Epsilon serializability (ESR) was proposed to relax serializability constraints by allowing transactions to execute with a limited amount of inconsistency (ε-spec). Divergence control algorithms, viewed as extensions of concurrency control algorithms, enable read-only transactions to complete if their inconsistencies do not exceed ε-spec. This paper studies the performance of two-phase locking divergence control (2PLDC) and optimistic divergence control (ODC) algorithms. We develop a central part of the ESR transaction processing system that runs with 2PLDC and ODC. We applied a comprehensive centralized database simulation model to measure the performance. Evaluations are conducted with multi-class workloads where on-line update transactions and long-duration queries progress under various ε-spec. Our results demonstrate that significant performance enhancements are achieved with a non-zero tolerable inconsistency. With sufficient ε-spec and limited system resources, both algorithms result in comparable performance. However, with low resource contention, ODC performs significantly better than 2PLDC. Furthermore, in the range of small ε-spec, the queries committed by ODC have more accurate results than those committed by 2PLDC.