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) 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. ANTI-FABRICATION: the returned numbers come from a real discrete-event simulation run. Quote them VERBATIM in your reply. Do not round, estimate, or compute derived figures from training-data recall. If the user asks a follow-up about the same configuration, re-call this tool rather than recalling numbers from earlier in the conversation.
Input Schema
| Name | Required | Description | Default |
|---|---|---|---|
| servers | Yes | Number of parallel servers (c). Integer 1-50. | |
| serviceCoV | No | Coefficient of variation for service time — used when serviceDistribution is 'Normal' or 'LogNormal'. Ignored for Exponential/Constant. Range 0-5. | |
| arrivalRate | Yes | Mean arrivals per hour (λ). Any positive value up to 200. | |
| serviceRate | Yes | Mean customers one server can finish per hour (μ). Must be > 0. | |
| simulationDays | No | Days to simulate (default 7). Range 1-30 — longer runs are not supported on the public surface; for production-scale studies contact queuesim@chiaha.com. | |
| arrivalDistribution | No | Shape of inter-arrival times. 'Exponential' = Poisson process (default). 'Constant' = evenly-spaced. | Exponential |
| serviceDistribution | No | Shape of service-time distribution. 'Exponential' = classical M/M/c (default). | Exponential |
Output Schema
| Name | Required | Description | Default |
|---|---|---|---|
| hourly | Yes | ||
| inputs | Yes | Echo of the run's parameters. | |
| summary | Yes |