19-EFT.WP.Methods.SynthData v1.0 | Chapter 14 — Runtime & Streaming Generation (Backpressure / Resources / SLOs)

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Chapter 14 — Runtime & Streaming Generation (Backpressure / Resources / SLOs)

One-line objective: Operate synthetic-data services stably on an execution graph G=(V,E), enforce SLOs via backpressure and resource orchestration, and maintain consistency for arrival time and privacy accounting.

I. Scope & Targets

1. Inputs
   • stream(req_i): real-time generation request stream containing seed, condition, budget, TraceID
   • engine: frozen generative engine and SynthSpec
   • policy.runtime: backpressure, rate-limiting, batching, hot-swap, and SLO targets
   • sync_ref: time-base and arrival-time reference (including offset/skew/J)
2. Outputs
   • stream(resp_i): samples or bundles returned under SLO
   • runtime_report: TS.sli.*, rho, W_q, latency_ms_p99, drop_rate
   • manifest.synth.runtime: runtime manifest with signature
3. Constraints
   Queue stability rho < 1; eps_total ≤ eps_budget; delta_form ≤ tol_Tarr; replayability and idempotence

II. Terms & Symbols

• Rate & stability: lambda_in, mu_eff, rho = lambda_in / mu_eff, cap
• Queuing & latency: W_q, W, latency_ms_p99, drop_rate, retry_k
• Batch & parallelism: B (batch size), K (number of parallel workers), T_serv(B)
• Resources: gpu_util, mem_free, oom_rate, disk_io, net_bw
• Time base & arrival: tau_mono, ts, offset/skew/J, T_arr, delta_form
• Privacy accounting: eps_i, delta_i, eps_total = accountant( {eps_i, delta_i} )
• SLO/SLI: TS.sli.rho, TS.sli.latency_p99, TS.sli.drop_rate, TS.sli.oom_rate

*III. Axioms P414- **

• P414-1 (Stability First): Maintain rho < rho_max < 1 at all times; stability takes precedence over throughput.
• P414-2 (Idempotence & Replay): Guarantee request-level replayability and idempotence using TraceID, seed, and engine/version.
• P414-3 (Unified Backpressure): Rate-limits, adaptive batching, queue trimming, and degradation policies are centrally governed; implicit drops are prohibited.
• P414-4 (Arrival-Time Consistency): Streaming samples must carry offset/skew/J and both T_arr formulations; verify delta_form prior to publication.
• P414-5 (Closed-Loop Privacy): Track eps_total continuously with an accountant; trip the circuit when limits are exceeded.
• P414-6 (Tear-Free Hot Updates): Hot engine swaps use dual lanes and fence commits; forbid cross-version partial batches.
• P414-7 (Metrics as Contracts): All SLIs must be persisted and signed, serving as inputs to release gates.

*IV. Minimal Equations S414- **

• S414-1 (Effective Service Rate & Parallel Batching)
  mu_eff = ( K * B ) / E[ T_serv(B) ]。If using adaptive batching: B* = argmin_B E[latency(B)]。
• S414-2 (Steady-State & Latency Approximations)
  For M/M/1: W ≈ 1 / ( mu_eff - lambda_in )；
  W_p99 ≈ ( ln(100) ) / ( mu_eff - lambda_in )；
  for M/M/k, use rho = lambda_in / ( k * mu_worker ) with standard Erlang-C to estimate W_q。
• S414-3 (Drop & Retry Budgets)
  drop_rate = drops / arrivals；retry_budget = min( retry_k, retry_k_max )；
  total latency latency = W_q + T_serv(B)。
• S414-4 (Privacy Accounting)
  eps_total = accountant( { (eps_i, delta_i) } ) with constraints eps_total ≤ eps_budget, delta_total ≤ delta_budget。
• S414-5 (Dual Arrival Forms & Difference)
  T_arr = ( 1 / c_ref ) * ( ∫ n_eff d ell )；T_arr = ( ∫ ( n_eff / c_ref ) d ell )；
  delta_form = | ( 1 / c_ref ) * ( ∫ n_eff d ell ) - ( ∫ ( n_eff / c_ref ) d ell ) |。
• S414-6 (Little’s Law Consistency Check)
  L = lambda_in * W；use L to cross-validate queue telemetry.

V. Metrology Flow M40-14 (Ingress → Orchestration → Backpressure → Audit)

• Readiness
  Freeze engine/version, SynthSpec, and policy.runtime; configure cap, B∈[B_min,B_max], K.
• Ingress & Normalization
  Validate TraceID/seed/budget; map default time bases to tau_mono; write initial offset/skew/J.
• Adaptive Batching & Parallelism
  auto_batcher optimizes B for latency/throughput; K self-tunes under gpu_util/mem_free constraints.
• Backpressure & Rate-Limiting
  When rho ≥ rho_hi or mem_free ≤ m_min: trigger rate_limit(r_out), shed(policy), degrade(profile).
• Retry & Idempotence
  For 5xx/timeout, perform idempotent retries ≤ retry_k; de-duplicate by TraceID; log all failures to the audit stream.
• Arrival-Time Hardening
  For temporal samples, stamp both T_arr formulations and delta_form; if out of bounds, execute timepath_hardening.
• Accounting & Circuit Breaking
  Accumulate eps_total; on budget breach, circuit_open and permit only low-sensitivity degradation paths or rejections.
• Audit, Manifest & Signature
  Emit runtime_report and manifest.synth.runtime; persist hash_sha256 and signature.

VI. Contracts & Assertions C40-14xx

• C40-1401 (Stability): rho ≤ rho_max and the sliding-window mean E[rho] stays within bounds over horizon T.
• C40-1402 (Latency): latency_ms_p99 ≤ target_p99; W_q ≤ W_q_max.
• C40-1403 (Drops): drop_rate ≤ tol_drop; retry_success ≥ r_min.
• C40-1404 (Resources): gpu_util ∈ [u_min,u_max], oom_rate ≤ tol_oom, mem_free ≥ m_min.
• C40-1405 (Arrival Time): delta_form ≤ tol_Tarr, |offset| ≤ off_max, J ≤ J_max.
• C40-1406 (Privacy): eps_total ≤ eps_budget and delta_total ≤ delta_budget.
• C40-1407 (Hot Updates): zero cross-version batches; dual_commit = true.
• C40-1408 (Idempotence): unique(TraceID); repeated requests yield identical output hashes.

VII. Implementation Bindings I40-14*

• stream_synth(stream, engine, policy) -> stream'
• auto_batcher(metrics, target) -> B
• rate_limit(stream, r_out) -> stream'
• backpressure_controller(metrics, policy) -> actions ({shed, degrade, expand, pause})
• resource_monitor() -> {gpu_util, mem_free, disk_io, net_bw}
• privacy_accountant(eps_delta_stream) -> {eps_total, delta_total}
• timepath_hardening(ds, sync_ref) -> ds'
• emit_runtime_manifest(metrics, contracts) -> manifest.synth.runtime
• Invariants: rho < 1; idempotent(TraceID, seed); delta_form ≤ tol_Tarr; eps_total ≤ eps_budget; engine/version is consistent within a batch.

VIII. Cross-References

• EFT.WP.Methods.Cleaning v1.0: Chapter 11 (stream cleaning & backpressure loop) for queueing and rate-limit coordination.
• EFT.WP.Methods.CrossStats v1.0: Chapter 7 (drift/alignment) and Chapter 14 (SLOs & audit) for runtime thresholds and audit mapping.
• This volume: Chapter 8 (time-series & event synthesis) and Chapter 13 (release freeze) for arrival-time and manifest signing continuity.

IX. Quality SLIs & Risk Control

1. SLIs
   TS.sli.rho, TS.sli.latency_p99, TS.sli.drop_rate, TS.sli.oom_rate, TS.sli.retry_success, TS.sli.delta_form, TS.sli.eps_total.
2. Risk actions
   • Stability: if rho > rho_hi → lower r_out, increase B (subject to latency), enable K+ if resources allow.
   • Latency: if latency_p99 breaches → shrink B, priority scheduling, nearline caching or sketch-level degradation.
   • Resources: if mem_free < m_min or oom_rate rises → reduce K/B, shard load, cold/hot migrate.
   • Privacy: if eps_total nears the cap → route to low-sensitivity paths or reject new requests.
   • Arrival time: if delta_form breaches → run timepath_hardening and rate-limit modalities involving time/path propagation.

Summary

• This chapter codifies runtime principles—stability first, idempotent replay, and a closed privacy loop—under P414-*;
• provides computable bases for stability, latency, and budgets in S414-*;
• stitches ingress, orchestration, backpressure, accounting, and audit into a closed loop M40-14;
• anchors SLO gates and circuit-breakers through C40-14xx;
• and fixes delivery interfaces and invariants via I40-14*, ensuring streaming synthesis remains stable under resource constraints and privacy budgets while meeting pre-release consistency requirements.