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E2-Conditioned Finite-Horizon Effective Capacity for Public-Safety MCX over Shared O-RAN

Jingqing Wang, Wenchi Cheng

arXiv:2608.25442v1cs.NI

TL;DR

Public-safety MCX over shared O-RAN needs finite-horizon, action-conditioned assurance despite heterogeneous E2 exposure and competition with ordinary traffic. The paper develops E2-conditioned FH-EC with correlation-aware service modeling, contract certification, and profile orchestration. Evaluations show short-horizon state effects, increasing capability loss with older E2 information, and improved MCX supportability under O-DU degradation while preserving QoS and non-MCX protection.

  • Problem

    Open interfaces expose observations and controls but do not directly quantify certifiable critical-service support, while heterogeneous E2 domains and stationary effective capacity omit executable finite-horizon conditions.

  • Method

    The paper builds an E2-conditioned correlation-aware Markov-additive FH-EC model and converts its capability into contract-preserving profile orchestration for shared O-RAN.

  • Results

    At short horizon ∆s=1, favorable and degraded initial E2-conditioned states differ by about 0.88 Mbit/s, while richer exposure reduces capability loss as observation age increases.

  • Takeaways & Limitations

    Adaptive SC/DP connectivity selection improves MCX supportability under progressive O-DU degradation while satisfying configured multi-QoS and non-MCX protection requirements.

Abstract

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Supporting public-safety Mission Critical Services (MCX) over a shared Open radio access network (O-RAN) requires service assurance over finite incident horizons, while ordinary mobile traffic competes for the same resources and heterogeneous E2 domains expose different observations, control actions, and actuation latencies. Existing RAN key performance indicators are retrospective, whereas conventional effective capacity characterizes an asymptotic stationary regime and therefore suppresses both the initial E2-observed condition and the finite selection-to-actuation transient. To solve this problem, in this paper we develop an E2-conditioned finite-horizon effective capacity (FH-EC) framework for public-safety MCX over shared O-RAN. Specifically, we first establish a finite-horizon O-RAN MCX-based service model that incorporates E2-observed network states, control actuation latency, and correlation-aware connectivity diversity. Based on this model, we derive an FH-EC formulation that characterizes the executable service capability within a finite mission horizon. Furthermore, we transform FH-EC into confidence-calibrated capability profiles and develop an MCX orchestration framework with contract certification, shared-resource protection, and FH-EC-driven profile selection at the Near-RT RAN Intelligent Controller (RIC). Coupled MATLAB/ns-3 evaluations demonstrate the predicted short-horizon state and actuation effects and show that adaptive connectivity selection improves MCX supportability under O-DU degradation while satisfying the configured multi-QoS and non-MCX protection requirements.

I. INTRODUCTION

Shared O-RAN MCX requires forward-looking, finite-horizon service assurance because E2 domains expose heterogeneous observations, controls, and actuation delays. The paper addresses this with E2-conditioned FH-EC and contract-preserving profile orchestration.

  • Open interfaces make RAN configurations observable and controllable, but not necessarily certifiably supportable for critical services.
  • MCX service assurance spans distinct QoS dimensions, including rate, delay, jitter, AoI, and reliability.
  • Heterogeneous E2 nodes expose different measurements, control actions, reporting periods, and actuation delays, which do not directly quantify executable service support.
  • A finite mission commitment includes the selected profile and certificate, while local scheduling, HARQ, and link adaptation continue under its fixed policy.
  • Conventional effective capacity suppresses the initial E2-observed condition and gives vanishing weight to finite control transients through its stationary asymptotic limit.
  • The proposed framework develops an E2-conditioned service model, establishes long-horizon consistency, and provides contract-preserving O-RAN profile orchestration evaluated with MATLAB/ns-3.

B. Finite-Horizon SC/DP Radio Service

The finite-horizon radio-service model represents MCX traffic, shared O-DU resource constraints, finite-blocklength transmission, and SC/DP delivery over selected connectivity legs.

  • MCX flows may carry control, video, data, or status-update streams, while MCX and non-MCX flows are modeled as disjoint sets.
  • Per-slot service accounts for O-DU bandwidth and power fractions, channel uses, interference, and finite-blocklength coding rates.
  • Packet delivery is determined from decoded leg-level service and lower-layer queue, RLC, and HARQ completion times.
  • SC uses a singleton O-DU set, whereas DP uses at least two O-DUs and selects the first successfully received copy’s delivery time.
  • Duplicated-packet payload is counted once in DP service even though resources are consumed on every selected leg.

C. Finite-Horizon Multi-QoS and Coexistence Requirements

The framework evaluates MCX over a finite mission-slot window using delivered-rate, delay, jitter, AoI, and reliability requirements, while constraining non-MCX coexistence loss.

  • Finite-horizon MCX requirements include minimum supported payload rate, delay, packet-delay variation, AoI, reliability, and tolerated within-window violation budgets.
  • Delay, jitter, AoI, and terminal non-delivery are represented through packet completion, consecutive-packet timing, freshness, and delivery outcomes.
  • The mission-slot set defines the finite operational horizon over which delivered service and QoS outcomes are evaluated.
  • The joint multi-QoS violation event aggregates active rate and QoS-dimension violations under service-specific budgets.
  • Non-MCX coexistence loss compares protected ordinary-user utility with a reference utility obtained without MCX-specific reservation and prioritization.
  • The shared-network protection requirement constrains coexistence loss to LN[l] ≤ρmax.

III. E2-CONDITIONED FINITE-HORIZON EFFECTIVE CAPACITY

The paper defines an E2-conditioned, actuation-aware FH-EC that preserves the finite mission horizon and initial E2-conditioned state while modeling pre- and post-actuation service. It also establishes its long-horizon consistency with conventional effective capacity.

  • The service model separates pre-actuation and post-actuation potential service, conservatively assigning zero pre-actuation service for newly admitted flows unless a default contract is modeled.
  • The E2-conditioned FH-EC is a finite-horizon conditional log-moment measure of the service process.
  • FH-EC retains the operational mission horizon and the initial conditional distribution induced by E2 exposure instead of replacing them with a stationary limit.
  • A finite-state Markov-additive abstraction represents radio, transport, O-CU-UP, shared-power, common-mode-failure, and HARQ states across connectivity legs.
  • The actuation transient affects short missions but contributes only a vanishing O(dctl/Ks) term asymptotically, preserving the conventional effective-capacity limit.
  • The framework converts FH-EC into a finite-horizon supportable admitted rate under a prescribed service-deficit probability and arrival envelope.

B. Capability Characterization under Connectivity Diversity

The framework uses FH-EC to quantify heterogeneous connectivity options and define delivered-rate and dimension-specific multi-QoS risks. Exact risk estimation uses complete finite-horizon trajectories because an exact augmented-state recursion would be high-dimensional.

  • FH-EC quantifies heterogeneous connectivity options through a fixed E2-executable policy rather than designing a new duplication mechanism.
  • The framework defines both delivered-rate risk and a dimension-specific multi-QoS risk vector for each fixed policy.
  • Exact Markov recursion would require accumulated violation counters, evaluable packet counts, packet-pair counts, and accumulated AoI violation time.
  • Because the resulting state grows with mission horizon and packet count, the risks are estimated from complete finite-horizon delivery trajectories.

1) Lower Confidence Bound on Finite-Horizon Capability:

The paper calibrates executable capability profiles over fixed context, execution-class, and QoS keys using independent mission trajectories, then derives simultaneous lower confidence guarantees for profile selection.

  • Each execution class records MCX composition, aggregate resource contract, radio legs, O-CU/O-DU policies, interference/load envelope, and common-mode failure class.
  • A finite calibration library fixes the context map, candidate-policy library, execution classes, and QoS requirements before calibration data are accessed.
  • The exact cell-and-execution-class-conditioned FH-EC is estimated from independent complete mission trajectories for each calibration key.
  • Applying individual coverage guarantees and a union bound yields simultaneous profile validity across the finite library.
  • The calibration procedure uses exact Clopper–Pearson upper confidence limits based on observed type-q mission-window violations.
  • After observing the current E2-context cell, selecting among calibrated profiles incurs no additional post-selection confidence penalty.
  • The guarantee is conditional on the calibrated context and execution class, not pointwise for every raw E2 realization within a context cell.

3) Confidence-Calibrated E2-Executable Profiles:

The framework constructs confidence-calibrated, E2-executable profile sets that account for context, shared-resource coexistence, and finite-sample uncertainty. These profiles form a calibration-safe inner restriction for non-MCX protection.

  • Profiles are screened against calibrated E2-context cells and finite candidate sets at the MCX admission epoch.The context descriptor includes the active MCX service composition used to construct the profile library.
  • The orchestration retains previously admitted flows with unexpired mission windows while forming candidate sets for new flows.Previously admitted profiles remain locked; the zero profile is available only to new flows and represents admission rejection.
  • A fixed residual non-MCX policy defines coexistence-supportable MCX contracts using non-MCX utility requirements in each context cell.The attainable contract set includes the zero contract, and the residual policy supplies an explicit feasible non-MCX allocation.
  • Hoeffding-based lower and upper confidence bounds, combined through simultaneous confidence budgets and a union bound, produce finite-sample calibration-safe sets.The resulting construction defines origin-anchored calibration-safe MCX budgets for each context cell.
  • The calibrated MCX budget is a calibration-supported inner restriction of the exact coexistence region over attainable profile contracts.

B. Joint Profile-Selection Problem and Finite-Library Profile Selection

The FH-EC orchestration problem selects profiles for new MCX flows while preserving locked contracts, prioritizing admission, and enforcing shared-resource and calibration-safe constraints. It is solved as a finite binary optimization using precomputed candidate properties.

  • B. Joint Profile-Selection Problem and Finite-Library Profile Selection: The conservative FH-EC surplus and secondary profile value quantify candidate profile utility for confidence-screened nonzero profiles.The secondary value penalizes resource consumption rather than profile reconfiguration.
  • B. Joint Profile-Selection Problem and Finite-Library Profile Selection: Binary variables select one candidate profile for each new flow, while the total MCX contract combines locked and newly admitted flows.The zero profile is used for admission rejection but cannot withdraw a previously certified mission-horizon contract.
  • B. Joint Profile-Selection Problem and Finite-Library Profile Selection: A sufficiently large admission-priority weight makes MCX admission dominate the secondary profile value, equivalently implementing a lexicographic objective.
  • B. Joint Profile-Selection Problem and Finite-Library Profile Selection: Forbidden hyperedges exclude profile combinations absent from the calibrated library or violating stored resource, interference, load, policy, or common-mode-failure envelopes.
  • B. Joint Profile-Selection Problem and Finite-Library Profile Selection: Problem P1[l] is a finite 0-1 linear program enforcing physical-resource availability, calibration-safe non-MCX budgets, and fixed previously admitted contracts.The orchestration separates capability generation from real-time decision making.

C. Simultaneous Post-Selection Validity of Finite-Library O-RAN Service Contracts

The paper certifies finite-library O-RAN service contracts through calibration-compatible execution conditions and simultaneous confidence guarantees. Runtime orchestration retrieves screened profiles, enforces invariants, and locks admitted profiles through their mission windows.

  • C. Simultaneous Post-Selection Validity of Finite-Library O-RAN Service Contracts: Calibration-compatible execution requires selected profiles to belong to the finite library and preserve their policy, radio-leg, resource, and identifier configuration throughout the mission window.Observation age, actuation delay, load, interference, and infrastructure state must remain within the calibrated execution-class envelope.
  • C. Simultaneous Post-Selection Validity of Finite-Library O-RAN Service Contracts: If a runtime invariant is violated, the corresponding statistical certificate becomes invalid and the profile is rejected or transferred to a separately calibrated fallback class.
  • C. Simultaneous Post-Selection Validity of Finite-Library O-RAN Service Contracts: The validity theorem assumes that execution mappings, candidate libraries, requirements, screening rules, residual policies, and hyperparameters are fixed before calibration data are accessed.It also assumes calibration-runtime exchangeability for every calibration key.
  • C. Simultaneous Post-Selection Validity of Finite-Library O-RAN Service Contracts: Algorithm 1 constructs execution classes, service kernels, FH-EC values, confidence bounds, calibration libraries, and forbidden-hyperedge sets offline.Online steps receive E2 information, identify the context cell, retain locked profiles, retrieve screened sets, solve P1[l], actuate controls, and monitor envelopes.
  • C. Simultaneous Post-Selection Validity of Finite-Library O-RAN Service Contracts: At runtime, the Near-RT RIC retrieves rather than re-estimates screened profiles, verifies execution-class labels, monitors stored envelopes, and locks admitted profiles until expiry.Reserved resources are released at the end of the mission window.
  • C. Simultaneous Post-Selection Validity of Finite-Library O-RAN Service Contracts: With calibration confidence at least (1 −αprof −αN), selected profiles satisfy the certified execution and non-MCX conditions, including the bounded conditional joint multi-QoS mission risk.The prescribed joint mission-risk target is satisfied when the stated inequality holds.

V. PERFORMANCE EVALUATIONS

MATLAB/ns-3 evaluations assess E2-FH against shared-resource baselines, showing finite-horizon and E2-state effects, multi-QoS support, non-MCX protection, and adaptive robustness to O-DU degradation.

  • Simulation Setup and Baselines: The evaluation models shared radio and transport resources for MCX and ordinary mobile services, with Markov-additive service states capturing channel variation and correlated connectivity failures.The wireless service process is evaluated in a shared O-RAN scenario.
  • Simulation Setup and Baselines: The comparison includes a Full-State Oracle, Static-QPP, LT-EC, FH-SC, SNC-Delay, and the complete proposed E2-FH framework.These schemes use the same radio resources and packet-level simulator.
  • Results and Discussion: At short horizon ∆s=1, favorable and degraded initial E2-conditioned states differ by about 0.88 Mbit/s, while FH-EC converges toward conventional EC as the horizon increases.The analytical FH-EC follows packet-level exponential service-transform estimates over the tested horizons.
  • Results and Discussion: E2 capability loss increases with observation age; rich exposure produces the smallest loss because it retains more informative observations and a broader executable action set.Outdated information can cause the selected profile to mismatch the current network state.
  • Results and Discussion: Under contract-preserving execution, the largest one-sided test upper confidence limit remains no larger than the stored profile upper bound.Incompatible profile combinations are excluded or recalibrated as joint profile tuples.
  • Results and Discussion: All active delivered-rate, delay, jitter, AoI, and terminal non-delivery requirements are satisfied up to 50 simultaneous MCX users.The result shows that improving one QoS dimension does not silently violate the others.
  • Results and Discussion: At the largest supportable MCX load, non-MCX utility loss remains below ρmax, while proposed contract adaptation avoids Static-QPP’s high-load violations and low-load excess reservation.The result validates the safe-budget construction.
  • Results and Discussion: Under progressive O-DU degradation, always-DP improves delivery diversity under severe independent degradation but admits fewer flows under normal operation because every copy consumes radio resources.Figure 7 compares SC-only, always-DP, and adaptive SC/DP selection.

APPENDIX A PROOF OF PROPOSITION 1

The appendix proves Proposition 1 by combining Perron–Frobenius asymptotics for a primitive kernel with finite-transient terms that vanish in the long-horizon limit.

  • Proof of Proposition 1: For the primitive matrix G, Perron–Frobenius theory supplies positive spectral radius and left and right eigenvectors normalized by uT v = 1.These spectral quantities support the asymptotic evaluation.
  • Proof of Proposition 1: The coefficient in Eq. (107) is strictly positive, enabling logarithmic asymptotic manipulation.Strict positivity follows from uT 1 > 0.
  • Proof of Proposition 1: Substituting the asymptotic expression and using d/Ks →0 before letting Ks →∞ yields the long-horizon result.This step completes the limiting argument for Proposition 1.
  • Proof of Proposition 1: The simultaneous calibration event combines profile and non-MCX events, with its probability controlled by the union bound.The proof then establishes simultaneous capability and risk bounds across the finite calibration library.
  • Proof of Proposition 1: Because the bounds hold across the entire finite library, selecting a calibration key after observing the E2-context cell introduces no additional post-selection confidence penalty.Forbidden-hyperedge constraints ensure selected nonzero profiles correspond to calibrated keys.
  • Proof of Proposition 1: Resource-availability and calibration-safe constraints enforce the aggregate MCX contract bound while preserving the non-MCX guarantees.The proof combines these constraints with simultaneous non-MCX rate bounds.
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