Modelling D2D Communications in Cellular Access Networks via Coupled Processors

1. Modelling D2D Communications in
Cellular Access Networks via Coupled
Processors
Christian Vitale Institute IMDEA Networks and Univ. Carlos III de Madrid
Vincenzo Mancuso Institute IMDEA Networks
Gianluca Rizzo HES SO Valais

2. HES-SO Valais-Wallis
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Outline
• Overview In-band Underlay D2D
• Our contributions:
– A new model for D2D communications: Coupled Processor
– How to study a D2D Coupled Processor model
– Sufficient conditions for stability D2D transmitters
– Effects of D2D transmissions on cellular transmitters
– Proportional Fair assignment of resources to D2D transmitters
• Future developments

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D2D Communications
• D2D: Device to Device communications
– Info among two device in proximity do not traverse any eNBs
but is directly exchanged
• D2D scope:
– Content Distribution
– Offloading cellular infrastructure
– Increase efficiency spectrum use
– …
• No standardization yet
– LTE Release 12 will contain D2D transmissions too

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In-band Underlay D2D
• D2D transmitters reuse Resource Blocks (RBs)
assigned to cellular transmitters (mutual
interference)
• Complex modeling and performance evaluation

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Analysed In-band Underlay D2D
• D2D – Uplink channel
• eNB schedules D2D transmissions too
• Cellular transmission scheduling:
– Equal Time
• Cellular transmitters in saturation
• D2D scheduling approach (FlashLinQ[1] like):
– Scheduling happens every RB, or blocks of RBs (when SC-
FDMA)
– D2D transmitters with traffic to serve are randomly ordered and
scheduled if:
• Interference to and from the concurrent cellular transmission
is under a given threshold
• Interference to and from the already scheduled D2D
transmissions is under a given threshold
[1] Wu, Xinzhou, et al. "FlashLinQ: A synchronous distributed scheduler for peer-to-peer ad hoc networks." IEEE/ACM Transactions on Networking
(TON) 21.4 (2013): 1215-1228.

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A Coupled Processor Model for D2D communications
• The Modulation Coding Scheme used by each transmitter is
univocally determined by the set of active transmitters in the same
RB
• Coupled processor
– Queueing system. Service rate at each time t univocally depends from the set of
not empty queues
• CPS can mimic the network behavior
∑+
=
≠
>−
>−
activej
ij
ii
ij
R
R
i
PN
P
SINR
|

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A Coupled Processor Model for D2D
communications(2)
• CPS model details:
– A queue per D2D transmitter
– System state I: set of not empty queues
– Service rate at each queue determined by I
• Average throughput achieved by the corresponding D2D
transmitter d when the set of transmitters is I
where pu is the probability of cellular transmitter u to be
scheduled; Io one of the possible ordering of I; is the
throughput of d under ordering Io and cellular transmitter u
|!|
)(
)(
I
IR
pIR OI o
u
d
ud
∑
=

8. HES-SO Valais-Wallis
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Coupled Processor Stability
• Find sufficient conditions for stability of CP is as
difficult as for D2D system
• Evaluation is done through simpler upper bounding
systems, i.e., simpler systems which stability implies the
stability of a CP[2]
[2] C. Vitale, G. Rizzo, and B. Rengarajan. Performance
Bounds in Coupled Processor Systems, 2013. Available
at
http://publications.hevs.ch/index.php/attachments/single/
665

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Sufficient condition for stability in
D2D system
• Arrivals considered are leaky bucket constrained {𝞺,
𝞼}
• Stability is studied through introduced upper
bounding networks and basic Network Calculus
results
Union over the
upper bounding
networks
GPS nodes
capacity given
the network
Maximum “absorbed”
capacity given the
network
Minimum
capacity,
saturation

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Sufficient condition for stability D2D system:
Results

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Effects on Cellular transmissions
• Previously cellular transmitters were considered in
saturation:
– Cellular transmitters are active in every system state I
• To evaluate effects on cellular transmitters, a new CP
model is studied
• Given the demands of the D2D transmitters, maximum
stable rate for the cellular transmitter is evaluated

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Effects on Cellular transmissions:
Results
• In all scenarios previously simulated, from position A to position B,
analytical and simulated stable rates for cellular transmitters are
compared
• Highest average underestimation of real simulated maximum
achievable rate in position B
– Average underestimation: 11.18%

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Proportional Fairness
• Objective: maximize a proportional Fairness measure
picking stable long term rates for the D2D transmitters
– Can be implemented at the application level through leaky bucket
shapers
where dO is a particular order of mapping D2D transmitters-> stages upper
bounding networks
STABILITY
REGION
ARRIVALS LIMIT
PROPORTIONAL
FAIRNESS

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Proportional Fairness-Brute Force
• Per-network optimization:
– Big-M transformation
– Branch and Bound over introduced binary variables
– Concave Optimization ->Unique solution
• Evaluation over each possible mapping D2D transmitters
GPS nodes upper bounding networks

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Proportional Fairness-Heuristic
• Per-network approximation:
– Branch and bound stopped when current solution not far than 𝟄% than
the optimum (𝟄=10)
• Selected set of analyzed networks
– Small set of starting networks
• For each starting network, D2D transmitters are assigned from top
to bottom proportionally to the inverse of the weight
The highest is the weight the best the interference is
modelled
– From each starting network, all networks achieved swapping two D2D
transmitters into the upper bounding networks are evaluated
– Such operation is repeated up to a local maximum

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Proportional Fairness
Results
• Utility Brute Force vs. Heuristic and Simulation optimized
system vs. simulations
– Utility is sensibly improved
– Simulations of optimized system gets analytical optimization results
– Heuristic very close to brute force
• Complexity

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Conclusions
• First analytical evaluation of performances underlay D2D
transmissions
– Sufficient condition for stability D2D transmission queues
– Quantification effects D2D transmission over cellular transmission
– Simple and effective proportional fairness scheme for D2D
transmissions
• Next step:
– Statistical characterization of stability of D2D system