Estimating customer impatience in a service system with unobserved balking

This paper studies a service system in which arriving customers are provided with information about the delay they will experience. Based on this information they decide to wait for service or to leave the system. The main objective is to estimate the customers' patience-level distribution and the corresponding potential arrival rate, using knowledge of the actual queue-length process only. The main complication, and distinguishing feature of our setup, lies in the fact that customers who decide not to join are not observed, but, remarkably, we manage to devise a procedure to estimate the load they would generate. We express our system in terms of a multi-server queue with a Poisson stream of customers, which allows us to evaluate the corresponding likelihood function. Estimating the unknown parameters relying on a maximum likelihood procedure, we prove strong consistency and derive the asymptotic distribution of the estimation error. Several applications and extensions of the method are discussed. The performance of our approach is further assessed through a series of numerical experiments. By fitting parameters of hyperexponential and generalized-hyperexponential distributions our method provides a robust estimation framework for any continuous patience-level distribution

Hydraulic Efficiency of Flood Detention Pools Evaluated by Means of Mathematical Simulation

The hydraulic efficiency to secure optimization of the flood detention pool system will be treated through mathematical simulation. The mathematical model is approximated by the point-sink virtually located at the center of the deversoir section. Numerical computations show that the optimization of the system in hydraulic efficiency will be given through a combination of the deversoir length and the initial diversion discharge. Furthermore, it is seen the whole pool volume will be nearly constant for any possible combination