Distributed Timeslot Allocation in mMTC Networkby Magnitude-Sensitive Bayesian Attractor Model
Tatsuya Otoshi, Masayuki Murata,
Hideyuki Shimonishi, Tetsuya Shimonkawa
Osaka University, Japan1

5G Network and Timeslot Allocation Challenges• 5G• Expanding coverage areas and simultaneous communication qualities• Three communication types: eMBB, URLLC, and mMTC

• Time slot allocation• Time slot allocation essential for satisfying different requirements• Random access: autonomous time slot selection by terminals• Challenges• Challenges in mMTC: collision avoidance and limited information• Previous Approaches: sparing transmission and reinforcement learning (limitations)2Approach• Proposed scheme inspired by human decision-making property• BAM: decision model applied to network control problems• Magnitude sensitivity: tendency to make choices based on the sum of the values of alternatives• Compatible with consensus building in group decision-making• Proposed method uses extended model of value-based BAM for autonomous decentralized

timeslot allocation• Devices independently determine timeslot and consider the option of waiting for transmission
based on magnitude sensitivity

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Magnitude Sensitivity[1] Pirrone, Angelo, et al. "Magnitude-sensitivity: rethinking decision-making." Trends in cognitive sciences 26.1 (2022): 66-80.
[2] Pais, Darren, et al. "A mechanism for value-sensitive decision-making." PloS one 8.9 (2013): e73216.

• Overview• Magnitude sensitivity refers to the tendency to make choices based on the sum of the values ofalternatives.
• When alternatives have high magnitude, accuracy is sacrificed to speed up the decision-making
process.
• Advantages• It allows waiting for a better choice in the future when alternatives have low magnitude.
• Magnitude sensitivity plays an important role in consensus building in group decision-making.

4Magnitude Sensitive Models• Leaky Competing Accumulator (LCA)• Drift term depends on the value• 𝑧!"# [𝑖] = 1 − 𝛾 𝑧! [𝑖] − 𝛽 ∑*+% 𝑧! 𝑗 + 𝑢! [𝑖]• Input Dependent Noise (IDN)• Noise term depends on the value• 𝑧!"# [𝑖] = 𝑧! [𝑖] +• 𝜖! ~𝑁(0,1)$! %+&"∑ ( %𝜎 ) + 𝜋𝑢!) 𝑖 𝜖! [𝑖]Input dependent noise𝑧: state
𝑢: value
𝜖: noise[3] Teodorescu, Andrei R., Rani Moran, and Marius Usher. "Absolutely relative or relatively absolute: violations of value invariance in human decision making." Psychonomic bulletin &review 23.1 (2016): 22-38.
[4] Ratcliff, Roger, Chelsea Voskuilen, and Andrei Teodorescu. "Modeling 2-alternative forced-choice tasks: Accounting for both magnitude and difference effects." Cognitive psychology 103(2018): 1-22.

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Bayesian Attractor Model (BAM)• Original BAM• Involves Bayesian updating based on observed values• Uses attractors and representative values• Generative model equations:• 𝑧! = 𝑓 𝑧!"# + 𝑞𝑤!
• 𝑥! = (𝜇# , ⋯ , 𝜇$ )𝜎 𝑧! + 𝑠𝑣!

𝑧: state
𝑥: observation
𝜇% : representative value𝑣, 𝑤: noise𝑞, 𝑠: dynamic-, sensory uncertainty𝑢&'( : maximum value• Value-Based BAM• Observed and representative values changed to values of alternatives• Value estimation obtained through reward feedback information• Finds highest-value alternative using recognition scheme• Representative values:• 𝜇% = (0, ⋯ , 𝑢&'( , ⋯ , 0)

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BAM with magnitude sensitivity• Changing sensory uncertainty with value (BAM-LCA)• State update with observation• 𝑧̂! − 𝑧̂!"# = )

*)!"

*"" +

#,$%

𝑥! − 𝑥6!

𝑧!+# [𝑖] = 1 − 𝛾 𝑧! [𝑖] − 𝛽 G 𝑧! 𝑗 + 𝑢! [𝑖]/0%LCA• Changing dynamic uncertainty with value (BAM-IDN)• Generative model of state• 𝑧! = 𝑓 𝑧!"# + 𝑞 w• 𝑞~Γ 𝑘, 𝜃 , 𝐸 𝑞 =𝑧!+# [𝑖] = 𝑧! [𝑖] +𝑞 . + 𝜋𝑢!.

u- 𝑖+𝜆 + ∑𝑢 𝑖

𝜎 . + 𝜋𝑢!. 𝑖 𝜖! [𝑖]IDN

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Magnitude Sensitivity of Proposed Model• All models show magnitude sensitivity:• Decision-making speed increases with the magnitude• Accuracy also improves with increasing magnitude:• Earlier decisions result in more correct answers• BAM-LCA has better decision time and accuracy compared to other models
1.075

Accuracy

0.8

methodbam50

bamidnbamlcamethodaccuracy

decision timeDecision time

100

BAM
BAM+IDN
bamlcaBAM+LCAbambamidn

0.62500.4
1020magnitude

magnitude

3040

1020magnitude

magnitude

30408

System Model of Timeslot Allocation• Resources• A subframe has K timeslots.

• Devices• Assumes a continuous packet generation model, more compatible with mMTC use cases (e.g.,sensor networks).
• N devices send data to the base station• Base station• Successful transmission: only one device sends a packet per timeslot; collision occurs if multiple

devices transmit simultaneously.
• Broadcast feedback: the congestion level[4] Sun, Yao, et al. "Service provisioning framework for RAN slicing: user admissibility, slice association and bandwidth allocation." IEEE Transactions on Mobile Computing 20.12 (2020): 3409-3422.
[5] Silva, Giovanni Maciel Ferreira, and Taufik Abrão. "Throughput and latency in the distributed Q-learning random access mMTC networks." Computer Networks 206 (2022): 108787.

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Value-based BAM for Timeslot Allocation• Attractors• K attractors (𝜙# , · · · , 𝜙, ) represent K timeslots in subframe• Feedback information:• +1 for successful transmission• Negative value for collision, discretized by b bits of congestion• Time-smoothed value used for stable understanding of congestion• α = 0.3 (smoothing parameter)• Decision-making:
1.
2.
3.

Maximum confidence selection if BAM’s confidence levels ratio for top two choices
exceeds threshold
Select timeslot k if attractor 𝜙- is selected, transmit packet
Wait for next subframe if no decision made in current subframe
10Simulation Setting• N devices occupy K timeslots simultaneously• N = 10
• K = 2^μ
• μ=4: numerology• Base station provides feedback in b bits for congestion level• b=2• Performance metrics: collision• The ratio of the number of timeslots in which collisions occur out of K timeslots

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Result• BAM-LCA achieves collision avoidance0.16• The greater the value, the stronger the decisive

movement, and the more likely it is that thesame terminals will segregate using the sametimeslot.

point of segregation of time slots.
• BAM-IDNs cannot segregate time slots
due to the noisecollisioncollision• BAM is slowly declining, but not to the0.12

0.08

type
BAM

BAM
IDN
BAM-IDNBAM-LCA
LCA

0.04

02550

75

100

time

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Timeslot access• Heatmap of the number of access for each subframe x timeslot pair
• BAM+LCA tends to select similar time slots
BAM

BAM-IDN
1515access

access5103

1

1000subframe

100

75

50

25

0

100

075

0500subframe

100

175

2

525

2

2

503

35subframe

44slot

slot

slot

4

access

550

1025

10015

BAM-LCA13

Summary• Summary• Magnitude-sensitive decision models applied for autonomous decentralized timeslot allocation inmMTC networks.
• Proposed magnitude-sensitive BAM, BAM-LCA, and BAM-IDN as extensions of BAM.
• Proposed method allows each device to autonomously select a suitable timeslot based on
feedback reflecting timeslot congestion.
• Simulation-based evaluation showed that BAM-LCA effectively avoids timeslot collisions
compared to other methods.
• Future Work• Conduct comprehensive performance evaluations in various settings to assess the effectivenessof the proposed models.
• Investigate strategies to dynamically adjust decision-making based on the number of devices
present in the network.
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Thank you for your attention

This work was supported by MIC under a grant entitled ”R&D of ICT Priority
Technology (JPMI00316)”.
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