A stochastic recirculation system with random access

A model for a stochastic recirculation system with randomly accessed multiple heterogeneous servers, no waiting rooms, and exponentially-distributed service times is provided. In this system the units are assigned to one of the servers upon arrival by random mechanism. Units which find all servers busy recirculate and combine with the incoming arrivals and join those already in the system to initiate the next cycle. The equilibrium behavior of the internal and external stochastic processes of the system is analyzed using a two parameter approximation. A simulation model is also developed and its behavior is compared against the analytical model at the steady state. The model with randomly-accessed servers is compared to a single server model already established in the literature. The performance of the model is then examined for a wide range of parameter values to obtain conclusions about its optimal performances.