The most powerful results in queueing theory are closed-form expressions for key performance metrics (e.g., waiting times, sojourn times, number of customers), because they explicitly show how the performance depends on the system parameters. Unfortunately, most queueing models prohibit the derivation of exact closed-form expressions. Faced by this, it is common practice to use numerical techniques (e.g., numerical algorithms, approximation methods, and simulations) or to develop exact expressions in asymptotic regimes (e.g., heavy-load, heavy-tails). Despite the fact that tremendous progress has been made in the development of efficient numerical techniques, by definition they provide limited insight into how the performance metrics depend on the system parameters. In this paper, we propose a new view on attacking queueing models by presenting a data-driven approach to develop closed-form approximations for key performance metrics based on the use of genetic algorithms (GAs), using the concept of symbolic regression (SR). SR is a regression method that searches the space of algebraic expressions to find one that ‘best’ fits a given data set, both in terms of accuracy and simplicity. Within the SR framework, an individual represents a specific formula, which is expressed as a tree. Like any other GA, SR forms an initial population of individuals. Next, the GA iteratively generates a new offspring of individuals (a new generation) by crossing and/or mutating already existing individuals. The idea is that over time, the population’s accuracy improves due to evolving the well-performing individuals (i.e., survival of the fittest). See Fig. 1 for an illustration.

doi.org/10.1007/s11134-022-09767-6
Queueing Systems

van der Mei, R., & Bhulai, S. (2022). A data-driven approach to deriving closed-form approximations for queueing problems using genetic algorithms. Queueing Systems, 100, 549–551. doi:10.1007/s11134-022-09767-6