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Scheduling: Contention, Fairness and Throughput
University of California at Berkeley
Motivations for a Multi-Channel Wireless MAC
t=0 frequencySender 1
t=1frequency
Sender 2
t=2frequency
Sender 3
Today: Each wireless network uses 1 channel only
: :
PowerDensity
t=0frequency
PowerDensity
Sender 1 Sender 3
t=1frequency
Sender 2 Sender 1 Sender 4
Sender 4
t=2 frequencySender 3: :
Sender 2Sender 4
Why not: simultaneous sending on different channels?
Channel 1 Channel 2 Channel 3
Wasted spectru
m
Simple Rendezvous Scheme
1. Node i generates a pseudo random sequence X(Si,ti) i.i.d. ~uniform({1,2,... ,C}). Si is the seed. ti is a local version of the real time.
2. Each packet sent by i contains i, Si and ti.3. Idle nodes occasionally broadcast empty packets.4. Eventually each node hears every neighbor once.5. Node i listens on the default channel X(Si,ti) at time t
Ch2
Ch1
98765432t=1
node2node1 node3
Rendezvous: Sending Illustrated
Ch2
Ch1
98765432t=1
2. RTS/CTS/Data
1. waiting to send
4. Hopping returns to the original hopping schedule
3. Hopping stoppedduring data transfer
Some simple improvements:1. A sender checks if any receivers will be on its default channel
during the coming time slot.2. If not, the sender chooses a channel c’ with a receiver in it
uniformly at random.3. Sender transmits an RTS on channel c’ with probability 1/N(c’,t)
where N(c’,t) is the estimated number of nodes on channel c’ at time t.
Limitations of Local Scheduling
Optimal schedulers (Maximum Weight Matching) require global communication – not practical for MAC.
What is the throughput of local scheduling? No explicit exchange of scheduling information. No scheduling state other than the backlog.
Idealization: iterated Longest Queue First (iLQF): Nodes with longer backlog transmit first.
e.g., MAC with backlog dependent backoff time.
Results Partial Pooling: graph condition for optimality of iLQF. Instability in the case that Partial Pooling (P.P.) is not
satisfied.
Contention model
Incidence matrix A=(Ajk). Set of matches S[K]={m2{0,1}K s.t. Am· 1}. Maximal matches M[K] ½S[K]. Optimal throughput: < 2 Co(M[K]).
Classes: k2 K Resources: j2 J
Activities: k2 K
1
2
3
λ2
λ3
λ1
12 3
conflict graph
Captures dynamic contention for shared resources, e.g., wireless network, packet switch, distributed computation.
Optimality under Partial Pooling
Def: P.P. holds for A½K if 9 nonempty B ½A s.t.
8 m2 M[A], k2 Bmk=Const(A,B).
Def: P.P. holds if P.P. holds for all A ½K.
P.P. class strictly includes tree conflict graphs.
If system conflict graph satisfies P.P., then iLQF is throughput optimal. Approach: fluid limits, longest queue size is a Lyapunov
function.
Instability when P.P. fails
Assume load close to capacity (1/2). “Efficient” matches: {1,3,5,7},{2,4,6,8} “Inefficient”: {1,4,6},… all size 3 matches
8 3
4
6
7
1 2
5 “meta-stability” in 8-cycle:
Most states activate efficient matches.
But, inefficient states are attracting.
Mu
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Wir
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Imp
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Back
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Lim
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Loca
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Antonis Dimakis [email protected]
Rajarshi Gupta [email protected]
Wilson So [email protected]
2+: guaranteedsuccess
1:contentionsuccess
Idle: no suitablereceivers on samechannel
Quiet:everyone backs off
Receiver Absent:receiver stuck on another
channel
Time Slot Utilization Breakdown
2+: guaranteedsuccess
Idle: no suitablereceivers on samechannel
Quiet: everyone backs off
1:contentionsuccess
Avg
Per
Nod
e Q
ueu
e L e
ngth
[M
ini-Pa
c ket
s]
Time [slot]
(10,000 slots = 5 sec)
Collision: >1 sendsReceiver Absent:receiver on another
channel
Exp.1 : High (80% ) load, Long (5-slot) packets.
Per Node Queue Length vs. Time
x 104
Avg
Per
Nod
e Q
ueu
e L e
ngth
[M
ini-Pa
c ket
s]
(10,000 slots = 5 sec)
x 104Time [slot]Exp.2 : High (80% ) load, Short (1-slot) packets.
Collision:>1 sends
SmartNets Research Group
EECS, U C Berkeley Fall 2004
Key Idea In exponential backoff (e.g. 802.11)
Upon collision, nodes back off and become less aggressive Problem in networks spanning multiple interference domains
Nodes in the middle face more collisions They backoff more. Get lesser share of bandwidth This is unfair towards nodes in the middle
Idea: Give higher priority to nodes facing more contention Key: Upon collision, nodes decrease their backoff delay Characteristics
Achieves stable system Maintains throughput in random networks Significant improvement in fairness
EECS, U C Berkeley Fall 2004
Mechanism Backoff Contention Phase
Each node has mean backoff b Picks backoff delay B using
exponential variable with mean b Sends out Slot Capture Message
after B mini-slots If a node carrier senses another
message sooner – it keeps quiet Packet Transmission Phase
Starts after completion ofBackoff Contention Phase
Nodes with successful Slot Capture Messages transmit
Constant packet length Confirmation using ack
If collision or quiet, b:= b/ m If successful transmission, b :=bm m > 1 Markov analysis indicates stability
and fairness
1 5432
interference
1
5
4
3
2
1's Packet Transmission
5's Packet Transmission
BackoffContentionPhase
PacketTransmissionPhase
backoff
slot capture
ack
ack
EECS, U C Berkeley Fall 2004
Resetting Rates Problem of MIMD scheme
When many congested neighbors all decrease backoffs
Resulting backoffs are small Many collisions
Solution: reset backoff delays when exceeds a limit
If any mean backoff goes below reset_limit
Multiply all mean backoffs by constant reset_factor
Simulation parameters m= 1.2 reset_limit = 16/5=3.2 reset_factor = 10
Reset propagation/loss Resets move hop-by-hop
across network May get lost Effect of lost reset
Keeps backoff low So node wins next few slots Increases mean backoff
Simulation Results Reset propagation Loss of up to 10% of resets Random walk movement
EECS, U C Berkeley Fall 2004
Simulations on Random TopologyExponential Backoff Impatient Backoff Algorithm
Jain’s Fairness Index = 0.58 Mean Throughput = 0.101
Jain’s Fairness Index = 0.68 Mean Throughput = 0.102
Circle = Node : Center = Location, Area = Throughput
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