{"id":24455290,"url":"https://github.com/1lmao/queuing-theory","last_synced_at":"2026-04-23T12:33:18.051Z","repository":{"id":271141860,"uuid":"912508136","full_name":"1lmao/Queuing-Theory","owner":"1lmao","description":"Modeling and simulating various queuing models such as: M/M/1, M/M/k, G/G/1, G/M/1, and M/G/1 for Large Language Model (LLM) inference systems. 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Simple random arrivals and service times with a single processor.\n\n* **M/M/k**\n    * **Arrivals:** Poisson (Random).\n    * **Service:** Exponential (Random).\n    * **Servers:** $k$ (Multiple).\n    * *Description:* A multi-server version of M/M/1. Think of a bank with a single line feeding into $k$ open teller windows.\n\n* **M/G/1**\n    * **Arrivals:** Poisson (Random).\n    * **Service:** General (Any distribution).\n    * **Servers:** 1.\n    * *Description:* Arrivals are random, but the service time follows a specific, non-random distribution (e.g., fixed time or heavy-tailed). Often analyzed using the Pollaczek–Khinchine formula.\n\n* **G/M/1**\n    * **Arrivals:** General (Any distribution).\n    * **Service:** Exponential (Random).\n    * **Servers:** 1.\n    * *Description:* The inverse of M/G/1. The service rate is random, but the incoming traffic follows a complex or specific pattern (e.g., bursty traffic).\n\n* **G/G/1**\n    * **Arrivals:** General.\n    * **Service:** General.\n    * **Servers:** 1.\n    * *Description:* The most complex single-server model. Both arrival and service times can follow any distribution. No simple formulas exist; typically solved via approximation or simulation.\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2F1lmao%2Fqueuing-theory","html_url":"https://awesome.ecosyste.ms/projects/github.com%2F1lmao%2Fqueuing-theory","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2F1lmao%2Fqueuing-theory/lists"}