MCP servercom.queuesim/public

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. Use this when the

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 traffic to each). Bo

Return full details for one preset scenario: title, description, teaching note, peak parameters, and per-hour arrival + staffing arrays. Use this before simulate_scenario to unders

Return a textbook-level description of six queueing complexity patterns beyond basic M/M/c: abandonment/reneging, priority tiers, overflow routing, skills-based routing, compound s

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 inputs. Use this when the

Given an M/M/c configuration (arrivalRate, serviceRate, servers) and optionally an observed average wait, returns a queueing-theory framed interpretation: where you sit on the util

List the four pre-built QueueSim scenarios. Returns key, title, and one-line description for each (Single Server, Coffee Shop, Grocery Checkout, Call Center). Call this when the us

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. Use this when the u

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 server count (c). Opti

Run one of the four preset scenarios (single, coffee, grocery, callcenter) with optional overrides. Overrides apply UNIFORMLY across open hours — e.g. setting servers=5 on 'coffee'

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., 'my coffee shop is