Queue Content Analysis in a 2-Class Discrete-Time Queueing System under the Slot-Bound Priority Service Rule

The paper we present here introduces a new priority mechanism in discrete-time queueing systems. It is a milder form of priority when compared to HoL priority, but it favors customers of one type over the other when compared to regular FCFS. It also provides an answer to the starvation problem that occurs in HoL priority systems. In this new priority mechanism, customers of different priority classes entering the system during the same time slot are served in order of their respective priority class—hence the name slot-bound priority. Customers entering during different slots are served on an FCFS basis. We consider two customer classes pertaining to two levels of priority such that type-1 customers are served before type-2 customers that enter the system during the same slot. A general independent arrival process and generally distributed service times are assumed. Expressions for the probability generating function PGF of the system content number of type-j customers, j 1, 2 in regime are obtained using a slot-to-slot analysis. The first moments are calculated, as well as an approximation for the probability mass functions associated with the found PGFs. Lastly, some examples allow us some deeper insight into the inner workings of the slot-bound priority mechanism.