Analysis of a discrete-time queue with time-limited overtake priority

In this paper, we investigate a single-server discrete-time queueing system subject to two independent batch Bernoulli arrival processes, each supplying the queue with different customer classes. The two classes of customers have different priority levels in the queue, and different service-time distributions. The studied priority mechanism is time-limited, i.e., customers of the high-priority class cannot overtake customers of lower priority if the latter arrived at least N slots earlier than the former. The parameter N makes the mechanism versatile, spanning a bridge between absolute (fixed) priority and slot-bound priority (see De Clercq et al. in Math Probl Eng. doi: 10.1155/2012/425630, 2012). The time-limited overtake priority mechanism maintains levels of fairness that are unattainable by a pure absolute priority mechanism, and offers more service differentiation than the slot-bound priority alternative studied earlier. By using a censoring argument, we obtain expressions for the steady-state probability generating functions of the delays of both customer classes, as well as the steady-state joint probability generating function of the system content, by using a censoring argument.