Application of Queueing Theory and Stochastic Particle Tracking Model to Simulating Stochastic Sediment Transport: Concentrations and Transport Rates

Sediment transport is typically simulated using deterministic models. However, the intermittent and stochastic features of sediment transport make it suitable to be described by discrete random processes. This study attempts to apply queueing theory to develop a stochastic framework that could account for the random-sized batch arrivals of incoming sediment particles into receiving waters. Sediment particles, control volume, mechanics of sediment transport (such as mechanics of suspension, deposition and resuspension) are treated as the customers, service facility and server respectively in queueing theory. In the framework, the stochastic diffusion particle tracking model (SD-PTM) and resuspension of particles are included to simulate the random transport trajectories of suspended particles. The most distinguished characteristic of queueing theory is that customers come to the service facility in a random manner. In analogy to sediment transport, this characteristic is suitable to model the random-sized batch arrival process of sediment particles including the random occurrences and random magnitude of incoming sediment particles. The random occurrences of arrivals are simulated by Poisson process while the number of sediment particles in each arrival can be simulated by a binominal distribution. Simulations of random arrivals and random magnitude are proposed individually to compare with the random-sized batch arrival simulations. Simulation results are a probabilistic description for discrete sediment transport through ensemble statistics (i.e. ensemble means and ensemble variances) of sediment concentrations and transport rates. Results reveal the different mechanisms of incoming particles (RM, RA and BA) will result in differences in the ensemble variances of concentrations and transport rates under the same mean incoming rate of sediment particles.