Physical vs Virtual Logical Networks The physical network refers to the set of optical nodes and fiber links connecting them The Virtual Logical network is an overlay onto the physical transport network It consists of a set of lightpaths established between a subset of node pairs in the network see Chart 47 in class notes titled Optical Network Architectures Of course the pattern of connectivity depends on the traffic demand between node pairs Hence in a Virtual topology a node corresponds to a routing node in the network and an edge corresponds to a lightpath So if two nodes are connected by a lightpath we say they can communicate in one light hop Note that if two routers are connected by a lightpath they become neighbors regardless whether or not they are connected directly by a fiber link in the Physical topology Note that it may not be possible to set up lightpaths between all node pairs due to technological limitations on number of available wavelengths If two nodes are not connected directly by a lightpath but are connected by a sequence of lightpaths we say that the two nodes are communicating over multi hops The traffic between non neighbors needs to be processed electronically at every intermediate router The traffic between node pairs is routed over the Virtual topology in one or more hops The virtual topology is designed to carry such traffic in a way to optimize some performance metric minimize delay maximize throughput etc Example Consider an 8 node Physical Ring and a 3 dimensional hypercube Virtual Topology The embedded virtual topology looks like this Problem 1 Homework 5 In this case the virtual logical topology is the 3 dimensional hypercube where as the Physical topology is a Passive 8 node Star coupler The average number of hops is found as follows Without loss of generality pick node 000 It is connected to nodes 100 010 and 001 by a single hop it is connected to nodes 110 011 and 101 by 2 hops and it is connected to node 111 by 3 hops so the average number of hops is 3x1 3X2 1x3 7 12 7 There are 12 edges in the hypercube remember each edge correspond to a light path so 12 wavelengths are needed but since the question states that each link represents the ability to transmit in either direction a total of 24 wavelengths are needed The question then states that each waveform can support OC 48 2 5 Gbps Since the traffic is uniform the total flow inside the network is 24 2 5G 60Gbps The question is asking what is the maximum end to end traffic that can be supported That means in our earlier charts on Network of Queues we referred to as the total external traffic offered into the network The total flow x average path length and hence 60G 12 7 35Gbps Problem 2 Homework 5 Here the Physical network is a 5 node unidirectional ring A single wavelength supporting 1n OC 192 is used between adjacent nodes At each node there is an ADM and a router The first Virtual topology is a Bi directional 5 node ring as shown below 1 1 L51 L12 5 2 L45 5 2 L23 L34 4 3 Physical Topology 4 3 Virtual Topology A circuit is a connection for example 1 2 is a circuit and so is 2 1 So from the Virtual topology it is clear that we have a total of 4 circuits The circuit between 1 2 traverses one link or segment which is L12 where as the circuit 2 1 traverses 4 segments namely L23 L34 L45 L51 and similarly for other circuits Note that we have 5 circuits of length 1 segment and 5 circuits of length 4 segments The average number of segments is hence 5 1 5x4 10 5 2 We need to figure out now what is the average of circuits per segment Take the segment L12 for example That segment is used to support circuits 1 2 3 2 4 3 5 4 and 1 5 Hence segment L12 can support 5 circuits Similarly for other segments remember the traffic is uniform Since the capacity of a wavelength is OC 192 each wavelength can supports roughly 5 circuits or channels each at OC 38 Note that OC 38 is not part of the SONET standard but the question is assuming all partitioning of OC 192 are possible Now back to the Virtual topology Remember a node in a Virtual topology a node corresponds to a routing node in the network Take node for example The average number of router hops is 1x1 1x1 1x2 1x2 4 3 2 Since there are 10 circuits and assuming the total external traffic is and the traffic is uniform the average flow per circuit 3 2 10 3 20 The flow matrix is found by considering the logical links There are 10 of them and finding the flows that go over them For example f12 flow between node 1 and node 2 12 13 52 f23 flow between node 2 and node 3 13 23 24 and so on for other logical links The Average network delay Review the charts on flows in network of queues is given by E T 1 f ij 10 log ical links C38 f ij 1 10 3 20 C38 3 20 30 20C38 3 Similar analysis can be carried for the case of fully connected Virtual Topology for that case the average number path length in router hops is 1 Try it and see me in my office Tuesday if you are having difficulty