Lock-Free Search Data Structures: Throughput Modelling with Poisson Processes

This paper considers the modelling and the analysis of the performance of lock-free concurrent search data structures. Our analysis considers such lock-free data structures that are utilized through a sequence of operations which are generated with a memoryless and stationary access pattern. Our main contribution is a new way of analysing lock-free search data structures: our execution model matches with the behavior that we observe in practice and achieves good throughput predictions. Search data structures are formed of linked basic blocks, usually referred as nodes, that can be accessed by two kinds of events, characterized by their latencies; (i) CAS events originated as a result of modifications of the search data structures (ii) Read events originated during traversals. This type of data structures are usually designed to accommodate a large number of data nodes, which makes the occurrence of an event on a given node rare at any given time. The throughput is defined by the number of events per operation in conjunction with the factors that impact the latencies of these events. We frame these impacting factors under capacity and coherence cache misses. In this context, we model the events as Poisson processes that we can merge and split to estimate the latencies of the events based on the interleaving of events from different threads, and in turn estimate the throughput. We have validated our analysis on several fundamental lock-free search data structures such as linked lists, hash tables, skip lists and binary trees.