Service Level What-If Simulator

What it does

The Service Level What-If Simulator is a queueing-theory engine for call center / WFM operations. It takes a base case (volume, AHT, agents, SL target) and one change ("3 fewer agents on shift", "volume +20%", "AHT -30s", "shrinkage 30%→38%"), solves both states with the same engine, and quantifies the difference.

The core engine is Erlang-C (M/M/c queue): traffic intensity A = (calls/period) × AHT (Erlangs) and agent count c yield the probability of waiting, from which SL and ASA are derived. When caller impatience (abandonment) matters, Erlang-A (M/M/c+M, Palm / Garnett-Mandelbaum-Reiman) computes abandon rate from average patience. Because solving a day with a single "average" hides the peak, a SIPP (Stationary Independent Period-by-Period) discipline reports the peak interval separately. Required staff is always converted to gross with shrinkage accounting: gross FTE = Erlang requirement ÷ (1 − shrinkage). Results are positioned against COPC / SQM benchmark bands (SL 80%/20s, abandon <5%, healthy occupancy 85–90%).

Output gives number + direction + meaning per metric, builds a Base vs Scenario delta table (ΔSL, ΔASA, Δabandon, Δoccupancy, ΔFTE), and produces a 0–100 weighted Operations/SL score with a verdict (healthy / borderline / risky / critical).

When to use it

Whenever you have a base case plus a "what if" question: headcount cuts for budget, a volume spike from a campaign or outage, AHT drift, shrinkage increases (training/leave season), SL target negotiation, shift redistribution, or an intraday understaffing alarm. Use it when defending an SLA to management or deciding "how many FTE can I save / how short will I be" with hard numbers.

Method / frameworks

• Erlang-C (M/M/c) — waiting probability for fixed agents + Poisson arrivals; the SL/ASA engine. Assumes no abandonment, so it reads SL optimistically.
• Erlang-A (M/M/c+M) — adds caller patience θ for realistic abandon and ASA.
• SIPP — interval-based solving; solve the peak interval separately, not a daily average.
• Shrinkage accounting — net Erlang FTE → gross headcount; typically 25–40%.
• COPC / SQM benchmark — reference bands and verdict thresholds for SL/abandon/occupancy.
• Stability rule — without c > A the queue is unstable (ASA→∞); c≤A is flagged as collapse rather than fabricated.