Accuracy assessment of analytical approximations in retrial queueing networks with impatient customers
Streszczenie
The study examines the accuracy of analytical results for a call center model represented as a retrial queueing network with impatient customers. A discrete-event simulation algorithm was developed that explicitly incorporates the structural specifics of the model, including a loss-type distributor, retrial orbit, and finite-capacity queues. Through simulation experiments, we identified the optimal number of model replications that provide sufficiently accurate approximations of the mean values of the network performance characteristics while maintaining an acceptable computational time. To enable an adequate comparison between the analytical and simulation results, the times required for both models to reach the stationary regime were analyzed. Subsequently, the accuracy of the analytical results was evaluated for the selected performance characteristics of the call center model over the stationary interval of the network. Comparative analysis revealed close agreement between simulation and analytical results in steady state, particularly under heavy load conditions. These results confirm that the asymptotic approach, based on the diffusion approximation and Fokker–Planck–Kolmogorov equation, provides accurate predictions under high load.
