# Integrated Backup Topology Control and Routing of Obscured Traffic in Hybrid RF/FSO Networks*

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3 Symbol T F T RF P R F,P R RF,P N G p i P i t f b f r i c l x l f s f,d f O n,i n TABLE I NOTATIONS Definition FSO topology RF topology Aggregate traffic profile Routes on FSO topology Routes on RF topology Number of nodes in the network Number of grids Probability of failure of grid i Set of paths and traffic in R F,P routed through grid i Traffic on path f in R F,P Backup traffic routed on RF topology for path f Minimum fraction backed up among paths in P i Capacity of RF link l Demand of path f routed on link l in R RF,P or R F,P Source and destination nodes for path f Set of outgoing and incoming edges at node n We assume that the probability of failure of grid i is p i.let P i denote the set of paths (which we call demands) and the corresponding traffic being routed through grid i by routing R F,P (of traffic profile P on FSO topology T F ). We refer to P i as the traffic profile for grid i. Each profile P i consists of a subset of demands (paths in R F,P ). The subsets may be overlapping. Since the grids cover the whole network, the union of all profiles P i contains all the paths in R F,P.We denote the backup routing for aggregate traffic profile P on the RF topology T RF,byR RF,P. We want to determine the RF topology and the backup routing in order to maximize the weighted average of the minimum fraction of backup traffic routed for each grid failure, where the weights correspond to the probability of failure of the individual grids. The objective function is stated in Equation 1. max T RF,R RF,P subject to: G i=1 b f p i min (1) f P i t f T RF satisfies interface and range constraints R RF,P satisfies RF capacity constraints Here the minimum is over the demands in P i for each grid i, and the weighted average is taken over the grids. Table I provides a list of notations we use in this paper. III. INTEGRATED TOPOLOGY CONTROL AND ROUTING In this section, we present algorithms for integrated backup topology control and routing. The procedure for computing routing on a given RF topology is the same in all algorithms, but the algorithms for determining that RF topology differ. We first discuss the procedure for computing a backup routing on a fixed RF topology that maximizes the objective function given in Equation 1. We formulate the problem as a multi-commodity flow problem [12], where the set of commodities is the set of demands in i P i, each demand being a commodity. Equation 2 gives a linear program (LP) to solve the routing problem for backup traffic. Equation 2a states the objective. Equation 2b ensures that for every demand in P i, a minimum fraction r i of the disrupted traffic is backed up. Thus, r i measures the minimum fraction of the traffic backed up for all paths (demands) affected when grid i fails. Equations 2d, 2e and 2c represent the flow conservation constraints at the source, the destination and the other network nodes respectively, for every commodity. Equation 2f represents the capacity constraints of RF links, and Equation 2g gives the bounds on the variables. G maximize p i r i (2a) i=1 s.t. b f r i t f, f P i,i {1,,G} x l f = x l f, l I j l O j j {1,.., N} {s f,d f }, f R F,P x l f x l f = b f, f R F,P l O sf l I sf x l f x l f = b f, f R F,P l I df l O df x l f c l, l T RF f R F,P r i 0, 0 b f t f, x l f 0 (2b) (2c) (2d) (2e) (2f) (2g) We now present the topology control and routing algorithms. A. Identical Topology and Routing Algorithm (ITRA) Identical Topology and Routing Algorithm (ITRA) assumes the RF topology to be the same as the FSO topology, and restricts the backup RF paths to be identical to the FSO paths. After identifying the RF topology and paths, it solves the LP of Equation 2 to determine the backup for each demand in R F,P in order to maximize the objective value. The restriction of fixing a set of paths can be incorporated in the LP by setting the flow variables x l f to zero for links l which are not in the path for flow f. We will compare our algorithms with ITRA, as it is based on the currently followed algorithms that use the FSO topology and routes for RF [10]. B. Unweighted Matching Based Algorithm (UMBA) Unweighted Matching Based Algorithm (UMBA) proceeds in two stages (steps). In the first step, it constructs a valid RF topology having maximum number of links using maximum weight matching based algorithm proposed in [6]. By valid topology we mean that the topology satisfies the interface and transmission range constraints at every node. Then the algorithm computes the backup routing R RF,P on this RF topology using the LP presented in Equation 2. In the second step, which we call the post-processing step, the algorithm iteratively modifies the RF topology and recomputes the backup routing to improve the value of the objective function. For doing this, a weight w f, as determined by Equation 3, is

6 TABLE II PERCENTAGE IMPROVEMENT COMPARED TO ITRA, UNIFORM FAILURE PROBABILITIES (UWM FSO TOPOLOGY) TABLE IV PERCENTAGE IMPROVEMENT COMPARED TO ITRA, NON-UNIFORM FAILURE PROBABILITIES (UWM FSO TOPOLOGY) After Step % % % After Step % % % TABLE III PERCENTAGE IMPROVEMENT COMPARED TO ITRA, UNIFORM FAILURE PROBABILITIES (TWM FSO TOPOLOGY) % 0.822% 0.050% performance come primarily from the topology change and not much from changing the routes from current FSO routes (if the topology is the same), and they are considerable. Also, in this case, UMBA is guaranteed to work at least as well as ITRA in each instance of the solution after the first step of UMBA has the same topology as ITRA, and the routing is at least as good as the one used in ITRA. The post-processing step changes the topology only if the objective value increases. Table III shows the performance of the algorithms when the FSO topology is TWM, i.e., it is optimized for the current traffic profile. Results show the performance of ITRA is better than UMBA, and almost as good as TWMA and WPWMBA. Thus, using the same topology and routes for RF as on FSO, along with the backup traffic calculated using the LP formulation of Equation 2 is a good solution in this case. However, each time the FSO topology is modified, there is a disruption in the traffic flowing through the network. Thus, it is not desirable to modify the FSO topology frequently, and it may not be optimized for the current traffic being routed. Therefore, it is desirable to construct an optimized RF topology and routes for the general case where the FSO topology is not optimized for the routed traffic. Thus, the algorithms we propose give significant performance improvements compared to ITRA (similar to the currently used backup strategy). Tables IV and V shows the performance of the algorithms when the FSO topology is UWM and TWM respectively, and the grids have an unequal probability of failure. The network is divided into four equal regions, and the grids in each region have the same probability (the ratio of probabilities between the regions is 1:10:20:30). Grids in multiple regions have failure probability as the maximum probability among those regions. For UWM FSO topology, results show that the algorithms work much better than ITRA as in the case of equal grid failure probabilities. For TWM FSO topology, UMBA, WPWMBA and TWMBA work better than ITRA, with TWMBA being the best. Therefore, the algorithms perform better than ITRA if grid failure probabilities are non-uniform even if the FSO topology is optimized for the current traffic profile % % % TABLE V PERCENTAGE IMPROVEMENT COMPARED TO ITRA, NON-UNIFORM FAILURE PROBABILITIES (TWM FSO TOPOLOGY) 0.218% 3.889% 2.396% V. CONCLUSION This paper considers the problem of integrated topology control and routing of backup paths in the RF component of a hybrid RF/FSO network. We provide a framework for modelling FSO link failures and formulate a routing problem to compute backup paths on a given RF topology, for the traffic flowing on FSO topology. We then integrate the problem of topology control of the RF component, and propose several algorithms. The best algorithm is shown to work much better than the currently employed solution that fixes the RF topology and routes to be the same as the FSO topology and routes, when the FSO topology is not optimized for the current traffic being routed. The algorithms are shown to have a performance gain even when the FSO topology is optimized for the current traffic, if the grid failure probabilities are non-uniform. REFERENCES [1] N. A. Riza, Reconfigurable optical wireless, IEEE LEOS, vol. 1, pp , [2] Z. Yaqoob and N. A. Riza, Smart free-space optical interconnects and communication links using agile WDM transmitters, Digest of the LEOS Summer Topical Meetings, [3] I. F. Akyildiz, X. Wang, and W. Wang, Wireless mesh networks: a survey, Computer Networks, vol. 47(4), pp , [4] A. Kashyap and M. Shayman, Routing and traffic engineering in hybrid RF/FSO networks, IEEE Intl. Conf. Comm. (ICC), [5] M. Garey and D. Johnson, Computers and Intractability: A guide to the theory of NP-Completeness. Freeman and Company, [6] A. Kashyap, S. Khuller, and M. Shayman, Topology control and routing over wireless optical backbone networks, Conf. Inf. Sci. Sys. (CISS), [7] A. Kashyap, M. Kalantari, K. Lee, and M. Shayman, Rollout algorithms for topology control and routing of unsplittable flows in wireless optical backbone networks, Conf. Inf. Sci. Sys. (CISS), [8] M. Kalantari, A. Kashyap, K. Lee, and M. Shayman, Network topology control and routing under interface constraints by link evaluation, Conf. Inf. Sci. Sys. (CISS), [9] S. Ramamurthy and B. Mukherjee, Survivable WDM mesh networks: Part I - Protection, IEEE INFOCOM, pp , [10] S. Bloom and W. S. Hartley, The last mile solution: Hybrid FSO radio, Airfiber, [11] R. K. Ahuja, T. L. Magnanti, and J. B. Orlin, Network Flows: Theory, Algorithms, and Applications. Prentice Hall, [12] T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein, Introduction to Algorithms, 2nd ed. The MIT Press, [13] S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge University Press, [14] CPLEX,

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