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Efficient link scheduling for online admission control

of real-time traffic in wireless mesh networks

P. Cappaneraa, L. Lenzinib, A. Lorib, G. Steab, G. Vaglinib

Dip. di Sistemi e Informatica, University of Florence, ItalyDip. di Ingegneria dell’Informazione, University of Pisa, Italy

Published in Computer Communications 2011

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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

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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

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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.

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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

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System model

• Transmission slots of a fixed duration Ts 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 Δe slots in a frame starting from an offset πe

– long-term minimum guaranteed rate equal to Re = ce*πe/N

– ϴe = (N- Δe)*TS

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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.

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System model (cont’d)

• A path Pi is a loop-free sequence of ni nodes, from an ingress node to the egress one.

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Worst-case delay in a sink-tree network

• li(hi) : the label of the hith node in path Pi

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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 Pi at node li(h), composed of both arriving from upstream nodes and fresh flow injected at node li(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).

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

•

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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 CRli(h) is the clearing rate at node li(h).

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

• Call the sequence of Wx1 bottleneck nodes for node x, sorted in the same order as they appear in any path that traverses that node, so that bx

1=x.

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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:

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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).

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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.

Delay-based admission control

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Minimum weighted latency scheduling

• We define the weighted latency of a network as follows:

– The link weight we is set to the aggregate flow of link e itself, i.e. we = re

• The MinWL scheduling problem is

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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:

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Heuristic feedback (cont’d)

• Its first downstream bottleneck is then given extra rate. This is done by substituting the constraints of Δe with

– where ae is the number of extra units of rate K to be scheduled for link e.

– Variable ae is initially null, and it is increased by one on each iteration.

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An example of the iterative solution

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

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Efficient approximate solution for the MinWL problem

• By relaxing the integrality for πe, Δe and assigning oij 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 oij 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.

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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

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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,

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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.

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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].

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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.

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Performance evaluation (cont’d)• Distribution of the solution times with the heuristic approach

for K = 100 and K = 500.

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

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Performance evaluation (cont’d)• Comparison between the optimal solutions to a TDMA-delay

minimization problem and the solutions obtained with our framework

(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.

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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.

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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.