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OPTIMAL SCHEDULING
ALGORITHMS FOR AD HOC
WIRELESS NETWORKS
3/31/2010
Siva Theja Maguluri
Qualifying Exam
Setting
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Adhoc Wireless Network – Interference Graph
Time is slotted – Packets are of same size
Schedule – Binary Vector – Independent Set
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Throughput Optimality
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Consider the Co(M[L])- Convex hull of Maximal
Schedules
Any vector strictly dominated by this is feasible
(Capacity Region)
Throughput Optimality
Algorithm based only on current queue length and
not arrival rate
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Scheduling Algorithms
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Max Weight (Tassiulas & Ephremides)
 Throughput
Optimal
 Excellent Performance
 High complexity; Centralized Implementation
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Q-CSMA
 Each
node tries to transmit after an exponential backoff time with rate proportional to its queue length
(Jiang and Walrand)
 Distributed Implementation; Asynchronous
 Throughput Optimal
 Poor Delay performance
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Longest Queue First (LQF)
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Approximate Greedy implementation of Max
Weight - Greedy Maximal Scheduling aka LQF
Greedily try to add longest queue link in the
schedule
Low complexity
Distributed Implementation of LQF
Data Slot and Control Slot
Control Slot
Data Slot
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Longest Queue First
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Throughput optimal under a topological condition
called local pooling (Dimakis and Walrand)
Local pooling  No vector in Co(M[L]) strictly
dominates another
Works well for practical networks
QoS Performance of Queue Lengths?
Variable Packet Sizes – Many Practical Scenarios
like 802.11 ?
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Large Deviation Optimality
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Second Order Performance Measure
Probability of Buffer Overflow of the maximum
queue
min P(maxQ  B)
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Largest set of allowed rates under upper bound on
probability of buffer overflow
  max lim 
B 
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1
log P (max( Q)  B)
B
To find a schedule with the Largest Large Deviation
Exponent
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Large Deviation Optimality
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Bernoulli Arrivals with mean p
If q is empirical mean, the LD cost for that event is
D(p||q)
Overflow happens along the path with the lowest
cost
Reduces to deterministic problem of finding
minimum cost path to overflow
Further reduced to one dimension by considering the
path of a Lyapunov function
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Large Deviation optimality of LQF
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Greedily try to minimize increase of the Lyapunov
function (Venkataraman and X Lin ‘09)
Use max as Lyapunov Function
Under localpooling, LQF is large deviation optimal
for overflow of max queue length
Compare with any other algorithm
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LQF with variable packet sizes
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Variable Packet Sizes – Exponential Distribution
Discrete time to Continous time
Add longest queue in the schedule whenever
possible
Exponential wait time – required ?
Throughput Optimal
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Further Work
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Is the wait period required?
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Is Asynchronous LQF large deviation optimal?
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Conclusion
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Asynchronous version of LQF, with small wait is
proved to be throughput optimal
To investigate if it works without the delay
LQF is found to be Large Deviation Optimal in the
synchronous case
To find if asynchronous LQF is also Large Deviation
Optimal
3/31/2010