QueueSim

• simulate_mmc — Run a generic M/M/c queue simulation. Provide an arrival rate (λ, arrivals/hour), a service rate per server (μ, customers/hour each server can finish), and a se
• list_scenarios — List the four pre-built QueueSim scenarios. Returns key, title, and one-line description for each (Single Server, Coffee Shop, Grocery Checkout, Call Center). C
• describe_scenario — Return full details for one preset scenario: title, description, teaching note, peak parameters, and per-hour arrival + staffing arrays. Use this before simulat
• simulate_scenario — Run one of the four preset scenarios (single, coffee, grocery, callcenter) with optional overrides. Overrides apply UNIFORMLY across open hours — e.g. setting s
• simulate_schedule — Run a queueing simulation against an arbitrary 24-hour staffing schedule. Take this when the user describes a custom day shape that doesn't match a preset (e.g.
• compare_separate_vs_pooled — Run the classic operations-research teaching demo: pooled queueing (one shared queue, c servers) vs separate queues (c independent queues, one server each, λ/c
• explain_queueing_theory — Return a ~500-word educational explainer of M/M/c queueing theory: Little's Law, utilization, why averages mislead, how simulation relates to Erlang-C. No input
• explain_advanced_patterns — Return a textbook-level description of six queueing complexity patterns beyond basic M/M/c: abandonment/reneging, priority tiers, overflow routing, skills-based
• recommend_staffing — INVERSE of simulate_mmc — given an arrival rate, service rate, and a target average wait time, returns the SMALLEST number of servers needed to meet the target.
• interpret_result — Given an M/M/c configuration (arrivalRate, serviceRate, servers) and optionally an observed average wait, returns a queueing-theory framed interpretation: where
• compare_analytical_vs_simulated — Run the same M/M/c configuration through BOTH the closed-form Erlang-C formula AND the discrete-event simulator, returning a side-by-side comparison with deltas

No long description beyond the summary.