Hybrid Q-CSMA: A Distributed Scheduling Algorithm for Wireless Networks
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Transcript of Hybrid Q-CSMA: A Distributed Scheduling Algorithm for Wireless Networks
R. SrikantCoordinated Science Laboratory and
Department of Electrical and Computer Engineering
University of Illinois at Urbana-Champaign
Joint work with Jian Ni and Bo Tan
Hybrid Q-CSMA: A Distributed Scheduling Algorithm for Wireless
Networks
Wireless Networks
Links may not be able to transmit simultaneously due to interference.
Scheduling algorithm determines which links transmit at each time instant.
Performance metrics: throughput and delay.
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Throughput-Optimal Scheduling
A schedule is a collection of links that can be activated simultaneously.
MaxWeight Scheduling (centralized, high complexity) [Tassiulas-Ephremides ‘92] Associate a weight with each link, equal to its queue lengthFind schedule x which maximizes w(x); w(x): weight of a
schedule x is the sum of the weights of the links in the schedule
Observation [Eryilmaz-Srikant-Perkins’05]: Throughput-optimal even under the following modification: pick the max-weight schedule with high probability, going to one as the weight of the MWS goes to infinity
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Distributed AlgorithmsJiang-Walrand (‘08): Distributed algorithms which
pick schedule x with probability
Distribution realized using a continuous-time model.Also see Boorstyn et al (‘87), Rajagopalan-Shah-Shin
(’08). Related work: Marbach, Eryilmaz, Ozdaglar (‘07)
Goal: Discrete-time model which explicitly models contentions and allows the algorithm to be combined with heuristics leading to dramatic delay reduction
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ex
xw )(
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Modeling Assumption
Divide each time slot into a control slot and a data transmission slot:
Links contend in control mini-slots to determine a collision-free schedule in the data slot.
Collisions are allowed in the control mini-slotsA Key Result: Two control mini-slots are
sufficient to achieve the product-form distribution. (Even one mini-slot is sufficient, thanks to Libin Jiang.)
time slot t time slot t+1
control mini-slots data slot control mini-slots data slot
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Interference Graph
Each vertex in the interference graph represents a link in the network.
If two links interfere with each other, they are neighbors in the interference graph.
A feasible schedule: a set of nodes such that no two nodes have an edge between them
We consider one-hop traffic only.
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schedule x = {a, d, g}
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Basic Scheduling Algorithm
Step 1. In control slot t, select a “decision schedule” m(t): a set of links that may decide to change their state from the previous slot; other links cannot change their state
Step 2. For any link i in m(t) doIf no links in its conflict set N(i) were active in the previous
data slot, link i will decide to becomeactive with probability pi: xi(t)=1inactive with probability 1-pi: xi(t)=0
Else, link i will be inactive: xi(t)=0
Step 3. In the data slot, use x(t) as the transmission schedule.
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Illustration of Scheduling Algorithm
Current schedule: {a, e}Decision schedule, m(t):
{c, f}Allowed decisions for
links in m(t):Link c, xc(t)=0 (no
choice)Link f, xf(t)=1 (w.p. pi)
Other links’ states are unchanged.
New schedule x(t)={a, e, f}
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Product-Form DistributionSchedule Evolution is a Markov chainProposition 1. If the set of possible decision schedules includes all the links, then the DTMC
is reversible and the steady-state probability of using schedule x is
Proof:
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(x) p(x,y) = (y) p(y,x)10
Throughput Optimality
Choose pi for link i (whose weight is wi) as
pi/(1-pi)=exp(wi),
then the probability of choosing a schedule x with weight w(x) is given by
Thus, a schedule with a large weight is picked with high probability.
Question: How to pick the decision schedule?
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Queue-Length Based CSMA (Q-CSMA)
Each time slot is divided into a data slot and control mini-slots
The control mini-slots are used to determine the decision schedule in a distributed manner; each link i selects a random control mini-slot Ti in [1,W].
Roughly, the idea is that a link will send a message announcing its intent to make a decision during its chosen control mini-slot if it does not hear such a message from its neighbors.
data slotcontrol mini-slots
link i : Ti = 3 (W = 4)
INTENT Message
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Case 1If link i hears an INTENT message from a link in its
neighborhood N(i) before its chosen mini-slot, it will keep its state unchanged from the previous time-slot.
If it was active in the previous time slot, it will continue to be active; will be inactive otherwise.
data slotcontrol mini-slots
link i : Ti = 3
data slotcontrol mini-slots
link j : Tj = 2
INTENT Message
Case 2Otherwise, link i will broadcast an INTENT
message to links in N(i) in the Ti-th control mini-slot.
Case 2: If there is a collision, link i will not change its state.
data slotcontrol mini-slots
link i : Ti = 3
data slotcontrol mini-slots
link j : Tj = 3
INTENT Message
INTENT Message
Case 3If there is no collision, link i will make its decision:
If no links in N(i) were active in the previous data slot, then link i’s state is chosen as follows:
active with probability pi
inactive with probability1-pi Otherwise: inactive
data slotcontrol mini-slots
link i : Ti = 3
data slotcontrol mini-slots
link j : Tj = 4
INTENT Message
Key Property of Q-CSMA
Proposition 2. The Q-CSMA algorithm achieves the product-form distribution if the window size W¸ 2.Any maximal schedule will be selected as the
decision schedule with positive probability.The set of maximal schedules includes all the links.
Modification: Works even if W=1. A link chooses to participate in the decision schedule with probability ½. Again, one can show that the above result is still valid.
PerformanceQ-CSMA is a randomized algorithm, the delay
performance can be badWhat are the alternatives?
MaxWeight algorithm: Performance is very good; but high complexity,
centralized implementationMaximal matching:
Add links to the schedule till no more links can be added
Very low complexity; decentralized implementation?; throughput can be small in certain networks
Longest Queue First (LQF) or Greedy Maximal Matching (GMS)
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LQF/GMSAlgorithm:
add link with the longest queue to the scheduleRemove the added link and its “neighbors” from
the graph and repeatvery low complexity; distributed implementation?
Networks that are unstable under maximal scheduling can be stable under LQFDimakis-Walrand, 2006; Brzezinski-Zussman-
Modiano, 2006; Joo-Lin-Shroff, 2008; Leconte-Ni-Srikant, 2009
Performance is very good in simulations; but not always provably throughput-optimal
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Hybrid Q-CSMAChoose a weight threshold w0; choose a
schedule with probability p(x) (defined previously) among those links whose weights exceed the threshold
Add additional links with weight smaller than the threshold, if possible, using a distributed approximation of the longest-queue-first policy
Key Result: the hybrid algorithm is still throughput optimal; Question: does it improve performance over Q-CSMA?
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Simulation Evaluation (1)24-Link Grid Network
(one-hop interference model)
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
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(pk
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(a) All the three algorithms
LQFQ-CSMAHybrid Q-CSMA
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
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Q (
pkt)
(b) The two algorithms with good delay performance
LQFHybrid Q-CSMA
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Simulation Evaluation (2)9-Link Ring Network
(two-hop interference model)
0.7 0.72 0.74 0.76 0.78 0.8 0.82 0.84 0.86 0.88 0.9
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Q (
pkt)
LQFQ-CSMAHybrid Q-CSMA
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Ongoing workPerformance of Hybrid Q-CSMA
Relationship between mixing time of the Markov chain and expected delays
Mixing time estimates are reasonable at light loads but not at heavy loads
w/ Jiang and Walrand
Paradigm shift: Finite-sized flows Instability with fading (van de Ven-Borst-Schneer ‘09)Very different algorithms are needed, somewhat
surprisingly being greedy is good (Liu-Ying-Srikant ‘09)
Ad hoc networks are very different, w/ Shroff and Tan
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Ongoing WorkParadigm shift: packets with deadlines
MaxWeight works here too!: Hou-Borkar-Kumar (‘09), Hou-Kumar (‘09), Hou-Kumar (‘09)
Derivation using purely optimization considerations: Jaramillo-Srikant ; allows extensions to ad hoc networks, fits into the dual decomposition view of network architecture (parallels the interpretation of the Tassiulas/Ephremides result in Lin/Shroff, Neely/Modiano/Li, Eryilmaz/Srikant and Stolyar)
GMS/LQF type ideas seem to work here tooTCP timeout and heavy-tailed file-sizes
Impact of wireless link losses on files with heavy-tailed distributed file sizes (w/ Towsley)
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SummaryQ-CSMA can achieve max throughput in
wireless networks with a fully distributed implementation.
Performance can be improved dramatically by using a hybrid algorithm, combining Q-CSMA with approximations of longest queue first algorithm.
Ongoing work addresses extensions, and several other network control problems in complex wireless networks
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