Consider the network fragment shown below.   X has only two attached neighbours, W and Y, with link costs as C(X,Y)=50, C(X,W)=8, C(Y,W)=4. W has a minimum-cost path to destination U (not shown) of 20, and Y has a minimum-cost path to U of 30. The complete paths from W and Y to U are not shown. All links in the network have strictly positive integer values. The network runs a distance vector routing algorithm (without poisoned reverse). Answer the following questions: What is the distance vector of X to destination U, DX(U)= ________

Operations Research : Applications and Algorithms
4th Edition
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Wayne L. Winston
Chapter20: Queuing Theory
Section20.10: Exponential Queues In Series And Open Queuing Networks
Problem 8P
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Consider the network fragment shown below.

 

  • X has only two attached neighbours, W and Y, with link costs as C(X,Y)=50, C(X,W)=8, C(Y,W)=4.
  • W has a minimum-cost path to destination U (not shown) of 20, and Y has a minimum-cost path to U of 30. The complete paths from W and Y to U are not shown.
  • All links in the network have strictly positive integer values. The network runs a distance vector routing algorithm (without poisoned reverse).

Answer the following questions:

  1. What is the distance vector of X to destination U,
    DX(U)= ________
  2. Suppose the link cost between X and Y decreases to 2.
    In response to the link cost change, the distance vector of X to destination U is updated to:
    DX(U) = _________
  3. Suppose the link cost between W and X increases to 60 (link (X,Y) still has cost of C(X,Y)=50).
    Immediately after this cost increase, the distance vector of W to destination X will be updated to;
    DW(X) = __________
    Node W will then send routing updates to all its neighbours about this change.
    After receiving W's routing update, Y will update its distance vector for destination X to:
    DY(X) =  .__________
    After the routing protocol converges, the distance vector of W to destination X will be updated to;
    DW(X) = __________

note: enter integer numbers only

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