Modeling and analysis of concurrent maintenance policies for data structures using pointers

We present a state reduction method that effectively reduces a two-dimensional Markov model to a one-dimensional Markov model for the performance analysis of a class of concurrent data structure maintenance policies. The reduced model allows the derivation of a closed form expression for the average service time per operation and facilitates the identification of priority allocation functions under which: the system is stable; and the service time per operation is minimized. The applicability of the model is exemplified with a binary tree data structure and the conditions under which concurrent maintenance strategies are better than a conventional incremental maintenance strategy are determined