A single server queueing model with two types of arrivals is discussed under the assumptions of Poisson arrivals, (possibly different) general services and finite waiting room for each type of customer. Under a dynamic non-preemptive priority service rule, the steady state analysis of the model is performed. A number of interesting and intuitive results are obtained. In the case when the services are of phase type, implementable algorithms are developed for computing various system performance measures. The recursive computational schemes can be used interactively in the design of such queueing systems. A number of numerical examples are discussed.