Two routers are connected through the transmission network below. (Routers are at the end points, X and Y ). Derive an expression (in terms of Ai,i=1,,7 ) for the end-to-end availability for the connection between the two routers assuming that the protection mechanism operates instantaneously. In the network above, link availabilities A6 and A7 are 0.95, link availabilities A1 and A5 are 0.96, link availability A3 is 0.92, and the availability of the intermediate nodes (A2 and A4) are both 0.999. Calculate the availability to 4 significant figures of the end-to-end connection between the two routers X and Y. If 1+1 protection is now provided on the three links with lowest availability, re-draw the network diagram with this extra protection included, and calculate the availability of the router connection to 4 significant figures again. (Assume each added protection link has the same availability as the link being protected.) Problem 6 Two routers are connected through the transmission network below. (Routers are at the end points, X and Y ). Using the class notes, complete the derivation of an expression (in terms of A1,A2,A3,A4, and A5 ) for the end-to-end availability of the connection between the two routers assuming that the protection restoration time for any end-to-end flow is instantaneous. Assume the availability of each of the two intermediate nodes is 1. Now assume that the availability of each of the two intermediate nodes between XandY(A6 and A7 ) is not 1 and thus needs to be considered. Derive an expression (in terms of A1,A2,A3,A4, A5,A6 and A7 ) for the end-to-end availability of the connection between X and Y. If link availabilities A1,A2, and A3 are each 0.96, both A4 and A5 are 0.91, and both A6 and A7 are 0.99, calculate the availability of the end-to-end connection to 4 significant figures