A Fair Scheduling for Wireless Mesh Networks Naouel Ben Salem and Jean-Pierre Hubaux Laboratory of Computer Communications and Applications (LCA) EPFL – Lausanne, Switzerland Presented by Yeong-cheng Tzeng

Outline 1. Introduction 2. State of the Art 3. System Model 4. Details of the Solution 5. Evaluation of the Solution 6. Discussion 7. Conclusion

1. Introduction WiFi networks have become increasingly popular: Communications are short-range Clients need to be in the immediate vicinity of the Internet HS Have to deploy hot spots at well-chosen locations

1. Introduction (cont’d) Wireless Mesh Networks: An extension of WiFi: One wired hot spot HS Several Transient Access Points (TAPs) Wireless communications Possible interference The TAPs are not directly connected to the Internet: They rely on HS relays to get Internet connectivity for their clients

1. Introduction (cont’d) If the medium access protocol is poorly designed Severe unfairness (starvation) Low bandwidth utilization Propose a fair scheduling mechanism that optimizes the bandwidth utilization. Assign transmission rights to the links in the WMN and maximizes the Spatial Reuse

2. State of the Art Mesh Networks [1] I. F. Akyildiz, X. Wang, and W. Wang. Wireless Mesh Networks: A Survey. Computer Networks Journal (Elsevier), 47(4), Present a survey on recent advances and open research issues in WMNs Point out an important research topic: Revise the design of MAC protocols based on TDMA or CDMA

2. State of the Art (cont’d) STDMA Scheduling [18] S. Nelson and L. Kleinrock. Spatial TDMA: A Collision-Free Multihop Channel Access Protocol. IEEE Transactions on Commnuications, 33(9), Propose a protocol which assigns transmission rights to nodes in the network in a local TDMA fashion and is collision-free [10] J. Gronkvist. Assignment Methods for Spatial Reuse TDMA. In Proceedings of MobiHOC, Compare the node assignment and the link assignment methods Node assignment: Low traffic loads and lower transmission time Link assignment: High traffic loads and higher reuse efficiency

2. State of the Art (cont’d) Fairness in Mesh Networks [8] V. Gambiroza, B. Sadeghi, and E. Knightly, “End-to-End Performance and Fairness in Multihop Wireless Backhaul Networks" in Proceedings of MobiCom Three main difference with [8]: The definition of fairness: Per-Client fairness vs Per-TAP fairness The network topology: The whole network vs One branch Traffic model: No inter-TAP communications vs possibility of inter-TAP communications

3. System Model A directed graph: V={HS, TAP i, 1≤ i ≤ n} Communication links Upstream (UL) Downstream (DL) Interference links (IL) Assumptions: One operator and fixed topology Omni directional antennas All the clients pay the same flat rate All the clients send and receive data at saturation rate Orthogonal channels for upstream and downstream traffic All communication links have the same capacity C

Per-client fairness condition: Network throughput: To max Γ, duration time to f a should be the same for all links The per-client fairness condition gives: The duration time dedicated to each flow on each link should be the same; we call this time a time slot 3. System Model (cont’d)

Link (i, j) is activated during l i,j time slots Each client sends the same amount of data The number of time slots in the cycle is T= =24 Each client sends the same throughput ρ = C/T No spatial reuse The solution is not optimal

3. System Model (cont’d) Some links can be activated at the same time A shorter cycle (T=19 instead of 24) Optimal spatial reuse: We have to minimize T

3. System Model (cont’d) Optimization of bandwidth Utilization Maximize the throughput Need to minimize T, while respecting the fairness condition T’s upper bound Links in the WMN mutually contend T’s lower bound Depend on the topology and the position of clients

4. Details of the Solution A scheduling mechanism: Fair: The per-client fairness condition is ρ a = C/T Optimal bandwidth utilization: Minimize T Three main components: Construction of the compatibility matrix/graph Construction of the cliques Definition of the fair scheduling (FS)

4. Details of the Solution (cont’d) Construction of the compatibility matrix/graph

4. Details of the Solution (cont’d) Construction of the cliques A clique is a set of links which can all be enabled at the same time.

4. Details of the Solution (cont’d) Definition of the fair scheduling (FS) A scheduling s is a set of cliques that fulfills:

4. Details of the Solution (cont’d) Rationale of FS: 1. s = Φ 2. G = compatibility graph 3. Search for the clique Cl max with the maximal gain in G 4. s = s U Cl max 5. G = G - Cl max 6. if |G|>0, go to step 3

5. Evaluation of the Solution The fair collision-free scheduling proof Proposition 1: ŝ is a fair scheduling. Proof: Conditions (6) and (7) guarantee that, during the cycle, each active link (i,j) is actived exactly once during l i,j time slots. Therefore, each end-to-end flow is activated during one time slot ts, which allows each flow client to send (or receive) the same amount of data ts ·C and shows that ŝ is a fair scheduling. Proposition 2: ŝ is a collision-free scheduling. Proof: The scheduling ŝ being a disjoint union of cliques (i.e., a union of cliques whose members are pairwise disjoint), two links that are in two different cliques in ŝ never contend as they are activated at two different time periods. Furthermore, a clique is, by definition, a set of non-contending links. Therefore, ŝ is a collision-free scheduling.

5. Evaluation of the Solution (cont’d) Matlab simulations Two network topologies: One-dimensional: 10, 15, 20 and 25 nodes Two-dimensional: 8, 16, 24 and 32 nodes Nodes distribution: m=2n Uniform distribution Peripheral distribution Central distribution We compare the performance of our solution with the scheduling without spatial reuse

5. Evaluation of the Solution (cont’d)

Optimality of our fair scheduling FS is an approximation of the optimal scheduling s * Implement an algorithm to search the optimal solution s * Enumerate all the possible schedulings Resulting schedulings ŝ to s * are identical for all the scenarios

6. Discussion Topology discovery HS use an ad hoc routing to construct the network topology and inform all the TAPs Exchange messages over the control channel Assume all links are stable over time Complexity of the solution Compatibility matrix construction phase and FS algorithm are polynomial Clique construction phase The clique enumeration problem is proven to be NP-hard Relative small size of WMN Capacity reuse A connected client remains idle for a long period of time Disconnect it

7. Conclusion If the medium access protocol is poorly designed Severe unfairness Low bandwidth utilization Propose a scheduling mechanism that: Fair Optimizes the bandwidth utilization Prove the efficiency of our solution by means of simulations Future work: Relax some of the assumptions

The End