1. Profile-Based Topology Control and Routing of Bandwidth-Guaranteed Flows in Wireless Optical Backbone Networks A. Kashyap, M.K. Khandani, K. Lee, M. Shayman Dept. of E.C.E & Institute for Systems Research, UMCP - presented by Joy Ghosh

2. Free space optics – an alternative to Radio Deliver unprecedented bandwidth Deliver unprecedented bandwidth Massive carrier reuse Massive carrier reuse Ultra-low inter-channel interference Ultra-low inter-channel interference Low power consumption Low power consumption Links are point-to-point rather than broadcast Links are point-to-point rather than broadcast

3. The main idea Wireless backbone network Wireless backbone network Free space optical point-to-point links Free space optical point-to-point links High throughput High throughput Low blocking rate Low blocking rate Offline algorithm Offline algorithm Topology control Topology control Bandwidth guarantees for aggregated demands Bandwidth guarantees for aggregated demands Online algorithm Online algorithm Routing Routing Admission control Admission control

4. Topology control Wireless RF networks Wireless RF networks Use of isotropic antennas Use of isotropic antennas Control power to vary transmission range Control power to vary transmission range Conserve power Conserve power Decrease interference Decrease interference BUT, provide adequate connectivity BUT, provide adequate connectivity Wireless Optical networks Wireless Optical networks Limited number of transceivers Limited number of transceivers Potential vs. Actual links Potential vs. Actual links

5. Wireline Optical vs. Wireless Optical Wireline Optical Networks Wireline Optical Networks Transmission range (lightpath length) is not an issue Transmission range (lightpath length) is not an issue One logical hop between source and destination pair possible on availability of sufficient resources and interfaces One logical hop between source and destination pair possible on availability of sufficient resources and interfaces Wireless Optical networks Wireless Optical networks Multihop connection required if source and destination are out of each other’s transmission range Multihop connection required if source and destination are out of each other’s transmission range Hence: logical topology design for wireline optical networks not directly applicable to free-space optical networks  contribution of this paper! Hence: logical topology design for wireline optical networks not directly applicable to free-space optical networks  contribution of this paper!

6. Algorithmic Overview Virtual Topology Traffic Profile Offline Phase Online Phase Routes & BandwidthGuarantees Accepted Flows & Admission Control Virtual Topology a.backbone nodes b.potential links c.interface constraints d.actual links Traffic Profile a.aggregate traffic demands b.statistical measure c.service level agreements ActualTrafficRequests

7. Network Model Graph G = (V, E) Graph G = (V, E) V = # of wireless backbone nodes (routers) V = # of wireless backbone nodes (routers) E = # of potential links E = # of potential links Assumptions Assumptions Very low (to almost none) mobility Very low (to almost none) mobility Wireless link can be set up in any direction within transmission range Wireless link can be set up in any direction within transmission range No optical beam obscuration (not necessary) No optical beam obscuration (not necessary) Links are unidirectional (varying power level of nodes) Links are unidirectional (varying power level of nodes) Link capacities may differ Link capacities may differ Interface constraint (fixed number of transceivers) Interface constraint (fixed number of transceivers)

8. Network Model (contd.) Traffic Profile Traffic Profile Aggregate traffic demands between sources & destinations Aggregate traffic demands between sources & destinations (x  y) traffic demand ≠ (y  x) traffic demand (x  y) traffic demand ≠ (y  x) traffic demand Collection of individual flows: Collection of individual flows: Poisson arrival time with rate λ Poisson arrival time with rate λ i Exponential holding times with mean T Exponential holding times with mean T i CBR for each flow with rate R CBR for each flow with rate R i Mean aggregate traffic for each ingress-egress pair is λTR Mean aggregate traffic for each ingress-egress pair is λ i T i R i

9. The Problem Definition Form sub-graph G’ = (V, E’) such that: Form sub-graph G’ = (V, E’) such that: Interface constraints are satisfied for all nodes Interface constraints are satisfied for all nodes E’ = # of actual links E’ = # of actual links Link capacities are respected Link capacities are respected For a given traffic profile the throughput is maximized For a given traffic profile the throughput is maximized Solution proposed Solution proposed Offline phase computes this sub-graph giving routes and bandwidth reservations Offline phase computes this sub-graph giving routes and bandwidth reservations Online phase uses this sub-graph to select routes and exercise admission control Online phase uses this sub-graph to select routes and exercise admission control Changes in either traffic matrix or node locations triggers Offline phase re-computation (estimated to no more than once per hour) Changes in either traffic matrix or node locations triggers Offline phase re-computation (estimated to no more than once per hour)

10. Integrated Topology Control and Routing Step 1 Step 1 A demand is chosen based on some criteria A demand is chosen based on some criteria Locally optimal paths (maximum K) are computed Locally optimal paths (maximum K) are computed Fractions of the demand are reserved on each of these paths based on some criteria Fractions of the demand are reserved on each of these paths based on some criteria Step 2 Step 2 Potential links on paths thus found, are marked as Actual links Potential links on paths thus found, are marked as Actual links Step 3 Step 3 Capacity on each link is decreased to reflect the reserved bandwidth Capacity on each link is decreased to reflect the reserved bandwidth Step 4 Step 4 Graph is updated by removing all potential links violating interface constraint Graph is updated by removing all potential links violating interface constraint Step 5 Step 5 Steps 1, 2, 3 and 4 are repeated till all demands are either met (partially or fully) or rejected Steps 1, 2, 3 and 4 are repeated till all demands are either met (partially or fully) or rejected

11. Ordering of Demand Selection Sequence Bi-directional links Bi-directional links Two interfaces each Two interfaces each All demands are same All demands are same Traffic Matrix Traffic Matrix {t 12, t 34, t 56, t 78 } {t 12, t 34, t 56, t 78 } 357 468 12 (a) Virtual Topology 357 468 12 (b) t 12 satisfied 357 468 12 (c) t 34, t 56, t 78 satisfied

12. Offline computations Basic Rollout Algorithm (one step look ahead) Basic Rollout Algorithm (one step look ahead) Optimal cost approximated by cost of base policy Optimal cost approximated by cost of base policy Example problem: Maximize G(u) where Example problem: Maximize G(u) where U is a finite set of feasible solutions U is a finite set of feasible solutions u є U ; u = (u 1, …, u N ) u є U ; u = (u 1, …, u N ) “Base heuristic” extends any partial solution to full “Base heuristic” extends any partial solution to full (u 1, …, u n ) (n < N)  (u 1, …, u N ) (u 1, …, u n ) (n < N)  (u 1, …, u N ) Let H(u 1, …, u n ) = G(u 1, …, u N ) Let H(u 1, …, u n ) = G(u 1, …, u N ) Rollout algo R extends partial solution by one component Rollout algo R extends partial solution by one component R(u 1, …, u n-1 )  (u 1, …, u n ) R(u 1, …, u n-1 )  (u 1, …, u n ) u n is chosen to maximize H(u 1, …, u n ) u n is chosen to maximize H(u 1, …, u n )

13. Rollout algorithm for TCR a) Path Computation Step 1 Step 1 i=0; // number of paths found for a demand i=0; // number of paths found for a demand d is aggregate demand for one ingress-egress pair (d 0 =0 ) d is aggregate demand for one ingress-egress pair (d 0 =0 ) Repeat Step 2 till Repeat Step 2 till No more path can be found No more path can be found Whole demand is met Whole demand is met i = K // the maximum paths allowed for one ingress- egress pair i = K // the maximum paths allowed for one ingress- egress pair

14. Rollout algorithm for TCR a) Path Computation (contd.) Step 2 Step 2 Find a path using Constrained Shortest Path First (CSPF) Find a path using Constrained Shortest Path First (CSPF) Should accommodate at least (d - d i ) / (K - i) bandwidth Should accommodate at least (d - d i ) / (K - i) bandwidth Constraints Constraints Interface constraint Interface constraint Available bandwidth on links Available bandwidth on links d i+1 = Route as much as possible of remaining demand d i+1 = Route as much as possible of remaining demand Decrease bandwidth on links of this path by d i+1 Decrease bandwidth on links of this path by d i+1 i = i + 1 i = i + 1

15. Rollout algorithm for TCR b) Base Heuristic Routes demands in decreasing order of magnitude Routes demands in decreasing order of magnitude Uses the path computation method discussed Uses the path computation method discussed Demands are either met (fully or partially) or are blocked (assigned ‘null’ routes) Demands are either met (fully or partially) or are blocked (assigned ‘null’ routes)

16. Rollout algorithm for TCR c) Index Rollout Algorithm At the n th step demands (t 1,…, t n-1 ) have been seen At the n th step demands (t 1,…, t n-1 ) have been seen Choose t n from amongst the demands remaining to maximize the throughput given by the “base heuristic” on partial solution (t 1, …, t n ) Choose t n from amongst the demands remaining to maximize the throughput given by the “base heuristic” on partial solution (t 1, …, t n ) Always performs at least as well as the “base heuristic” Always performs at least as well as the “base heuristic”

17. Online routing and Admission Control When a flow arrives at source When a flow arrives at source Check available reserved BW on all pre-computed paths for that ingress-egress pair Check available reserved BW on all pre-computed paths for that ingress-egress pair If not enough BW available on any one path, check reserved and also unreserved BW on all pre-computed paths for that pair (leave other pairs alone!!) If not enough BW available on any one path, check reserved and also unreserved BW on all pre-computed paths for that pair (leave other pairs alone!!) If still not enough BW, block flow  admission control If still not enough BW, block flow  admission control Path selection from amongst pre-computed paths Path selection from amongst pre-computed paths Minimum BW first: allows larger demands in future Minimum BW first: allows larger demands in future Maximum BW first: ensures fairness amongst routes Maximum BW first: ensures fairness amongst routes

18. Computational Complexity Online algorithm Online algorithm O(K) for routing decision for at most K paths O(K) for routing decision for at most K paths ~ O(1) since K is fixed ~ O(1) since K is fixed Offline algorithm Offline algorithm N = # of nodes; M = # of traffic demands; N = # of nodes; M = # of traffic demands; Shortest path = O(N 2 ) // modified Dijkstra’s Shortest path = O(N 2 ) // modified Dijkstra’s Sorting demands = O(MlogM) << O(N 2 ) // ignored Sorting demands = O(MlogM) << O(N 2 ) // ignored Base Heuristic = O(KMN 2 ) Base Heuristic = O(KMN 2 ) Max of K paths for each of M demands Max of K paths for each of M demands Index rollout = O(KM 3 N 2 ) Index rollout = O(KM 3 N 2 ) Each decision step, for each M demand “base heuristic” is used Each decision step, for each M demand “base heuristic” is used M decision steps in all M decision steps in all

19. Simulation Parameters 50 nodes uniformly distributed (avg. 7.5 neighbors) 50 nodes uniformly distributed (avg. 7.5 neighbors) Transmission ranges for all nodes are same Transmission ranges for all nodes are same Capacity of each link = 100 units in each direction Capacity of each link = 100 units in each direction # of nodes capable of being source/destination = 12 # of nodes capable of being source/destination = 12 # of source-destination pairs = 100 # of source-destination pairs = 100 Arrival Poisson rate (λ): uniform between 10 and 20 per unit time Arrival Poisson rate (λ i ): uniform between 10 and 20 per unit time Mean Holding time (T i ): uniform between 1 and 2 units of time Mean Holding time (T i ): uniform between 1 and 2 units of time # of transmitters = # of receivers = 3 # of transmitters = # of receivers = 3 Max # of paths per ingress-egress pair (K) = 3 Max # of paths per ingress-egress pair (K) = 3 Weight of each link for CSPF = 1 // shortest path = min-hop path Weight of each link for CSPF = 1 // shortest path = min-hop path Simulation was run 10 times for 30 units of time each, starting each time with above parameters Simulation was run 10 times for 30 units of time each, starting each time with above parameters

20. Simulation results I

21. Simulation results II

22. Simulation results III

23. Conclusion Index rollout works better than “base heuristic” Index rollout works better than “base heuristic” 10.83% increase in throughput 10.83% increase in throughput 73.86% decrease in flow rejects 73.86% decrease in flow rejects On passing same traffic parameters to both Offline and Online phase, rollout admits 12.61% more calls than the “base heuristic” On passing same traffic parameters to both Offline and Online phase, rollout admits 12.61% more calls than the “base heuristic” On fixing K and also M, we get O(N 2 ) time complexity On fixing K and also M, we get O(N 2 ) time complexity