A Delicate Union of Batching and Parallelization Models in Distributed Computing and Communication

The Fork-Join (FJ) model has been extensively studied in the past due to its natural ability to capture computation and communication systems that employ split and merge techniques, i.e., boosting performance through splitting and parallelizing the input and finally merging the results. This model finds applications ranging from multipath communications to distributed databases.In this work, we explore the effect of batching within FJ systems, i.e., when servers collect the input to benefit from a so-called speedup, observed as a service time reduction due to batching. We numerically compare the performance when the speedup assumes different analytical forms. Our numerical evaluation shows that the steady-state waiting time of such an FJ system is heavily dependent upon the form of the speedup achieved through batching while the optimization thereof is non-trivial.