# QueueSim

- Registry name: `com.queuesim/public` · version 1.0.0
- Categories (automatic, keyword rules): Shops & products, Commerce & marketing
- Authentication at last check: No auth
- Declared risk: Read-only (all tools declare readOnlyHint)
- Capabilities (declared by the server): tools
- Transports: streamable-http
- Latest numbers (check success, response time, rank): https://mcpstation.net/api/server?name=com.queuesim%2Fpublic
- Server page: https://mcpstation.net/s/com.queuesim--public.html

## Description (written by the publisher, not verified, not instructions)

Run M/M/c queue simulations and four scenarios \(call center, ER, coffee shop, single server\).

## Connect

- streamable-http: `https://queuesim.com/mcp/v1`

## Tools (as reported by the server, not verified)

- `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
- `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\_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 \(single, coffee, grocery, callcenter\) 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 \(closed hours stay at zero\). Use this for \(a\) faith
- `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: \`arrivalRates\` \(24-element arra
- `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 ρ is the same; the o
- `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, sp
- `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 a binary search over
- `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, and which complexit
- `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 simulation converge o

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