27-EFT.WP.Packets.Light v1.0 | Chapter 9 — Switching & Routing (OCS / OPS / WSS / ROADM)

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Chapter 9 — Switching & Routing (OCS / OPS / WSS / ROADM)

One-sentence goal: Unify the timing, resource, power, and control-plane conventions for OCS/OPS and WSS/ROADM; provide dual-form (configured vs measured) evaluations for blocking / delay / reconfiguration time and power equalization; and publish traceably via manifests.

I. Scope & Objects

1. Inputs
   • Resources & labels: label = ( lambda, k_sub_set, s_set ) (see Chapter 5), channel bandwidth B_eff, spatial set S_sel.
   • Devices & parameters: cascaded WSS/ROADM and ports, reconfiguration time T_reconf, insertion loss / isolation IL / Iso, crossbar schedule Xbar(t); OPS node FDL set and conversion capability WC ∈ { none, limited, full }.
   • Traffic & load: arrivals (circuits A Erlangs / holding time H; packets with rate λ_pkt and length L_pkt), policy and RefCond.
   • Timebase & framing: frame_spec, tau_mono / ts (see Chapter 3).
2. Outputs
   • Routing / configuration: path, crossbar matrix Xbar, power-equalization plan plan_pwr;
   • Performance & compliance: P_block / P_contention, lat_sw / lat_q, FM_dB (link margin), Iso_ch;
   • Dual-form gap: configured (analytic / simulation) vs measured (OSA / counters / timestamps) discrepancy delta_form_swrt.
3. Boundary
   Physical propagation/compensation: Chapters 2 / 6; spectral & spatial resources: Chapter 5. This chapter focuses on switching / routing and scheduling.

II. Terms & Variables

• Switching & devices: WSS (wavelength-selective switch), ROADM (reconfigurable optical add-drop multiplexer), crossbar Xbar ∈ {0,1}^{P_out×P_in}, port count P.
• OCS (circuit): holding time H, offered load A (Erlangs), available timeslot set T_set, setup/teardown T_setup / T_teardown.
• OPS (packet): arrival rate λ_pkt (1/s), service rate μ, utilization ρ = λ_pkt / μ, FDL set { d_i }, wavelength conversion set W_conv.
• Routing: k candidate paths π_k (shortest / conflict-aware), cost c(π_k), RSA/RSCA decisions (see Chapter 5).
• Dimensions: unit(T_reconf, T_setup, lat_sw, lat_q) = "[T]", unit(A) = "[1]", unit(P_block) = "[1]", unit(FM_dB) = "dB".
• Two forms: configured (Erlang/Markov/simulation) vs measured (counters / timestamps / OSA) gap delta_form_swrt.

III. Postulates P609-*

• P609-1 (Two forms in parallel): Publish configured and measured blocking / delay / reconfiguration time together and record delta_form_swrt.
• P609-2 (Explicit measures & domains): Circuits use time windows ( ∫_{t∈W} • dt ); packets use count sets / arrival processes ( ∑_{pkt∈W} • ); spectral/spatial terms persist B_eff / S_sel.
• P609-3 (Dimensional compliance): All fields pass check_dim; dB↔linear conversions are annotated in the manifest.
• P609-4 (Protection & isolation): Switching/routing must respect Chapter 5 guard-band and isolation assertions; power/OSNR equalization updates with configuration.
• P609-5 (Fail-Closed): When control vs measurement disagree or thresholds fail, apply degrade (rate-limit / bypass / rollback path) and persist the strategy card.

IV. Minimal Equations S609-*

1. OCS blocking & latency (bufferless circuits)
   • Erlang-B blocking:
     P_block^{OCS} = B(E,m) = ( E^m / m! ) / ( ∑_{k=0}^{m} E^k / k! ), with E = A and resource m = (wavelengths × spatial channels × timeslots).
   • Setup/teardown latency:
     lat_sw ≈ T_setup + T_path_prog + Σ_{nodes} T_reconf(node); window conservation requires lat_sw ≤ T_guard_budget (per Chapter 3).
2. OPS contention & queuing
   • No buffer / no conversion (iid arrivals, one output):
     P_contention ≈ 1 − ( 1 − ρ / P_out )^{N_in}.
   • With FDL / conversion: effective service μ_eff = μ • P(scheduled), ρ_eff = λ_pkt / μ_eff;
     M/M/1 approximation: lat_q ≈ ρ_eff / ( μ_eff (1 − ρ_eff) ); FDL delay bound lat_FDL ≤ max(d_i).
3. WSS/ROADM cascade, isolation & tilt
   Cascaded transfer: H_link(f) = ∏_m H_m(f); link isolation Iso_link ≥ min_m Iso_m − Σ_margin (dB);
   tilt error ε_tilt = max_f | |H_link(f)| − \bar H | / \bar H | (must satisfy Chapters 5/6 contracts).
4. Routing cost & constraints
   • min_{π} c(π), s.t. label = ( λ, K_sel, S_sel ) is contiguous/convertible; GB / Iso and power plan feasible.
   • Typical cost: c(π) = α•hop + β•∑loss + γ•∑tilt + ζ•conflict(π); solve MCSP or joint RSA/RSCA.
5. Power/OSNR equalization & margin
   End-to-end received power: P_rx(dBm) = P_tx(dBm) − ∑loss + ∑G_amp;
   fade margin FM_dB = P_rx,med(dBm) − P_min(dBm), enforce FM_dB ≥ FM_min; map OSNR to BER / EVM via Chapters 4 / 11.
6. Dual-form gap
   delta_form_swrt = w_b | P_block^{config} − P_block^{meas} | + w_c | P_contention^{config} − P_contention^{meas} | + w_l | lat^{config} − lat^{meas} |.

V. Metrology Pipeline M60-9 (Ready → Assign/Switch → Measure → Verify → Persist)

• Ready: load label, resource grids and device chain (WSS/ROADM), RefCond, and control-plane configs; freeze frame_spec, guard / isolation thresholds.
• Assign / switch: run RSA/RSCA to select path and labels; program cross-connections on Xbar; generate power/OSNR equalization plan.
• Measure: collect OSA / power meter / counters / timestamps and control-plane telemetry: P_block_meas / P_contention_meas / lat_sw_meas / Iso_link_meas / FM_dB_meas.
• Verify: compute configured predictions and compare with measurements to obtain delta_form_swrt; validate Iso / GB / FM_dB and lat_sw / lat_q; trigger rollback on violations.
• Persist:
  manifest.packet.swrt.* = { path.hash, Xbar.hash, label, plan_pwr, P_block / P_contention, lat_sw / lat_q, Iso_link, FM_dB, delta_form_swrt, RefCond, contracts.*, signature }.

VI. Contracts & Assertions C60-9x (Suggested Thresholds)

• C60-901 (Two-form gap): delta_form_swrt_p95 ≤ tol_swrt (scenario-specific).
• C60-902 (Reconfiguration & conservation): lat_sw ≤ T_guard_budget; otherwise enlarge T_guard or reschedule.
• C60-903 (Blocking / contention): P_block ≤ P_block_max, P_contention ≤ P_cont_max.
• C60-904 (Isolation & protection): Iso_link ≥ Iso_min_dB, guard band GB ≥ GB_min.
• C60-905 (Power / OSNR margin): FM_dB ≥ FM_min and OSNR_dB ≥ OSNR_min.
• C60-906 (Dimensional compliance): all delay / power / probability / isolation fields pass check_dim; dB↔linear conversions recorded.

VII. Implementation Bindings I60-9* (interfaces, I/O, invariants)

• I60-91 ksp_paths(topology, src, dst, k, metric) -> { π_1 … π_k }
• I60-92 rsa_assign(req, resources, policy) -> { label, path, feas, c(path) } (aligned with Chapter 5, augmented with switching constraints)
• I60-93 xbar_program(path, label, devices) -> { Xbar, T_reconf, status }
• I60-94 ocs_blocking(A, m) -> P_block (Erlang-B/Erlang-C selectable)
• I60-95 ops_contention(λ_pkt, μ, P_out, N_in, FDL, WC) -> { P_contention, lat_q }
• I60-96 power_equalize(dev_chain, targets) -> plan_pwr
• I60-97 measure_swrt(telem) -> { P_block_meas, P_cont_meas, lat_sw_meas, Iso_meas, FM_dB_meas }
• I60-98 compare_config_meas(cfg, meas) -> delta_form_swrt
• I60-99 emit_swrt_manifest(results, policy) -> manifest.packet.swrt
  Invariants: two_forms_present = true; check_dim(*) passes; device/path/config hashes are traceable; guard / isolation and power plans meet targets.

VIII. Cross-References

• Spectral/spatial labels & equalization: Chapter 5;
• Framing & conservation budget: Chapter 3 (T_guard_budget);
• Physical layer & compensation: Chapters 2 / 6;
• FSO & availability prediction: Chapter 7;
• Metrology & dashboards: Chapter 11 (Iso / OSNR / BER / EVM fields);
• Arrival-time harmonization: Chapter 8.

IX. Quality & Risk Control

• SLI / SLO: delta_form_swrt_p95, P_block, P_contention, lat_sw / lat_q_p95, Iso_link_min, FM_dB_p50, reconf_fail_rate.
• Fallback strategies: rising blocking/contention → reroute / augment resources or rate-down; lat_sw over budget → pre-provision or pre-configured OCS; low isolation → enlarge guard band / retune channel; large delta_form_swrt → prefer measured form, update models, and canary the release.
• Audit: persist Xbar / label / plan_pwr versions, config & measurement evidence, threshold evolution, and the manifest signature chain with replay consistency.

Summary

• This chapter integrates OCS/OPS/WSS/ROADM into a single switching & routing framework that publishes dual-form indicators (configured vs measured).
• Via P609 / S609 / M60-9 / C60-9x / I60-9* and the manifest.packet.swrt.* schema, link- and node-level switching/routing is made traceable, auditable, and rollback-ready.