Insensitivity for Loss Systems with Compatibilities

In the study of queueing systems, we are often interested in finding the stationary distribution of the system state, which in turn can be used to compute various performance measures of interest. Under the assumption that the arrival process is Poisson and the service time distribution is exponential, many queueing systems have elegant productform stationary distributions. However, the exponentiality assumption is often unrealistic. Although relaxing this assumption typically makes the analysis of the stationary distribution less tractable, a number of queueing systems are insensitive to the service time distribution, meaning that they have the same stationary distribution under all service time distributions. Below we describe several examples.