1. Efficient link scheduling for online admission control of real-time traffic in wireless mesh networks P. Cappanera a, L. Lenzini b, A. Lori b, G. Stea b, G. Vaglini b Dip. di Sistemi e Informatica, University of Florence, Italy Dip. di Ingegneria dell’Informazione, University of Pisa, Italy Published in Computer Communications 2011 1

2. Outline Introduction System model Worst-case delay in a sink-tree network Delay-aware link scheduling Iterative solution approach Efficient approximate solution for the MinWL problem Performance evaluation Conclusions 2

3. Introduction Wireless mesh networks are an emerging class of networks, usually built on fixed nodes that are inter- connected via wireless links to form a multi-hop network. – radio resource management challenges come into play. – The fact that mesh routers are fixed makes the backhaul of a WMN inherently different from distributed wireless networks – This makes it sensible to opt for a centralized network management 3

4. Introduction (cont’d) One of the most widely used techniques to achieve robust and collision-free communication is link scheduling, operating in the TDMA. – very few works published so far have addressed the problem of computing a link schedule with maximum end- to-end delays as a constraint Objective of this paper – Find a conflict-free link scheduling such that the delay bounds of all its flows are not violated. 4

5. Introduction (cont’d) We consider leaky-bucket-shaped flows traversing a sink-tree WMN which get aggregated as soon as they proceed towards the gateway. – the maximum end-to-end delay at the flow level can be computed using a Network Calculus approach. The link scheduling problem is mixed integer/nonlinear non-differentiable, and, as such, very hard to solve in practice. – We propose an alternative strategy to solve the same problem 5

6. System model Transmission slots of a fixed duration T s are grouped into a frame of N slots. Each slot is assigned to sets of non-interfering links through conflict-free link scheduling. a link e which is activated for Δ e slots in a frame starting from an offset π e – long-term minimum guaranteed rate equal to R e = c e *π e /N – ϴ e = (N- Δ e )*T S 6

7. System model (cont’d) We assume that a FIFO service discipline is in place at each link, meaning that traffic from different flows is queued First-Come-First-Served. Each flow has a delay constraint, specified as a required end-to-end delay bound δ. We assume that traffic is fluid, leaving packetization issues for further study. 7

8. System model (cont’d) A path P i is a loop-free sequence of n i nodes, from an ingress node to the egress one. 8

9. Worst-case delay in a sink-tree network 9 l i (h i ) : the label of the h i th node in path P i

10. Worst-case delay in a sink-tree network (cont’d) Based on Theorem 1 and Property 2, we can also model the aggregate traffic that joins path P i at node l i (h), composed of both arriving from upstream nodes and fresh flow injected at node l i (h) itself, as a single flow. We call it the interfering flow (i,h), and we denote its leaky- bucket parameters as σ (i,h), ρ (i,h). 10

11. Worst-case delay in a sink-tree network (cont’d) 11

12. Worst-case delay in a sink-tree network (cont’d) In order for queues not to build up indefinitely at a node x, the following stability condition must be ensured: The worst-case delay for the flow traversing that path is upper bounded by: – where CR li (h) is the clearing rate at node l i (h). 12

13. Worst-case delay in a sink-tree network (cont’d) Call the sequence of W x  1 bottleneck nodes for node x, sorted in the same order as they appear in any path that traverses that node, so that b x 1 =x. 13

14. Delay-aware link scheduling Each link must accomplish its transmission within the frame duration For any pair of active links i and j connected by an edge in the conflict graph we have: 14

15. Delay-aware link scheduling (cont’d) The end-to-end delay feasibility problem (E2EFP) is – where S is the feasible region of a conflict free schedule, i.e. the set of variables that satisfy constraints (6) and (7). 15

16. Iterative solution approach This problem is very hard to solve even for trivial instances, due to the fact that it is simultaneously integer, non-linear and non-differentiable. – Hence, we design a heuristic iterative solution approach. 16 Delay-based admission control

17. Minimum weighted latency scheduling We define the weighted latency of a network as follows: – The link weight w e is set to the aggregate flow of link e itself, i.e. w e = r e The MinWL scheduling problem is 17

18. Heuristic feedback The heuristic feedback consists in reformulating the MinWL problem forcing a solver to give a higher rate to the bottlenecks of those flows that violate their deadline. More specifically, at each iteration the violating flow with the maximum difference between the actual and the required delay bound is selected: 18

19. Heuristic feedback (cont’d) Its first downstream bottleneck is then given extra rate. This is done by substituting the constraints of Δ e with – where a e is the number of extra units of rate K to be scheduled for link e. – Variable a e is initially null, and it is increased by one on each iteration. 19

20. An example of the iterative solution 20

21. The end-to-end delay bounds for each flow computed at each iteration of the MinWL problem 21

22. Efficient approximate solution for the MinWL problem By relaxing the integrality for π e, Δ e and assigning o ij a value, we obtain a continuous linear problem, which can be solved in polynomial time. Capitalizing on this, we devise a solution algorithm which is composed of two blocks – a first block that assigns values to each conflict orientation o ij using a customized dive-and-fix heuristic; – a second block that solves a reduced MinWL problem, which emerges from the previous step once the conflict orientations are set, with relaxed integrality constraints. Its solutions are then rounded preserving the conflict-free property. 22

23. Efficient approximate solution for the MinWL problem (cont’d) Dive-and-fix heuristic – It iteratively does the following: it solves (i.e. ‘‘dives’’ into) a linear relaxation of the MILP, it identifies a subset of integer variables to target (i.e. to ‘‘fix’’), and rounds them to the closest integer As variables are fixed, smaller MILPs are obtained for subsequent iterations 23

24. Efficient approximate solution for the MinWL problem (cont’d) we maintain an iteration counter i, which is increased at every iteration if i is a multiple of a configurable parameter H, both the dive- and-fix and the reduced MinWL are executed on the new problem instance as modified by the feedback otherwise, only the reduced MinWL problem is solved, 24

25. Performance evaluation As a first study, we show that the feedback granularity K has an impact on the overall computation time – The instance is a network with 30 homogeneous flows with σ = 150, ρ = 300 and δ = 22, for which the E2EFP is indeed feasible. 25

26. Performance evaluation (cont’d) We now move to considering the effectiveness of the heuristic solution of the MinWL. – 100 instances were created by generating the flow rate from a uniform distribution within [50,300]. 26

27. Performance evaluation (cont’d) The percentage of E2EFP instances which can be solved using the heuristic approach, for different values of H, for K = 100 and K = 500. 27

28. Performance evaluation (cont’d) Distribution of the solution times with the heuristic approach for K = 100 and K = 500. 28

29. Performance evaluation (cont’d) Achievable rates for different required delay bounds and bursts 29

30. Performance evaluation (cont’d) Comparison between the optimal solutions to a TDMA-delay minimization problem and the solutions obtained with our framework 30 (Fix δ= 35, ρ = 300,) [17] P. Djukic, S. Valaee, “Delay aware link scheduling for multi-hop wireless networks,” in IEEE/ACM Transactions on Networking 17 (3) (2009) 870–883.

31. Conclusions This paper has addressed the problem of link scheduling in Wireless Mesh Networks – this one has brought end-to-end delay bounds in the picture We adopted a heuristic iterative solution scheme, – a mixed integer-linear formulation of the link scheduling problem – a feedback module which tests whether the delay bound constraints are met in the current schedule. The suboptimal approximated solution allows link schedules to be computed in hundreds of milliseconds in large-scale mesh networks, without losing much as far as solution quality is concerned with respect to the optimal approach. 31

32. Comments This paper calculate the end-to-end delay bounds of flows with shaped traffic in WMN. The iterative solution with feedback mechanism is interesting. – Similar to our bulk scheduling. (Find the bottleneck, then increase the bandwidth of bottleneck) For a VBR traffic flow, the shaping delay must be taken into account. 32