QueueSim
QueueSim is a free Model Context Protocol server that gives Claude — and any MCP-speaking AI — the ability to run real discrete event queueing simulations…
What it can do
- 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 server count (c). Optional:
- List Scenarios: List the four pre-built QueueSim scenarios. Returns key, title, and one-line description for each (Single Server, Coffee Shop, ER Waiting Room, Call Center). Call this when the user's
- Describe Scenario: 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 underst
What data it sees
Do you need an account
No: the server works without sign-in
QueueSim is a free Model Context Protocol server that gives Claude — and any MCP-speaking AI — the ability to run real discrete event queueing simulations inside a conversation. Ask "I run a 3-agent call center, 30 calls/hr, 4-min handle time — what's my wait?" and get an actual number from a simulator, not a guess.
Six tools cover the common cases: direct M/M/c with arrival rate / service rate / server count, four preset scenarios (single server, coffee shop, ER waiting room, call center) with optional overrides, plus two textbook explainers covering basic queueing theory and six common patterns beyond M/M/c (abandonment, priority tiers, overflow routing, skills-based routing, compound service, server outages).
Free, no auth, no API key. By ChiAha — 35 years of discrete event simulation. For modeling beyond M/M/c against your own data, contact queuesim@chiaha.com.
Server tool list (6)
Raw names from tools/list. Only developers need these.
| 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 server count (c). Optional: distribution shapes, service coefficient of variation, run length. Returns per-hour metrics and an overall summary (avg wait, queue length, offered load, throughput). This is the primary tool for 'how many servers do I need?' / 'what's my average wait?' style questions. ALSO preferred over simulate_scenario for what-if questions about scheduled scenarios (Coffee Shop, ER) when the user wants flat uniform numbers — pull the peak params from describe_scenario and run them here. That usually matches user intent better than collapsing a schedule. |
| list_scenarios | List the four pre-built QueueSim scenarios. Returns key, title, and one-line description for each (Single Server, Coffee Shop, ER Waiting Room, Call Center). Call this when the user's problem matches one of the preset shapes — use describe_scenario for more detail and simulate_scenario to run one. |
| describe_scenario | 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 understand the default shape and what overrides make sense. |
| simulate_scenario | Run one of the four preset scenarios (single, coffee, er, callcenter) with optional overrides. Overrides apply UNIFORMLY across open hours — e.g. setting servers=5 on 'coffee' replaces the 4/6/4 staffing pattern with a flat 5 during open hours (closed hours stay at zero). Use this for (a) faithful reproduction of a scenario's defaults, or (b) uniform scaling (everywhere it was open, use these new numbers). Do NOT use this when the user wants to keep a scheduled scenario's shape but tweak just one part — there's no per-hour override here, and collapsing a 4/6/4 pattern to 5 often isn't what the user meant. For flat what-if analysis on scheduled scenarios, prefer simulate_mmc using peak params from describe_scenario. |
| 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 inputs. Use this when the user asks a conceptual 'why' or 'how does this work' question rather than asking for a number. |
| 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 routing, compound service, and server outages. Use this when the user describes real-world complexity (customers hanging up, VIP queues, specialist escalation, agent breaks, transfers) that plain M/M/c doesn't model. The tool frames each pattern conceptually and points users at ChiAha for custom modeling. |