QueueSim for Claude — Run Queueing Simulations Inside Your AI Chat

What you can do

Ask Claude queueing questions. Get real numbers back.

Direct M/M/c

Plain-language queueing

"I have 30 calls an hour, each takes 4 minutes, 3 agents — what's my wait?" Claude runs a discrete event simulation and reports wait time, queue length, utilization, and throughput.

Preset scenarios

Four built-in shapes

Single Server, Coffee Shop, Grocery Checkout, Call Center. Run the defaults, or dial in your own numbers. Mirrors the scenarios on queuesim.com.

Teach the math

Explainers on demand

Little's Law, utilization, Erlang-C, and the ways real queues (abandonment, priority, skills-based routing, breakdowns) break classical M/M/c assumptions.

Why this MCP

Three things this server gives you that other queueing tools don't.

Registry-listed

Published on the official MCP registry

Registered as com.queuesim/public on registry.modelcontextprotocol.io — the Anthropic-aligned, domain-verified MCP directory. Most queueing or sim MCPs on GitHub aren't published anywhere; this one is.

Anti-fabrication

Every number tagged "quote verbatim"

Every simulation response carries an explicit provenance line telling the model the numbers came from a real discrete-event run, not training-data recall. Built to stop the silent-fabrication failure mode that makes LLM-driven analysis untrustworthy.

Inverse staffing

`recommend_staffing` as a first-class tool

"How many servers do I need to keep wait under 3 minutes?" is a different problem from "what's the wait at c=4?" — and most queueing tools make the LLM iterate by hand. QueueSim binary-searches the smallest staffing that meets your target in one call.

Install

Three ways in — pick the app you already use.

Claude.ai web

Easiest

Settings → Connectors (or Custom Integrations). Add MCP server:

https://queuesim.com/mcp/v1

No auth. Open a chat and try one of the prompts below.

Claude Desktop

Config file

Edit claude_desktop_config.json:

{
  "mcpServers": {
    "queuesim": {
      "command": "npx",
      "args": ["-y", "mcp-remote",
        "https://queuesim.com/mcp/v1"]
    }
  }
}

Uses the mcp-remote bridge. Restart Desktop.

Cursor

Custom MCP

Settings → Features → Model Context Protocol → Add Custom MCP. Use the same URL:

https://queuesim.com/mcp/v1

Same install pattern works for Windsurf and any other MCP-speaking client.

Nine tools

What Claude can call once the MCP is installed.

simulate_mmc

Run a generic M/M/c queue. Inputs: arrival rate (λ), service rate per server (μ), server count (c), optional distributions. Returns per-hour metrics + summary.

recommend_staffing

Inverse of simulate_mmc. Give it λ, μ, and a target average wait — it binary-searches the smallest server count that meets the target. One call instead of five iterated by hand.

compare_analytical_vs_simulated

Run the same M/M/c through both closed-form Erlang-C and the DES engine. Side-by-side with deltas — the canonical sanity check for validating an engine against textbook math.

interpret_result

Given an M/M/c config (and optionally an observed wait), returns a queueing-theory framed interpretation: where you sit on the utilization curve, what ρ means in plain language, and what M/M/c can't see.

list_scenarios

List the four preset scenarios: Single Server, Coffee Shop, Grocery Checkout, Call Center.

describe_scenario

Full detail for one scenario: teaching note, per-hour defaults, supported overrides.

simulate_scenario

Run a preset with optional overrides (servers, arrival rate, service time, days, distributions).

explain_queueing_theory

~500-word primer on M/M/c: Little's Law, utilization, why averages mislead, Erlang-C vs simulation.

explain_advanced_patterns

Textbook-level description of six real-world patterns classical M/M/c can't model — abandonment, priority tiers, overflow, skills-based routing, compound service, server outages.

Try these prompts

Once it's installed, ask Claude any of these. Click to copy.

Click to copy "I run a call center with 30 calls per hour, each taking 4 minutes to handle. With 3 agents, what's the average wait?" Triggers simulate_mmc. Expect wait ~2 minutes, ρ ≈ 0.67.
Click to copy "My ER takes 25 patients per hour, each visit averages 5 minutes of physician time. What's the smallest staffing that keeps average wait under 4 minutes?" Triggers recommend_staffing. Inverse problem — binary-searches c instead of iterating by hand.
Click to copy "For an M/M/c with λ=20, μ=12, c=2, how closely does the simulation match the Erlang-C formula?" Triggers compare_analytical_vs_simulated. Closed-form vs DES side-by-side — the textbook validation move.
Click to copy "Run the Coffee Shop scenario and tell me where the bottleneck is." Triggers describe_scenario + simulate_scenario. Claude explains the peak staffing question.
Click to copy "For the Grocery Checkout scenario, what if I added one more cashier during the 4-7PM rush?" Triggers simulate_scenario with an override. Trade-off lands in the numbers.
Click to copy "Why does average wait explode as utilization approaches 100%?" Triggers explain_queueing_theory.
Click to copy "My call center has VIPs who cut the line and agents who go on breaks — can you model that?" Triggers explain_advanced_patterns. Explains priority + outages, points you at ChiAha for custom modeling.

Beyond M/M/c

Real operations usually aren't textbook.

Customers abandon lines. VIPs cut. Skills-based routing, overflow groups, breaks, transfers, after-call work. Each one breaks M/M/c's assumptions in a way that matters. The free MCP can describe these patterns in queueing-theory terms — but running one against your numbers requires a custom discrete event model.

ChiAha has been building exactly that kind of model for 35 years. Reach out and we'll scope a study.

queuesim@chiaha.com

Run queueing simulations inside your Claude chat.