Fluid approximation of pool depletion systems

Today’s most of high performance computing applications use parallel programming paradigms to reach the desired efficiency objectives. In particular, they divide the problem into small elements that can be solved in parallel by as many computing devices as available. Some examples are Apache Spark, the evolution of Hadoop and mapreduce, GPGPU (General Purpose Graphical Processing Units) applications, many-core and multi-core embedded systems. In many cases this type of applications can be modeled by pool depletion systems, i. e. queuing models characterized by a set of parallel servers whose goal is to execute a predetermined number of tasks. Although the modeling paradigm is very simple, it suffers from state space explosion, and can be used to model systems with a limited degree of parallelism only. The main contribution provided by this work consists of presenting a fluid approximation approach capturing the main features of the considered pool depletion systems and solving the above mentioned issues.