QueueSim

Connect Remote server

claude mcp add --transport http public https://queuesim.com/mcp/v1

{
  "mcpServers": {
    "public": {
      "url": "https://queuesim.com/mcp/v1"
    }
  }
}

{
  "servers": {
    "public": {
      "type": "http",
      "url": "https://queuesim.com/mcp/v1"
    }
  }
}

Settings > Connectors > Add custom connector
URL: https://queuesim.com/mcp/v1

Tools 14 found in our last check

• 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 a…

• 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). Call this when the user's problem matches one of the preset shapes — use describe_scenario for more detail and simulate_…

• 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, grocery, 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). U…

• 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., 'my coffee shop is open 6am–10pm with 4 baristas off-peak, 7 at the 8am rush, 5 at the 4pm rush'). Inputs: `arrivalRa…

• 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 traffic to each). Both runs have identical total capacity (c × μ) and identical total arrivals (λ), so the offered load…

• 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 hangi…

• 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. Use this when the user asks 'how many servers do I need?' / 'what staffing keeps wait under N minutes?'. The tool runs…

• interpret_result

  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 utilization curve, what ρ means in plain language, what one more or fewer server would qualitatively do…

• 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. Use this when the user is validating QueueSim's engine against textbook values, learning queueing theory by watching…

• queue_model_guide

  How to build a QueueSim Cloud model: the node types (arrivals, service, delay, split, settype, bytype, exit), staff groups, distributions, plan limits and a worked example. Call this before check_queue_model or run_queue_model when the user's system has more than one step (sever…

• check_queue_model

  Check a QueueSim Cloud model (a multi-step queueing system built from nodes and staff groups) without running it. Returns every problem found (missing links, a line that would grow without limit, plan limits) tied to the node it is about, and a link that opens the model in Queue…

• run_queue_model

  Run a QueueSim Cloud model (a multi-step queueing system built from nodes and staff groups) on the QueueSim Cloud discrete event engine. Returns, per service node: customers joined, served, gave up and turned away, mean and percentile waits in minutes and service levels; per sta…

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