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# HW9_Sol - Telcom 2110 Network Design Homework#9 Spring 2010...

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Telcom 2110 Network Design Homework #9 Spring 2010 1. In the packet based VPN design discussed in class an equivalent capacity calculation is used at an edge node to determine the amount of bandwidth requires on a LSP. Consider the sink tree LSP 2 shown in the MPLS network below. At nodes A and B the offered load to node C has the characteristics ( R peak =5Mbps, b =500 msec, ρ =0.3, B = 2000msec at peak rate, = 10 ‐4 , m = 1Mbps, = .24 ). (a) Determine the amount of capacity that should be allocated to the LSP at the entry nodes of LSP 2. The amount of capacity that should be allocated to the entry LSP at the entry nodes can be estimated from ˆ c i R peak a 1 ( a 1) 2 4 a 2 a where a   b B (1 )ln From the characteristics given, we have a   500*10 3 2000*10 3 (1 0.3)ln(10 4 ) 1.612 and ˆ c i 5*10 6 1.612 1 (1.612 1) 2 4 *0.3*1.612 2*1.612 3.306*10 6 = 3.306Mbps (b) One of the motivations for using sink trees is save bandwidth where branches of a tree merge. Determine the equivalent capacity needed for the traffic from nodes A and B to C in LSP 2 at the merger point and compare it to peak rate allocation. At the merged link with 2 traffic connections multiplexed, we have ˆ C 2* R peak ˆ C min{2* m * ,2* ˆ c i } 2ln( ) ln(2 ) 2ln(10 4 ) ln(2 ) where Thus, the equivalent capacity needed for the traffic from nodes A and B to C in LSP2 at the merger point is ˆ C min{2*1*10 6 2ln(10 4 ) ln(2 ) *0.24,2* 3.306*10 6 } min{2*10 6 ,6.6*10 6 } 2*10 6 = 2 Mbps which is significantly lower than peak rate allocation.

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