Integrity certificate: contact center queueing (Erlang C)
Re-run against these exact files on 2026-08-30.

Every line was measured, not asserted. The checks are ordinary pandas over
the CSVs sitting beside this file, so you can re-run them yourself.

  PASS  agents_staffed exceeds traffic_intensity_erlangs on all 2,400 intervals (queue stability)
  PASS  'Billing Support' clears its 80% SLA target on 100.0% of intervals
  PASS  'Retention' clears its 75% SLA target on 100.0% of intervals
  PASS  'Sales' clears its 90% SLA target on 100.0% of intervals
  PASS  'Technical Support' clears its 80% SLA target on 100.0% of intervals
  PASS  service_level_pct matches an independent Erlang C recomputation on all 2,400 intervals
  PASS  calls_answered + calls_abandoned equals offered_calls on all 2,400 intervals
  PASS  occupancy_pct and service_level_pct correlate at -0.31 (higher load, worse service)
  PASS  'Billing Support' midday volume (40.7) exceeds opening volume (13.8)
  PASS  'Retention' midday volume (14.9) exceeds opening volume (6.1)
  PASS  'Sales' midday volume (25.8) exceeds opening volume (9.2)
  PASS  'Technical Support' midday volume (29.5) exceeds opening volume (10.7)
  PASS  'Billing Support' abandons 1.8% of calls over the full month
  PASS  'Retention' abandons 4.0% of calls over the full month
  PASS  'Sales' abandons 0.8% of calls over the full month
  PASS  'Technical Support' abandons 1.7% of calls over the full month
  PASS  intervals.queue_id has zero orphans against queues.csv
  PASS  every interval_start falls exactly on a half-hour mark, on all 2,400 intervals
  PASS  agents_staffed is a positive integer on all 2,400 intervals

19 checks, 19 passing.

Composition, measured from these files:
  queues: 4 (Billing Support, Technical Support, Sales, Retention)
  intervals: 2,400 (30 business days x 4 queues x 20 half-hour slots)

Sources for every named formula:
  Erlang C               A.K. Erlang, 1917. Computed via the numerically
                          stable Erlang B recursion (Sundt-Jewell), not the
                          raw factorial form.
  ASA / service level     Standard Erlang C results (Gross & Harris,
                          "Fundamentals of Queueing Theory").
  Shrinkage               Standard WFM planning concept (ICMI); applied
                          here as a flat 20% buffer over the bare Erlang
                          requirement.
  Abandonment             This example's own competing-exponentials
                          extension of the exact Erlang C conditional-wait-
                          time result, not a claim to reproduce Erlang A
                          (Palm, 1957) exactly.

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