Brownian Models of Queueing Networks with Heterogeneous Customer Populations

Consider an open queueing network with I single-server stations and K customer classes. Each customer class requires service at a specified station, and customers change class after service in a Markovian fashion. (With K allowed to be arbitrary, this routing structure is almost perfectly general.) There is a renewal input process and general service time distribution for each class. The correspondence between customer classes and service stations is in general many to one, and the service discipline (or scheduling protocol) at each station is left as a matter for dynamic decision making.