Frame-bound priority scheduling in discrete-time queueing systems

A well-known problem with priority policies is starvation of delay-tolerant traffic. Additionally, insufficient control over delay differentiation (which is needed for modern network applications) has incited the development of sophisticated scheduling disciplines. The priority policy we present here has the benefit of being open to rigorous analysis. We study a discrete-time queueing system with a single server and single queue, in which $N$ types of customers enter pertaining to different priorities. A general i.i.d. arrival process is assumed and service times are generally distributed. We divide the time axis into 'frames' of fixed size (counted as a number of time-slots), and reorder the customers that enter the system during the same frame such that the high-priority customers are served first. This paper gives an analytic approach to studying such a system, and in particular focuses on the system content (meaning the customers of each type in the system at random slotmarks) in stationary regime, and the delay distribution of a random customer. Clearly, in such a system the frame's size is the key factor in the delay differentiation between the $N$ priority classes. The numerical results at the end of this paper illustrate this observation.