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Blockchain-based Proportional Fair Scheduling for Multi-Operator O-RAN

Kun Huang, Xintong Ling, Meining Wu, Jiaheng Wang, Zhi Ding, Xiqi Gao

arXiv:2609.07473v1cs.NI

TL;DR

Cross-operator O-RAN scheduling needs trustworthy coordination, but conventional PFS does not provide a trust mechanism and existing approaches leave analytical performance gains unclear. The paper proposes blockchain-based proportional fair scheduling with smart contracts and throughput analysis. It reports that pooling increases with both the number of operator networks and users, and simulations support the analysis and show superiority over non-cooperative approaches.

  • Problem

    Cross-operator O-RAN scheduling lacks explicit trust mechanisms for reliable coordination, and the performance gains of blockchain-enabled cooperation remain insufficiently analyzed.

    Source: §I · p. 1, §III · p. 4

  • Method

    BC-PFS integrates proportional fair scheduling with blockchain smart contracts for cross-operator coordination and develops probabilistic, ODE, and simplified closed-form throughput analyses.

    Source: §I · p. 2

  • Results

    The pooling effect increases monotonically with the numbers of operator networks and users, and simulations validate the analysis and show superiority over non-cooperative approaches.

    Source: §I · p. 2, §VIII · p. 13

  • Takeaways & Limitations

    The analysis characterizes pooling gains from trustworthy cross-operator collaboration in O-RAN, with gains rising as networks and users are added.

    Source: §I · p. 2

Abstract

from arXiv · show

The openness and disaggregation of Open radio access network (O-RAN) facilitate resource sharing and coordination across networks, creating new demands for efficient and trustworthy cross-operator scheduling. However, such scheduling is beyond the scope and capability of conventional proportional fair scheduling (PFS), which lacks mechanisms for establishing trust among independent operators. To fulfill this gap, we propose the blockchain-based proportional fair scheduling (BC-PFS) that enables trustworthy inter-network coordination and resource pooling across operators in O-RAN. Specifically, we design four core smart contracts including registration, status reporting, scheduling, and settlement contracts with corresponding Solidity implementations to ensure trustworthy on-chain execution. Theoretically, to evaluate the BC-PFS performance, we develop an analytical framework to derive the user average throughput via both probabilistic and ordinary differential equation (ODE) approaches, and provide a simplified closed-form solution. Based on the above performance assessment, we quantify the pooling effect in O-RAN achieved through trustworthy cross-operator collaboration via BC-PFS, and point out that this effect grows monotonically in both the numbers of operator networks and users. Simulations validate the theoretical analysis and show the performance of the BC-PFS in O-RAN.

I. INTRODUCTION

O-RAN’s cross-operator resource sharing needs scheduling that is both efficient and trustworthy, but existing approaches often lack explicit trust mechanisms and adequate performance analysis. The paper proposes BC-PFS, develops its analytical basis, and characterizes how pooling changes with network scale.

I. INTRODUCTION

  • Existing collaborative scheduling generally assumes trustworthy information exchange and execution, while blockchain-based approaches also face complexity and limited physical-layer integration.The introduction identifies limited quantitative analysis of blockchain-enabled cross-operator scheduling as a further gap.Source: §I · pp. 1–2
  • BC-PFS integrates proportional fair scheduling with four smart contracts—registration, status reporting, scheduling, and settlement—to support trustworthy multi-operator O-RAN scheduling.The paper also presents Solidity implementations of the contracts.Source: §I · p. 2
  • The paper derives user throughput through probabilistic and ODE analyses and provides a simplified closed-form solution under a relatively weak assumption..Source: §I · p. 2
  • The pooling effect increases monotonically with both the number of operator networks and the number of users per network.Simulations validate the theoretical analysis and report superiority over conventional non-cooperative approaches.Source: §I · p. 2

A. Multi-operator O-RAN

  • The modeled O-RAN has K operators serving N users, with each operator maintaining isolated O-DU and O-CU instances and RICs supporting coordination and orchestration.Users can dynamically access multiple operators, but each operator’s channel serves at most one user per time slot.Source: A. Multi-operator O-RAN · pp. 2–3
  • The system model assumes uniformly spaced time slots and independent instantaneous rates across distinct operators.Source: A. Multi-operator O-RAN · p. 2

B. Wireless Channel Model

The paper models wireless rates under Rayleigh fading and uses proportional fair scheduling to balance throughput and fairness. It then describes how conventional PFS selects users and adapts their throughput over time, while identifying the trust gap that complicates multi-operator use.

B. Wireless Channel Model

  • Rayleigh fading models each user’s SNR as exponentially distributed, and Shannon’s formula is used to express the instantaneous transmission rate.The linear rate approximation is presented as a first-order Taylor simplification for low-SNR conditions.Source: B. Wireless Channel Model · p. 3

III. REVISIT PROPORTIONAL FAIR SCHEDULING

  • Proportional fairness balances network throughput and fairness, with logarithmic utility assigning diminishing marginal returns to throughput increases.Source: §III · p. 3
  • PFS selects the user with the highest ratio of instantaneous rate to average throughput, then updates throughput using the selected user’s rate.The smoothing factor α controls adaptation: smaller values produce gradual updates, while larger values respond faster to channel fluctuations.Source: §III · p. 3
  • Conventional PFS faces a trust gap in multi-operator O-RAN, where unreliable commitments or opportunistic behavior can make coordinated scheduling globally suboptimal.Source: §III · p. 4

IV. BLOCKCHAIN-BASED PROPORTIONAL FAIR SCHEDULING

BC-PFS uses blockchain to coordinate proportional-fair scheduling across operators through a two-layer architecture. Edge chains execute scheduling from reported user states and throughput records, while a global chain aggregates records for coordination and settlement.

IV. BLOCKCHAIN-BASED PROPORTIONAL FAIR SCHEDULING

  • A two-layer blockchain places edge chains in sub-regions for cross-operator scheduling and a global chain near the SMO for aggregation and network-wide management.Source: A. Overview · p. 4
  • Each O-DU reports user states to the edge chain, which runs PFS through smart contracts using those states and historical throughput, then returns decisions for radio allocation.Source: A. Overview · p. 4
  • The global chain aggregates edge-chain state and transaction records to support settlement, spectrum management, and network coordination.Scheduling information held by the global chain can also support long-term policy optimization by the SMO and Non-RT RIC.Source: A. Overview · p. 4
  • Operators independently schedule one user per time slot according to the proportional-fair rule, then update throughput to reflect allocated rates.BC-PFS preserves PFS’s responsive adaptation while adding blockchain-based coordination and verifiable execution.Source: A. Overview · p. 4

B. Workflow

The BC-PFS workflow registers users and operators, updates authenticated status reports, schedules users through a smart contract, and settles cross-operator services. Its consensus mechanism adds delay, making block time relative to channel coherence a material operating constraint.

B. Workflow

  • Registration contracts verify user identities at the edge chain, while operators register through the SMO and synchronize necessary information across chains.Source: B. Workflow · p. 4
  • The status-reporting contract aggregates and validates periodically submitted channel reports, updating on-chain user states for scheduling.Source: B. Workflow · p. 4
  • At each scheduling interval, the scheduling contract uses current user states and prior-block throughput records to select users and update throughput records.The resulting decisions go to O-DUs for resource allocation and UL grants or DL assignments to UEs.Source: B. Workflow · p. 5
  • The settlement contract calculates cross-operator charges from service records, while the Non-RT RIC and Near-RT RIC use long-term data to optimize policies and scheduling parameters.Source: B. Workflow · p. 5
  • If channel coherence time is shorter than block time, scheduling can rely on outdated channel states and performance may degrade; consensus delay may also matter in high-mobility cases.The paper therefore prefers permissioned ledgers with short block times.Source: B. Workflow · p. 5

C. Implementation via Smart Contracts

BC-PFS implements registration, status reporting, scheduling, and settlement through smart contracts that coordinate and record the cross-operator scheduling process.

C. Implementation via Smart Contracts

  • The registration contract validates credentials and assigns registered users and operators IDs and role flags.Successful registrations update the registry and emit a RegistrationSuccess event.Source: C. Implementation via Smart Contracts · p. 6
  • The status reporting contract validates user CSI, estimates transmission rates, and records approved reports for each operator-user pair.Successful updates emit ReportSubmitted events.Source: C. Implementation via Smart Contracts · p. 6
  • The scheduling contract selects each operator’s highest-priority user using instantaneous rate divided by historical throughput, then updates throughput records.Scheduling results are notified to participants and recorded in Scheduled events.Source: C. Implementation via Smart Contracts · p. 6
  • The settlement contract scans active allocations, calculates service costs using operator-specific pricing, initiates payment, and emits transaction confirmations.It uses the scheduling matrix to identify allocations for settlement.Source: C. Implementation via Smart Contracts · p. 7

A. Analysis on Throughput

The analysis characterizes long-term BC-PFS throughput through stochastic convergence and average-throughput derivations. It also identifies conditions and computational costs relevant to that characterization.

A. Analysis on Throughput

  • Under stationary user rates, BC-PFS throughput weakly converges to an ODE limit point that is unique and independent of initial conditions.The long-term average throughput equals that limit point, enabling steady-state analysis.Source: A. Analysis on Throughput · p. 7
  • Under Rayleigh fading, the cited proportional-fairness bounds constrain average-throughput ratios by users’ average-rate differences and channel variability.The analysis extends the bound to multiple operators under the assumption that each user’s average rate varies only slightly across networks.Source: A. Analysis on Throughput · pp. 7–8
  • The analysis derives average throughput probabilistically, relates it to user rates, and presents a formulation that characterizes throughput in multi-operator O-RAN.The formulation’s accuracy is verified by simulations, but its computational overhead may remain large for many operators or users.Source: A. Analysis on Throughput · pp. 7–8

B. ODE Approach

The ODE approach provides an alternative derivation of BC-PFS throughput and agrees with the probabilistic result. Its generalization to many users and operators requires solving a high-dimensional system.

B. ODE Approach

  • For two operators and one user per operator, the derivation computes expected rates under a linear rate model and solves the coupled ODE at equilibrium.The equilibrium is obtained by setting the throughput derivatives to zero.Source: B. ODE Approach · p. 8
  • Extending the ODE derivation to K operators and KN users requires constructing conditional expectations and solving a high-dimensional system.The analysis states that a universal analytical solution can be obtained through this generalization.Source: B. ODE Approach · p. 8
  • The ODE solution is exactly equivalent to the probabilistic result, establishing consistency between the two BC-PFS throughput analyses.Its expression captures competition among users within and across operator networks.Source: B. ODE Approach · p. 8

C. Simplified Solution

The simplified closed-form throughput uses a weak assumption about rate variation across operators. It provides a lower bound and relates pooling benefits to the total number of users and networks.

C. Simplified Solution

  • The simplifying assumption treats each user’s rates across operators as minor fluctuations around that user’s average rate over K networks.The deviation from the average is denoted by δ.Source: C. Simplified Solution · p. 9
  • The closed-form throughput depends on average user rate, operator count K, and users per network N; its ω(KN) factor quantifies pooling advantages as total users increase.The passage describes the pooling effect as increasing with total user number KN.Source: C. Simplified Solution · p. 9
  • The simplified user-throughput expression is a lower bound; cross-network rate fluctuations can add multi-network diversity gain beyond it.Simulations are reported to show that the simplified solution closely approximates performance and verifies the lower-bound property.Source: C. Simplified Solution · p. 9

VI. POOLING EFFECT

The section defines a pooling gain for cooperative BC-PFS in O-RAN and shows that it is positive and grows with both network count and users per network. The simplified analysis gives a conservative lower bound because it excludes multi-network diversity.

VI. POOLING EFFECT

  • The pooling gain ψ(N, K), defined as the utility gap, is positive, so cooperative O-RAN outperforms isolated non-cooperative PFS.The comparison is based on network utility.Source: §VI · p. 9
  • The simplified pooling gain is a conservative lower bound because its analysis excludes multi-network diversity, which can further enhance actual network utility.The paper attributes the additional enhancement to network-level diversity.Source: §VI · p. 9
  • ψ(N, K) strictly increases with both operator-network count K and users per network N.The theorem establishes monotonicity in both dimensions.Source: §VI · p. 9
  • Increasing N reflects multi-user diversity, while increasing K reflects network-level diversity and resource pooling beyond isolated networks.The paper says collaborative scheduling amplifies multi-user diversity and BC-PFS breaks through isolated-network resource limits.Source: §VI · p. 10

VII. SIMULATION AND ANALYSIS

Simulations support the throughput analysis and show that BC-PFS improves O-RAN performance over non-cooperative scheduling. The pooling gain grows with both operator and user counts, while the simplified solution’s accuracy depends on rate variation and network scale.

VII. SIMULATION AND ANALYSIS

  • For K = 2 and K = 5, the accurate throughput solution tracks simulations, while the simplified solution has negligible deviation when rate distributions are concentrated.The comparison uses δ = 0.05 and δ = 0.1 with 10 users per network.Source: Figure 3 · p. 10, §VII · p. 10
  • With 10 users per network and K = 2, 3, or 4, throughput rises with rate fluctuation; the simplified-solution deviation shrinks as K increases.At δ = 0, throughput reaches its lower bound; more operators tighten the actual rate around its average.Source: §VII · pp. 10–11, Figure 4 · p. 11
  • In the two-user throughput comparison, BC-PFS achieves higher average user throughput than single-network scheduling, with gains amplified by more cooperating networks.The independent-network benchmark strategies lie along the throughput boundary.Source: Figure 5 · p. 11, §VII · p. 11
  • For two networks, BC-PFS improves utility over non-cooperative schemes; its utility also grows with rate fluctuation δ as coordination harnesses diversity.Among non-cooperative schemes, PFS outperforms max-sum and max-min fair scheduling.Source: Figure 6 · p. 11, §VII · p. 11
  • BC-PFS’s network-utility advantage over non-cooperative PFS grows with both operator count K and users per network N.Fig. 7 varies K at fixed N = 10 and N at fixed K = 2.Source: §VII · pp. 11–12, Figure 7 · p. 12
  • Pooling gain increases monotonically with operator count K and users per network N, and simulated values agree with theoretical results.Fig. 8 evaluates pooling gain across both network dimensions.Source: Figure 8 · p. 12, §VII · p. 12
  • Pooling gain grows nonlinearly at small network scales, then approaches quasi-linear scaling with the product KN as scale increases.The contour plot uses darker shades for higher gains; the change in scaling is linked to the harmonic-number approximation.Source: Figure 9 · p. 12, §VII · p. 12

VIII. CONCLUSION

The conclusion presents BC-PFS as a blockchain-based framework for trustworthy cross-operator scheduling in O-RAN. Its analysis and simulations support a pooling gain that increases with network and user counts.

VIII. CONCLUSION

  • BC-PFS integrates blockchain with PFS in a decentralized smart-contract framework for on-chain scheduling, enhancing trust and traceability in O-RAN resource management.The paper presents accurate and simplified closed-form expressions for average throughput.Source: §VIII · p. 12
  • Pooling gain increases monotonically with both the number of networks and the number of users.Simulations validate the theoretical analysis and confirm BC-PFS’s superiority over non-cooperative approaches.Source: §VIII · p. 13
  • The paper reports that simulations validate its theoretical analysis and show BC-PFS outperforming non-cooperative approaches in O-RAN.The conclusion frames BC-PFS as a solution for trustworthy cross-operator user scheduling.Source: §VIII · pp. 12–13
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