Dept. of Electronic & Electrical Engineering, University College London. Over the last 25 years he has undertaken and directed research in networking and network/service management, having extensively published in these areas. He has contributed to ISO, ITU-T and IETF standardization activities and has been instrumental in a number of key European and UK projects that produced significant results. His current research interests include traffic engineering, informationcentric networking, autonomic networking, communications middleware and infrastructure-less wireless networks. Lefteris Mamatas is a postdoctoral researcher at the University College London. His research interests lie in the areas of autonomic network and services management, delay-tolerant networks and energy efficient communication. He participated in several international research projects, such as UniverSELF (FP7), Autonomic Internet (FP7), Ambient Networks (FP7) and Extending Internet into Space (European Space Agency). He published more than 30 papers in international journals and conferences. He served as a TPC chair in the WWIC 2012 and E-DTN 2009 conferences. Alex Galis is a Visiting Professor at University College London. He has co-authored 7 research books and more than 190 publications in journals and conferences in the Future Internet areas: networks, services and management. He acted as PTC chair of 14 IEEE conferences and reviewer in more than 100 IEEE conferences agalis. He worked as a Vice-Chairman for the ITU-T Focus Group on Future Networks, which is defining design goals and requirements in the Future Network focusgroups/fn/index.html. 15

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