# A Closed-Loop Control Traffic Engineering System for the Dynamic Load Balancing of Inter-AS Traffic

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7 optimized, while the other one is constrained so as not to exceed a tolerance value. Since primary EP changes result in service disruption and reconfiguration overhead, we therefore choose to place a constraint on the number of EP reconfigurations that are attained by the re-optimization while minimizing the inter-as MLU. Hence, the optimization problem to be tackled by the re-optimizer can be formulated with the obective: max J k i I k K J cinter x t( i,k ) Minimize U ( ) = MinimizeMax( u ) = MinimizeMax( ) (1) subect to the following constraints: r X (2) k K : x k = 1 Out ( k ) (3) J, k K : x k { 0,1} (4) Constraint (2) ensures that the number of reconfigurations does not exceed the reconfiguration limit X. Constraints (3) and (4) ensure that only one EP is selected for each destination prefix as the. The re-optimization is an NP-hard problem since it is a special case of the wellknown makespan problem, which is known to be NP-hard. In the rest of Section 3.1, we present a strategy to determine the reconfiguration limit and an efficient algorithm to solve the problem DETERMINING THE RE-CONFIGURATION LIMIT Note that there are two possible ways of determining the reconfiguration limit X. One is operator-based in which the limit can be defined according to the decision of the network operator based on its obectives. The other one is performance-based in which the limit is computed based on examining the tradeoff between minimizing the MLU and reducing the number of reconfigurations. In fact, the larger the number of reconfigurations, the better the expected value of the obective function (1). The examination can start with a suboptimal selection solution (i.e. congestion on several EPs), then improving the solution by increasing the number of reconfiguration. As shown in Figure 3, a convex curve of MLU as a function of actual number of reconfiguration can be obtained by this examination. The knee of this convex shape curve is the point that further reconfiguration beyond that point results in very small EP utilization reduction (i.e. load balancing improvement). This point can be chosen as the reconfiguration limit X. Figure 3. Determining the re-configuration limit RE-OPTIMIZATION HEURISTIC Since the re-optimization problem is NP-hard, we need to resort to heuristic approaches. Local search algorithms have been shown to produce good results for many combinatorial optimization algorithms [15]. We therefore propose an iterative local search algorithm for the re-optimizer as the following steps:

8 Step 1. Set r to zero and identify EPs with the maximum and minimum utilization (U max ( ),U min ( )). Step 2. Among all the prefixes whose is the EP with maximum utilization (U max ( )), search for the prefix that by reassigning it to the EP with minimum utilization (U min ( )) reduces the maximum EP utilization by the maximum value. Re-assign the prefix to that EP, update both values of U max ( ) and U min ( ), and set r = r + 1. Step 3. Repeat step 2 until either r reaches the limit X or there is no performance improvement for U max ( ) in comparison to the previous iteration BEP RE-OPTIMIZER PROBLEM FORMULATION The BEP re-optimizer requires as input the current BEP configuration as well as those inputs required by the re-optimizer. The task of the BEP re-optimizer is to re-assign backup EPs for destination prefixes, with the obective of minimizing the worst-case inter-as MLU across all FSs (we assume single inter-as link failures) while reducing the number of backup EP reconfigurations. As mentioned earlier, changing backup EPs does not cause any service disruption. But the network operator might be able to handle only a limited total number of EP reconfigurations at each reoptimization. Therefore, if we denote the total number of and BEP reconfigurations limit by R, and taking into account the actual number of reconfigurations r imposed by re-optimizer and limited to X, the total number of backup EP reconfigurations will be limited to (R r ). Hence, in a similar fashion to the re-optimizer, we place a constraint on the number of backup EP reconfigurations while minimizing the worst-case inter-as MLU. Therefore, the optimization problem in the BEP re-optimizer can be formulated with the obective: Minimize Uworst = MinimizeMaxU max ( s ) (5) s S where x t( i, k) s S : U ( s) = Max( u ) = Max( ) max s s sk i I k K s cinter (6) subect to the following constraints: r R r (7) sk (8) Out ( k) k K, s S : x = 1 { } J, k K, s S : x sk 0,1 (9) xsk = 1 s S /{ } J, k K if x k = 1 then x sk = 0 s = (10) The term xskt( i, k) consists both of flows that are assigned to EP as their and also flows that are assigned to EP as their BEP. Constraint (7) ensures that the number of BEP reconfigurations does not exceed the limit R-r. This BEP reconfiguration limit can be determined using the approach described in Section for the reconfiguration limit. Constraints (8) and (9) are equivalent to constraints (3) and (4), ensuring that only one EP is selected for each destination prefix as the BEP under each FS. Constraint (10) ensures that if prefix k is assigned to EP under NS, then this prefix remains on for all FSs except when the current FS is the failure on. Note that, in comparison to the re-optimization problem that minimizes the MLU only under NS, the BEP re-optimization problem optimizes the worst-case MLU across all the states as expressed by obective function (5). It is not surprising that the BEP re-optimisation problem is NP-hard, since it is an extension of the reoptimisation problem, which itself is NP-hard BEP RE-OPTIMIZATION HEURISTIC As with the re-optimization, we also propose an iterative local search algorithm for the BEP re-optimizer. The following steps outline the proposed algorithm:

9 Step 1. Set r BEP to zero and calculate the maximum EP utilization under each potential FS (U max (s)). Step 2. Identify the EP with the worst-case maximum link utilization U worst under all FSs (i.e. the link with the highest U max (s) for all FSs). Calculate the utilization of EP ^ with the minimum link utilization (U min (s)) for the state when has the maximum utilization. Step 3. Among all the prefixes whose BEP is, search for the prefix that by re-assigning it to ^ within that state would minimize the worst-case maximum EP utilization by the maximum value. Re-assign the prefix to ^, update both values of U max (s) and U min (s), and set r BEP = r BEP + 1. Step 4. Repeat steps 2 to 3 until either r SER reaches the limit (R-r ) or there is no pre-defined performance improvement for the worst-case performance in comparison to the previous iteration SOLUTION IMPLEMENTATION Due to the increasing use of multi-homing by ASes, most destination prefixes can be reached through multiple EPs. When multiple routes through different EPs are present, routers select the best one according to the BGP route selection process. The BGP route selection process is based on path attributes such as local-preference, AS path length etc. A detailed explanation of this process can be found in [16]. The highest criterion in the BGP route selection process is the local-preference: the route assigned with the largest local-preference value is chosen as the best route to the destination prefix. Therefore, the traffic destined to a destination prefix will exit the AS through the EP that has the largest local-preference value. (a) (b) (c) Figure 4. Traffic demand assignment (a) under NS implemented by BGP local-preference, (b) under FS implemented by BGP local-preference and (c) under FS implemented by IP tunneling for achieving fast failure recovery The local-preference can be used for a simple implementation of the and BEP solutions as follows: for each prefix, we assign the largest value of BGP local-preference for its selected and the second largest value for its selected BEP. Whenever a fails, the EP with the next largest localpreference (i.e. the BEP) becomes the exit point for the traffic towards the destinations. Figure 4 shows an example of this implementation, comprising ingress points i1 and i2, egress points 1, 2 and 3, traffic demands t(i1,k2) and t(i2,k2) and destination prefix k2 that can each be reached through all the three EPs. Figure 4a shows the traffic demand assignment by BGP local-preference setting. In this case, the largest value of BGP local-preference, e.g. 100, is assigned to its selected (i.e. EP 2), the second largest value, e.g. 80, is assigned to its selected BEP (i.e. EP 3) and any BGP local-preference value less than 80, e.g. 50, can be assigned to the remained EP (i.e. EP 1). As a result, as shown in Figure 4a the traffic demand assignment under NS is: t(i1,k2) 2 and t(i2,k2) 2. Also, as shown in Figure 4b under FS (i.e. s=2) the traffic demand assignment is: BEP t(i1,k2) 3 and BEP t(i2,k2) 3. However, measurements from a BGP/MPLS VPN environment [17] have revealed a long BGP convergence time and network instability after the failure of an EP. Several proposals [18,19] have been made to reduce the convergence time by reducing the number of BGP messages that must be exchanged after a failure. However, as they rely on the exchange of messages, the achieved convergence time does not typically meet the stringent requirements of real time services. In order to avoid the long BGP convergence time and achieve fast failure recovery, the fast rerouting approach proposed in [8] can be implemented in which IP tunnels are used to protect inter- AS link failures by diverting the traffic from the failed s to ingress routers of the downstream ASes via the pre-computed BEP. In this approach, the IP tunnel is pre-established at the and terminates at the ingress point of the downstream AS with which the pre-computed BEP is connected. An example of using IP tunneling is illustrated in Figure 4c. Assume that EP2 and EP3 are the and BEP for prefix k2. The dash path indicates the IP tunnel. When EP2 first detects a failure at its attached inter- AS link, it suppresses the advertisement of this route failure to any other routers in the network. As a result, BGP convergence and its problems are eliminated and the BGP routing tables of all other routers

10 except EP2 remain intact. Afterwards, EP2 activates the IP tunnel and diverts the traffic to the tunnel rather than traversing the failed link. The affected traffic is delivered through the tunnel via EP3 and terminates at the ingress point of the downstream AS. In this case the BGP local-preference value of EP1 and EP3 can be any value below the BGP local-preference value of EP2. By using IP tunneling, the traffic on failed inter-as links can be recovered within 50 milliseconds [8]. This rapid recovery time is sufficient to sustain QoS for most of the stringent real-time services such as VoIP. Some implementation approaches of IP tunneling are discussed in [8]. 4. IOTE SYSTEM PROCEDURE Having described all the components of the IOTE SYSTEM in detail, we present an overall system operation as illustrated in Figure 5. Step 1. Network monitoring and traffic measurement: first of all, NMTM is activated to generate global views of network and traffic conditions. Step 2. re-optimization triggering decision making: The triggering module is signaled to calculate the inter-as MLU under the NS according to obective function (1). If the current MLU under the NS exceeds the tolerance threshold 1, the procedure proceeds to the next step. Otherwise it is diverted to the BEP re-optimization triggering decision making block in step 7. Step 3. re-optimization: the re-optimizer is invoked to optimize the current solution by using the proposed local search heuristic algorithm. Step 4. re-optimization stopping decision making: if the number of required reconfiguration exceeds the total reconfiguration limit X or there is no significant performance improvement in the Iteration( n ) Iteration( n 1 ) U max ( ) U max ( ) last iteration of local search (i.e. γ 1 Iteration( n 1 ) < ), the algorithm proceeds to the U max ( ) next step. Otherwise the procedure goes back to the re-optimization and repeats steps 3 and 4 (i.e. the re-optimization cycle) till one of the stopping criteria is met. Step 5. re-configuration decision making: this step determines the new MLU under NS new U max( ) new current U max( ) U max ( ) from the re-optimization cycle and computes the performance gain (i.e.. If current U ( ) the desired gain β 1 is achieved the solution is passed to the next step. Otherwise the procedure is diverted to step 7. Step 6. configuration: this step enforces the r configuration produced by the re-optimizer. current new It updates the current MLU under NS (i.e. U max ( ) = U max( ), calculates and updates the current worst-case MLU across all potential FSs and updates the NIB with new reconfigurations. Step 7. BEP re-optimization triggering decision making: The triggering module calculates worst-case current current inter-as MLU across all FSs (i.e. U max ( ),U worst ). If the current worst-case MLU exceeds the tolerance threshold α 2, the procedure proceeds to the next step. Otherwise it is diverted back to step 1 to continue network monitoring and traffic measurement. Step 8. BEP re-optimization: the BEP re-optimizer is invoked to optimize the current BEP solution by using the proposed BEP local search heuristic algorithm. Step 9. BEP re-optimization stopping decision making: if the number of required BEP reconfiguration exceeds the total BEP reconfiguration limit R-r or there is no significant performance improvement Iteration( n ) Iteration( n 1 ) U worst U worst in the last iteration of local search (i.e. < γ 2 ), the procedure proceeds to the Iteration( n 1 ) U worst next step. Otherwise the procedure goes back to the BEP re-optimizer block and repeats steps 8 and 9 (i.e. the BEP re-optimization cycle) till one of the stopping criteria have been met. Step 10. BEP re-configuration decision making: this step determines the new worst-case MLU across new all potential FSs (i.e. U ) from the BEP re-optimization cycle and computes the performance gain (i.e. U U new current worst worst current U worst worst ). If the desired gain β 2 is achieved the solution is passed to the next step. Otherwise the procedure is diverted back to step 1 to continue network monitoring. max

11 Step 11. BEP configuration: this step enforces the r BEP configuration obtained from the BEP reoptimization cycle. Updates the current worst-case MLU across all potential FSs (i.e. U current new worst = U worst ). Update the NIB with the new BEP reconfigurations. Then the procedure goes back to step 1 to continue network monitoring and traffic measurement. Figure 5. IOTE system procedure 5. ALTERNATIVE STRATEGIES In this section, we present two alternative outbound TE strategies: 1) NO-REOPT: In this strategy neither the nor the BEP re-optimization is considered. Therefore, in the presence of any network changes, the and BEP configurations are always fixed. 2) -REOPT-ONLY: this strategy solely considers the re-optimization. Therefore, in case of an EP failure (transient or non-transient) and also in case of routing changes, the affected traffic will be shifted in accordance with the current BEP configuration. In comparison to NO-REOPT, this strategy attempts to reactively improve the network performance under non-transient FSs and routing changes, if the latest network performance obtained by the monitoring violates the threshold criterion (i.e. the network utilization exceeds the tolerance threshold). In fact, in this case, the re-optimization is triggered to minimize the inter-as MLU under the particular FS (i.e. in this special case that EP has failed we have s= instead of s= ) or under the corresponding routing changes. Note that this strategy cannot improve the network performance in case of a transient failure due to the very short duration of the failure. 6. EVALUATION METHODOLOGY 6.1. NETWORK TOPOLOGY AND DESTINATION PREFIXES According to [20], the typical number of ISPs that a content provider would multi-home to is not higher than We therefore perform our experiments on topologies with 5 and 20 EPs. We assume equal EP capacities and consider their value to be OC-48 (2.5Gbps). However, our approach can be

12 directly applied to EPs with different capacities. For scalability and stability reasons, outbound TE can focus only on a small fraction of Internet destination prefixes, which are responsible for a large fraction of the traffic [2]. In line with [3,21], we consider 1000 such popular destination prefixes. In fact, each of them may not merely represent an individual prefix but also a group of distinct destination prefixes that have the same set of candidate EPs [22] in order to improve network and TE algorithm scalability. Hence, the number of prefixes we consider could actually represent an even larger value of actual prefixes. Recall that, according to Table 1, we can denote Out(k) as the total number of EPs that have reachability to destination prefix k. Without loss of generality, we consider Half Prefix Reachability (HPR) i.e. Out(k) =0.5 J which means that each prefix k is reachable through only half of the total EPs INTER-AS TRAFFIC MATRIX We generate synthetic traffic matrix for our evaluation. Our traffic matrix consists of a set of inter-as traffic flows that originate from each ingress point towards each of the destination prefixes. Previous work has shown that inter-as traffic is not uniformly distributed [23]. According to [22], the volume of inter-as traffic demand is top-heavy and it can be approximated by a Weibull distribution with the shape parameter equal to We generate the inter-as TM following this distribution with the shape parameter equal to 0.3. We remark that our TM generation process is a simple attempt to model inter-as traffic, as no real network based model can be found in the literature IOTE SYSTEM PARAMETERS We realized that by setting the IOTE SYSTEM parameters to the following values we can achieve sufficiently good results: we set the tolerance thresholds 1 and 2 to 1=2=50% as the borderline of congestion to trigger and BEP re-optimizations. This chosen tolerance threshold value is inline with the resource management rule of some ISPs such as Sprint that aim to maintain the average utilization of any link under 50% [24]. For the re-configuration limits, we opt for the operator-based approach since ISPs generally aim to reduce service disruptions [25]. Hence, we assume that for each re-optimization only up to 10% of the total destination prefixes can be disrupted. In other words, X = = 100. We also assume that for each re-optimization only up to 30% of the total destination prefixes can be changed or reconfigured. In other words, R = = 300. This results in the fact that depending on the actual number of re-configurations, only between 20% and 30% of the total destination prefixes can have their BEP to be reconfigured by the BEP re-optimizer at each reoptimization. For the stopping criterion of the local search of and BEP re-optimizer, we consider the pre-defined performance improvement 1 and 2 to be 1=2=5% PERFORMANCE METRICS The following metrics are used in our evaluation. For all these metrics, lower values are better than high values. Inter-AS MLU: This refers to both U max ( ) under NS and the U max (s) under FS s in obective functions (1) and (6) respectively. Service disruption per re-optimization: A traffic flow (service) is disrupted if it is shifted from EP to EP due to re-optimization. We calculate this metric by adding the volume of all traffic flows disrupted for the re-optimization. This metric can be formulated as follows: = (11) sk sk J i I k K J /{ } ServiceDisruption x t(i,k ) y Number of actual and BEP reconfigurations per re-optimization: These refer to r in (2) and r BEP in (7) respectively GENERATED EVENTS Since no realistic model has been investigated for changes in network conditions, such as traffic variations, routing changes, inter-as transient failures (TF) and non-transient failures (NTF), we generate various series of random events that attempt to emulate those realistic changes by assigning an occurrence probability to each event. In addition, due to possibly changes of user behaviour and varying demand for different services [7], gradual traffic changes are quite frequent. As a result we consider half of the event intervals to include the gradual changes in traffic while the other half to include ust small traffic fluctuations. We assume that these intervals are randomly distributed.

15 Figure 6a. The set of randomly generated events for 5-EP topology 5500 UnderLying Traffic Matrix (Mbps) Routing Changes Routing Changes Routing Changes 2500 t0 t Time (5 EP,HPR) Figure 6b. Total underlying traffic during the events for 5-EP topology TF and NTF 1 0 t0 t Time(5 EP,HPR) Figure 6c. Transient and Non-Transient Failures for 5-EP topology

16 Inter AS MLU (No ) t0 Time(5 EP,HPR) Figure 7a. Inter-AS MLU performance of NO-REOPT for 5-EP t 100 Inter AS MLU ( Only) t0 Time(5 EP,HPR) Figure 7b. Inter-AS MLU performance of -REOPT-ONLY for 5-EP 100 t 90 Inter AS MLU (IOTE) t0 Time(5 EP,HPR) Figure 7c. Inter-AS MLU performance of IOTE SYSTEM for 5-EP t

17 Figure 8a. The set of randomly generated events for 20-EP topology 2 x 104 UnderLying Traffic Matrix (Mbps) Routing Changes Routing Changes 1.3 t0 t Time (20 EP,HPR) Figure 8b. Total underlying traffic during the events for 20-EP topology TF and NTF 1 0 t0 t Time (20 EP,HPR) Figure 8c. Transient and Non-Transient Failures for 20-EP topology

18 Inter AS MLU (No ) t0 Time (20 EP,HPR) Figure 9a. Inter-AS MLU performance of NO-REOPT for 20-EP t 100 Inter AS MLU ( Only) t0 Time (20 EP,HPR) Figure 9b. Inter-AS MLU performance of -REOPT-ONLY for 20-EP t Inter AS MLU (IOTE) t0 Time (20 EP,HPR) Figure 9c. Inter-AS MLU performance of IOTE SYSTEM for 20-EP t 7.2. RE-OPTIMIZATON COST METRICS In this section, we compare the re-optimization cost metrics (i.e. Service Disruption, r, r BEP ) of the -REOPT-ONLY and the IOTE SYSTEM. Obviously, for the NO-REOPT, all these cost metrics are zero since this strategy does not perform any re-optimization.

19 Table 2. Re-optimization cost metrics for -REOPT-ONLY and IOTE SYSTEM for 5-EP topology Interval Event Service Disruption r r BEP IOTE IOTE IOTE 2 STI NTF RC GTI RC STI NTF GTI RC NTF Total Table 3. Re-optimization cost metrics for -REOPT-ONLy and IOTE SYSTEM for 20-EP topology Interval Event Service Disruption r r BEP IOTE IOTE IOTE 2 GTI GTI RC NTF STI STI NTF RC NTF STI GTI Total In Tables 2 and 3, each row represents the Nth interval in which re-optimization occurs. The second column represents the type of event that causes the re-optimization and the other columns represent the re-optimization cost metrics. The two tables deal separately with 5-EP and 20-EP topologies. In each metric column, the first value corresponds to the -REOPT-ONLY and the second value corresponds to the IOTE SYSTEM. Both Tables show that in total the -REOPT-ONLY has higher service disruption and more reconfigurations compared to the IOTE SYSTEM. This result was expected since the -REOPT-ONLY

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