Analysis of a threshold-based priority queue

This paper considers a discrete-time single-server queueing system, with two classes of customers, named class 1 and class 2. We propose and analyze a novel threshold-based priority scheduling scheme that works as follows. Whenever the number of class-1 customers in the system exceeds a given threshold $$m \ge 0$$ m ≥ 0 , the server of the system gives priority to class-1 customers; otherwise, it gives priority to class-2 customers. Consequently, for $$m=0$$ m = 0 , the system is equivalent to a classical priority queue with absolute priority for class-1 customers, whereby the (mean) delay of class-1 customers is lowered as much as possible at the expense of longer (mean) delays for class-2 customers. On the other hand, for $$m\rightarrow \infty $$ m → ∞ , the system is equivalent to a priority queue with absolute priority for class-2 customers, with the opposite effect on the class-specific (mean) delays. By choosing $$0