Markovian Queue with Garbage Collection

Garbage collection is a fundamental component of memory management in several software frameworks. We present a general two-dimensional Markovian model of a queue with garbage collection where the input process is Markov-modulated and the memory consumption can be modeled with discretisation. We derive important performance measures (also including garbage collection-related measures like mean garbage collection cycle length). The model is validated via measurements from a real-life data processing pipeline.