Provisioning algorithm for minimum throughput assurance service in VPNs using nonlinear programming

Provisioning algorithm for minimum throughput assurance service in VPNs using nonlinear programming Masayoshi Shimamura (masayo-s@isnaistjp) Guraduate School of Information Science, Nara Institute of Science and Technology, Takayama cho 896 5, Ikoma, Nara, 63 92, Japan Katsuyoshi Iida Global Scientific Information and Computing Center, Tokyo Institute of Technology, Tokyo, Japan Hiroyuki Koga Department of Information and Media Sciences, University of Kitakyushu, Fukuoka, Japan Youki Kadobayashi Guraduate School of Information Science, Nara Institute of Science and Technology, Nara, Japan Suguru Yamaguchi Guraduate School of Information Science, Nara Institute of Science and Technology, Nara, Japan Abstract The traditional virtual private network (VPN), which provides best effort or static bandwidth allocation services, does not support bursty Internet traffic well As a way of supporting bursty traffic, a VPN provider can offer minimum throughput assurance (MTA) service to customers MTA service provides higher throughput predictability than best effort VPN service Although there are many proposed network architectures for MTA service, certain parameters should be decided offline as provisioning The difficulty in such provisioning is to meet the minimum throughput requirements in any active state matrices We propose a provisioning algorithm that uses nonlinear programming for MTA service We also quantitatively evaluate our algorithm and its performance Introduction Virtual private networks (VPNs) are used by many organizations as private information networks connecting distant sites at costs lower than those possible with a network of leased lines However, VPNs have difficulty meeting quality of service (QoS) requirements because they must share resources among all users To overcome this problem and satisfy some of the QoS requirements, a framework called provider provisioned VPNs (PPVPNs) was developed by VPN providers The current PPVPN does not support bursty Internet traffic well because it only allocates network resources statically If VPN providers guarantee customers a static amount of This work of K Iida was supported in part by the Ministry of Education, Science, Sports and Culture, Japan, Grant-in-Aid for Young Scientists, 8754, 26 bandwidth, to the result is low bandwidth utilization One way of supporting bursty Internet traffic is to assure minimum throughput to customers With minimum throughput assurance (MTA) service, a customer can obtain much more throughput than the minimum agreed throughput during periods of non-congestion During periods of congestion, the minimum agreed throughput is provided as an average in a certain period Therefore, MTA service can provide higher throughput predictability than best effort VPN service To explain MTA service, we illustrate throughput allocation scenarios in the MTA service in Fig In the figure, aggregated traffic from site A to site A2 and that from site B to site B2 is assigned 5 Mb/s as a minimum throughput Note that hereafter we denote as macro flow the aggregated traffic Fig (a) depicts a no congestion scenario, ie, the macro flow from site B to site B2 is idle In this case, the macro flow from site A to site A2 can obtain a larger throughput than the minimum throughput On the other hand, the throughput for the macro flow from site A to site A2 is only 5 Mb/s in a congestion scenario, as illustrated in Fig (b) However, even in the congestion scenario, MTA service can provide the minimum throughput for any macro flows A lot of research has been done on MTA service Clark et al proposed random early drop routers with in/out bit (RIO) to allocate capacity for best effort service [] According to their performance evaluation, RIO can allocate capacity independent of the effect of RTT This research is considered an important milestone in MTA service provision Fàbrega et al proposed a guaranteed minimum throughput service for TCP flows using measurement-based admission control [2] Methods have also been proposed for MTA service using the idea of ATM s ABR service Li et al proposed the corestateless congestion avoidance scheme for IP networks [5] Lee

(a) No congestion scenario (b) Congestion scenario Figure : Throughput allocation in MTA service et al proposed the weighted proportional fair rate allocation (WPFRA) method for differentiated service (DiffServ) in the Internet [4] Yokoyama et al proposed a one-way version of the WPFRA method to improve its performance [7] Shimamura et al proposed a hose model extension of the WPFRA method [6] To put these proposed methods into practice, certain parameters should be decided offline as a provisioning For example, RIO requires a target rate for each TCP micro/macro flow and the WPFRA method requires the weight for each macro flow However, no such provisioning algorithm has been proposed The difficulty with such provisioning algorithm is to meet the minimum throughput requirements in any active state matrices, in which each element of the matrix represents an active/idle state of traffic from a source to a destination site Since the MTA service must support bursty traffic, some elements of the active state matrix may be idle and may frequently switch from active to idle states We propose a provisioning algorithm that uses mathematical programming, especially nonlinear programming (NLP), to provide MTA service in PPVPNs Mathematical programming is widely and effectively used for network provisioning [3] We describe our algorithm in detail, investigate whether it can meet the throughput requirements in any active state matrix, and evaluate the bandwidth utilization throughout the network The rest of the paper is organized as follows Sect 2 presents our proposed provisioning algorithm for MTA service We evaluate the effectiveness of our approach with quantitative results in Sect 3 and conclude the paper in Sect 4 2 Weight determination algorithm In the Introduction, we argued that MTA service improves the throughput predictability of bursty traffic To implement MTA service, we set three requirements: ) meet the minimum throughput requirement from customers in any active state matrices; 2) fairly distribute the spare bandwidth; and 3) utilize network resources efficiently The WPFRA method and its variants are approaches Formal definition of active state matrix will be described in Fig 3, Sect 22 to MTA service that meet these three requirements The WPFRA method can distribute spare bandwidth based on weight value, therefore it can provide weighted proportional fairness Before using the WPFRA method, the VPN provider must decide the weight values for all combinations of source and destination sites Deciding the weight values to satisfy the minimum throughput requirement of the first requirement is still a challenge The difficulty in deciding the weight values lies in finding a common matrix of weight values that satisfies the minimum throughput requirement for all active state matrices In this section, we first briefly explain the WPFRA method Then we propose a common weight matrix determination algorithm to satisfy the minimum throughput requirements for all elements of the active state matrix 2 WPFRA method and weight matrix determination algorithm We first summarize the WPFRA method The WPFRA method can distribute bandwidth in proportion to the weight value of each macro flow In the WPFRA method, edge and core routers form a VPN providers network and provide a feedback-driven traffic control to utilize the network bandwidth efficiently Ingress and core routers periodically measure the amount of arriving traffic and calculate a fair share rate r f that indicates the amount of allocated capacity for a macro flow with the weight of one A fair share rate is calculated for each output link in a router Egress edge routers periodically send a notification packet to each ingress edge router, and core routers update the value of r f inside the notification packet if it is smaller than the current value stored in the packet Ingress routers obtain the value of r f from the received notification packet and set the value to the explicit rate ER, which indicates that the allocated throughput for a macro flow has a weight of one Finally, they calculate the allocated throughput as ER multiplied by the customer s weight To illustrate how the WPFRA method decides the allocated throughput, we show the following algorithm based on [4] in the following Initialization Let C be the link capacity and S be the spare bandwidth in the current iteration, which is set to where (s, t) is a link S (s,t) C (s,t), Step Let W (s,t) be the sum of each weight value corresponding to all macro flows passing through a link (s, t) and r f(s,t) be the allocated capacity for a macro flow with the weight of one in the link Then, undetermined r f(s,t) is given by r f(s,t) S (s,t) W (s,t) Step 2 After r f(s,t) is calculated, explicit rate ER (i,e) is calculated by ER (i,e) min(r f(s,t) ), 2

Table : Throughput calculation results in Fig 2 Active state B (A,A2) B (B,B2) A A2 B B2 (ER (I,E) ) (ER (I2,E) ) () 5 (25) () (5) () 6 (3) () (6) Figure 2: Example of throughput calculation: Network topology Objective function * Maximize the average of the link utilization rate where (i, e) is a path between ingress and egress routers that contains link (s, t) Step 3 Let w be the previously assigned weight and B be the allocated capacity of each customer given by B (m,n) ER (i,e) w (m,n), () where (m, n) is a path between source and destination sites that contains path (i, e) Step 4 Then, S (s,t) and W (s,t) are updated by S (s,t) S (s,t) B (m,n), (2) W (s,t) W (s,t) w (m,n), where path (m, n) also contains link (s, t) Step 5 Finally, the calculation is terminated if all W (s,t) become zero, ie, all r f(s,t), ER (i,e), and B (m,n) are determined If not, go back to Step To give readers a better understanding, we provide the example depicted in Fig 2 In this example, there are four sites: customer A has two sites, A and A2, and customer B has two sites, B and B2 The traffic of customer A (B) originates at A (B) and is destined for A2 (B2), respectively As described in the figure, the values w (A,A2) and w (B,B2) are respectively assigned weights of one and two The numbers attached with a link indicates the amount of bandwidth for each link in Fig 2 If C (I,C) is larger than 2, B (A,A2) and B (B,B2) become 2 and 4, respectively The fact that C (I,C) is limited to makes throughput calculation difficult Suppose the traffic of customer A and B are both active Then, r f(i,c), r f(i2,c) and r f(c,e) converge, respectively, at, 45 and 25 based on the above algorithm As a result, ER (I,E) becomes and ER (I2,E) becomes 25 Since w (A,A2) and w (B,B2) are one and two, B (A,A2) becomes and B (B,B2) becomes 5 This result is also included in Table Next we develop an algorithm to calculate weight values based on topology, minimum throughput matrix, and active state matrix Since the allocated throughput and spare bandwidth can be calculated using () and (2), we can now formulate the following mathematical programming: Constraints * Allocated throughput Required throughput * Bandwidth usage Link capacity * Weights Note that the allocated throughput, spare bandwidth, and utilization are all represented by polynomials of weights Thus, this mathematical programming can be classified into nonlinear programming (NLP) Table 2 shows an example of calculated weights in a simple NLP In this example, three customers (X, Y, Z) share a single bottlenecked link The required minimum throughput of (X, Y, Z) is (, 2, 6); the bandwidth of the bottlenecked link is The calculated weight values are listed for all active state matrices, ie, (X, Y, Z) = (,, ), (X, Y, Z) = (,, ) and so on All resulting allocated throughputs are grater than the minimum throughput requirement 22 Common weight matrix determination algorithm As we saw in Tables and 2, the allocated throughput is affected by the active state matrix A general illustration of this effect is given by Fig 3 The active state matrix represents an active/idle state of traffic from a source to a destination site, ie, the values of and are idle and active states, respectively The minimum throughput matrix is used to describe the amount of customers minimum throughput requirements from a source site i to a destination site j The zero element of the active state matrix results in zero value in the minimum throughput matrix at the same element in the active state matrix The weight matrix is a weight value used by the WPFRA method When we fix the active state matrix, we can calculate a weight matrix using NLP However, if we change the active state matrix, the weight matrix W k also changes Since dynamically changing the weight value is very difficult to be implemented, we wish to find a common weight matrix that meets the minimum throughput requirement in any active state matrix Therefore, we need a strategy to find a common weight matrix to meet these minimum throughput requirements We then try to derive a common weight matrix Since NLP requires an initial weight matrix, the previously derived weight matrix for an active state matrix can be used as the initial NLP 3

Table 2: Example of weights calculated by NLP Active state Calculated weights Allocated bandwidth Util X Y Z X Y Z X Y Z 3 2 2 6 % 8 357 643 % 8 357 643 % 5 5 % Single bottlenecked link: Required minimum throughput: (X, Y, Z) = (, 2, 6) Active state matrix Minimum throughput matrix Weight matrix j j m 2 m 2j w 2 w Calculated by NLP 2j = W m i m ij w i w ij m m 2j Calculated by NLP w w j w 2 w 2j = W k w i w ij Figure 3: Common weight matrix weight matrix with the input of another active state matrix We hypothesize that this iteration of NLP will converge on the common weight matrix and meet the minimum throughput requirements Based on this hypothesis, we create a basic strategy to obtain the common weight matrix Iteration Previously output values (ie, the weight matrix calculated by NLP) are utilized as an initial weight matrix in the next step Normalization The weights represent a proportional ratio of the allocated bandwidth, ie, the calculated weight matrix (a, b, c) is equivalent to (ka, kb, kc), where k is a variable To avoid this effect, we divide the weight matrix into collision groups, and then we normalize the grouped elements of the weight matrix, such as (ka, kb, kc)/k (a, b, c), in each collision group Stabilization An element of the weight matrix corresponding to the zero element in the active state matrix can be selected for any value To avoid needless change in weight values, we make constraints for such elements, ie, we simply choose the value obtained in the previous iteration We construct our common weight determination algorithm based on this strategy and illustrate it in Fig 4 as a pseudocode Users of our provisioning algorithm must specify the required minimum throughput for each customer site so that the weight matrix satisfying the minimum throughput can be obtained The fundamental calculation complexity will be l u k= 2v k(v k ), where u, v and l is the number of customers, sites per customer, and calculation cycles, respectively 3 Quantitative evaluation In the previous section, we presented our common weight matrix determination algorithm, which is based on the hypothesis that elements converges through the iteration of NLP In this section, we demonstrate that our algorithm converges on a common weight matrix that meets the minimum throughput requirement We also investigate the impact of the imbalanced amount of minimum throughput requirements and whether there is spare bandwidth We use the simple topology illustrated in Fig 5 There are one core and three edge routers, and they form a star topology with a link capacity of 8 in all links All edge routers behave as both ingress and egress routers, ie, traffic is bidirectional between each of a particular customer s sites There are two customers (A, B); each of whom has three sites (A, A2, A3) and (B, B2, B3) Each of customers A and Bs sites is connected to its respective edge router We vary the required minimum throughput to investigate the impact of imbalance ratio and the amount of the minimum throughput as follows: (a) A (x,y) : A (x,z) : B (x,y) : B (x,z) = 2 : 2 : 2 : 2 (b) A (x,y) : A (x,z) : B (x,y) : B (x,z) = : : : 4

LoopNLP(iteration){ InitAllWeights(weights); SetInputValue(topology, reqbw); for ( i=; i<iteration; i++ ) { foreach (pattern) { weights = RunNLP(topology, pattern, reqbw, weights); normalization(pattern, weights); RunNLP(t, p, b, w){ foreach (p) { if( active[i] == ){ # Stabilize value of w[i] SetConstraint(w[i]); ans = SolveNLP(t, p, b, w); return ans; InitAllWeights(weights){ weights = (,,, ); normalization(pattern, weights){ group = divide_group(pattern); foreach (group) { normalized_w[i] = weights/min(weights); return normalized_w[i]; Figure 4: Pseudocode of weight determination algorithm (c) A (x,y) : A (x,z) : B (x,y) : B (x,z) = 3 : : : 3 (d) A (x,y) : A (x,z) : B (x,y) : B (x,z) = 5 : 5 : 5 : 5 There is spare capacity in both scenarios (b) and (d), and the amount of requests are imbalanced in (c) and (d) In this evaluation, we determine the representative weight matrix among a large number of calculated weight matrices in order to utilize a convergence index, which is defined as the maximum ratio of the number of common weight matrices to the number of all weight matrices Using the convergence index, we evaluate our proposed algorithm using the following two convergence indices The first is an average of the highest distributions of each element of the weigh matrix; the second is the highest distribution of a set of all calculated weight values in a weight matrix Here we call the former independent convergence index and the latter dependent (means batched) convergence index We show an example in the context of Table 2 In the independent convergence index, the average of the highest distributions of each site is 83 (= ( + + 5)/3) In the dependent convergence index, the highest distribution of batched tuples of (,, 8) is 5 Both indices adopt (,, 8) as the representative weight matrix in the first processing cycle of our iterative algorithm Figs 6 and 7 show results for the four required minimum throughputs with two convergence indices The x-axis repre- Figure 5: Experimental topology sents the amount of processing from to 3 iterations; the y-axis represents the convergence index, success rate, and average link utilization for each curve Average link utilization is always unchanged at approximately 85 even though the number of iterations increases This shows that our algorithm retains the fundamental advantage of mathematical programming, ie, it maximizes utilization under constraints, even if the iterations increase We found that the success rate progressively converges to for all required throughputs except that shown in Fig 7(d) in the independent convergence index The success rate in Fig 7(d) is low because all convergence indices for each site are independent, ie, not appropriate for the whole network However, the independent indices are always higher than the dependent one because they are determined in the absence of other factors We conclude that the dependent convergence index is more applicable Next we describe the impact of spare capacity on the success rate Under spare capacity scenarios (b) and (d), the difference between the success rate and convergence index is higher than that in scenarios (a) and (c) The convergence index is low because the calculated weights vary over a wide range due to the high latitude of the values Finally, we discuss the impact on the success rate of imbalanced required throughput among sites Our algorithm requires a large number of iterations to make the success rate converge in imbalanced request scenarios (c) and (d) This is due to the complicated topology and requests, though it also demonstrates the effectiveness of our iterative algorithm 4 Conclusion To satisfy customers required minimum throughput, we proposed a provisioning algorithm for MTA service First, we created an NLP to find a weight matrix for each active state matrix Then we proposed a common weight matrix determination algorithm based on the hypothesis of convergence in elements of the iteration of the NLP Through performance evaluations, we showed that our algorithm can converge on a common weight matrix using the convergence indices We also evaluated the impact on convergence of the imbalanced amount of required throughput and the presence of spare bandwidth In future work, to converge these indices more precisely 5

8 8 6 6 4 4 2 2 5 5 2 25 3 5 5 2 25 3 (a) Balanced requests/no spare capacity (b) Balanced requests/spare capacity 8 8 6 6 4 4 2 2 5 5 2 25 3 5 5 2 25 3 (c) Imbalanced requests/no spare capacity (d) Imbalanced requests/spare capacity Figure 6: of independent convergence index 8 8 6 6 4 4 2 2 5 5 2 25 3 5 5 2 25 3 (a) Balanced requests/no spare capacity (b) Balanced requests/spare capacity 8 8 6 6 4 4 2 2 5 5 2 25 3 5 5 2 25 3 (c) Imbalanced requests/no spare capacity (d) Imbalanced requests / Spare capacity Figure 7: of dependent convergence index 6

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