QUALIFYING CHARACTERISTICS OF LINK SHUTDOWN METHOD WTC 2012 Conference 4-7 March 2012 Miyazaki, JAPAN Simon Tembo, and Ken-ichi Yukimatsu Department of Computer Science and Engineering, Graduate School of Engineering and Resource Science, AKITA UNIVERSITY Shohei Kamamura, Takashi Miyamura and Kohei Shiomoto NTT Network Service Systems Laboratories, NTT CORPORATION 1
INTRODUCTION Cause of IP Network Failures Shutting down a link due to Currently, ISPs use a graceful link shutdown method by first setting up routine maintenance is the Interior Gateway Protocol (IGP) considered as a planned link metric to MAX_METRIC - 1 and network failure. then shutdown the link. The link metric of a link can be Cause of IP Network Failures increased to a larger metric by progressively increasing the metric 20% of a link by 1, until the target metric m m 1 is reached 1 0 such that it cannot carry traffic 80% anymore at which point the link can then be safely shutdown. We present that a Pythagorean Triple Metric Sequence can be used Due to Routine Maintenance Due to Unplanned Failures to shutdown a link during routine 2 maintenance.
Using Pythagorean Triple Properties to Compute MAX_METRIC – 1 1. Using Euclid Formula: Pythagorean triples from any two positive integers 2 2 m n m and n; m>n . In terms of sequence we 2 mn have : {a, b, c} 2 2 2 2 { , 2 , } a m n b mn c m n 2 2 m n If n = 1, the triples are 2 2 2 a m n 256 1 65,535 2 2 { a m 1, b 2 , m c m 1 } b 2 mn 512 Graceful Link Shutdown Method: MAX_METRIC – 1 2 2 2 c m n 256 1 65,537 Where m=256; n=1 16 2 a MAX _ METRIC 1 2 1 256 1 65,535 3
Using Pythagorean Triple Properties and Genealogical Tree to Compute Pythagorean Triple Metric Sequence - Starting from {3,4,5} 4,3 3,2 8,3 2m-n, m c 7,2 b 8,5 2m+n, m m,n 5,2 12,5 2,1 a 9,2 m+2n, n 7,4 4,1 9,4 6,1 {7,24,25} {a-2b+2c, 2a-b+2c, 2a-2b+3c} {5,12,13} {55,48,73} {45,28,53} {a+2b+2c, 2a+b+2c, 2a+2b+3c} {a,b,c} {39,80,89} {-a+2b+2c, -2a+b+2c, -2a+2b+3c} {21,20,29} {119,120,169} {3,4,5} {77,36,85} {33,56,65} {15,8,17} {65,72,97} 2 2 2 2 { a m n b , 2 mn c , m n } {35,12,37} 4
Using the Pythagorean Triple Metric Sequence Method we Compute Target Metrics for Link Shutdown If {a, b, c} is a Pythagorean triple, so is {ka, kb, kc} for any positive integer k , and that the smallest Pythagorean Triple is {3, 4, 5} when k=1 . The {3, 4, 5} triple and its multiples {3n, 4n, 5n} are the only Pythagorean triple that are in arithmetic progression and consecutively incrementing. We use the Pythagorean Triple Sequence {3n, 4n, 5n} to determine a sequence of link metrics as target metrics to use to shut down a link. n PRIMITIVE TARGET METRIC 2 1 1 x 3, 4, 5 3, 4, 5 n 2 2 x 3, 4, 5 6, 8, 10 n 3 3 x 3, 4, 5 9, 12, 15 n 4 1 4 4 x 3, 4, 5 12, 16, 20 5 5 x 3, 4, 5 15, 20, 25 n n … … … n n x 3, 4, 5 3n, 4n, 5n 3 0 n 5
Result of using Pythagorean Triple to Shut Down a Link When we shutdown links 1-2/2-1 0.35 traffic destined for node 2 routing is: 0.30 UTILIZATION 0.25 2 0.20 0 n 5n 0.15 0.10 n 4 1 1 3 0.05 n n 0.00 4 lk 0-1 lk 0-3 lk 1-0 lk 1-2 lk 1-4 lk 2-1 lk 2-4 lk 3-0 lk 3-4 lk 4-1 lk 4-2 lk 4-3 Routing 3 2 0 n All Links @n All Links @n; Except Links 1-2 & 2-1@5n Link Cost Result of using Pythagorean Triple to Shut Down Two Links We are also able to shutdown 0.50 0.45 two links (e.g. 1-2/2-1 and 1-4/4-1) 0.40 using our Method. UTILIZATION 0.35 2 0.30 0.25 n 5n 0.20 0.15 4n 4 1 0.10 0.05 n n 0.00 lk 0-1 lk 0-3 lk 1-0 lk 1-2 lk 1-4 lk 2-1 lk 2-4 lk 3-0 lk 3-4 lk 4-1 lk 4-2 lk 4-3 Routing 3 0 n All Links @n All Links @n; Except Links 1-2 & 2-1@5n; & Links 1-4 & 4-1 @4n 6 Link Cost
Links that can be shut down when link cost reaches the link metric of {3n, 4n, 5n} During our experiments each link was configured to {n, 2n, 3n, 4n, 5n} 0.084314573 0.1 UTILIZATION 0.08 link metric; 0.084314573 0.042157287 0.06 0.04 Some links it is only when the link 0.02 0 0.042157287 0 0 0 metric reached {3n, 4n, 5n} that the 0 n 0 2n 0 link utilization was zero. 3n 4n 5n LINK METRIC SEQUENCE lk 1-2 lk 2-1 Links that can be shut down ONLY when link cost reaches the link metric of {4n, 5n} Whereas other links it is only when 0.268273642 0.3 the link metric reached {4n, 5n} that UTILIZATION 0.25 0.268273642 the link utilization became zero. 0.2 0.15 0.1 0.009263101 0.05 0.009263101 0.0061754 0 0 0 0.0061754 n 0 0 2n 3n 4n 5n LINK METRIC SEQUENCE lk 0-3 lk 3-0 7
Our Simulation Results in Summary & Conclusion 50% of the links were shutdown when link cost reached the link metric of {3n, 4n, 5n} 50% of the links were shutdown ONLY when link metrict reached the link metric of {4n, 5n} 50% 50% We have presented a link shutdown method using the Pythagorean Triple Metric Sequence that can be used to configure and shutdown a link for routine maintenance. Thus when a link is scheduled for routine maintenance the link can be configured to one of the metric in the sequence {3n, 4n, 5n} as the target metric before shutdown. Future work, we plan to investigate the use of other Pythagorean Triple Sequences other than the {3 n, 4n, 5n}. 8
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