A discrete-time queueing system under frame-bound priority

A well-known problem with priority policies is starvation of delay-tolerant traffic. Furthermore insufficient control over delay differentiation (which is needed for modern network applications) has incited the development of other scheduling disciplines. Processor sharing is one of many solutions to this problem. The priority policy we present here has the added benefit of being more 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 (we will refer to packets as customers) pertaining to different priorities. A general i.i.d. arrival process is assumed and service times are deterministic. 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 queue content (meaning the customers of each type in the system at random slotmarks) in stationary regime. Clearly the frame's size is the key factor in the delay differentiation between the two priority classes. The numerical results at the end of this paper illustrate this fact.