Parametric delay differentiation between packet flows using multiple reserved spaces

We analyse a discrete-time queueing model with packet arrivals that are either classified as delay-sensitive (type 1) or delay-tolerant (type 2). The queue has a single server and each packet requires a service time of exactly one slot. The prominent feature of this model is its reservation-based queueing discipline, which has the purpose of reducing the queueing delay perceived by the 1-packets at the cost of allowing higher delays for the 2-packets. Our suggestion is to introduce a total of N reserved spaces in the queue, intended for future arrivals of type 1. Specifically, whenever a 1-packet enters the queue, it takes the position of the most advanced reservation and creates a new reservation at the end of the queue. Type 2 arrivals on the other hand, are always stored in the usual FIFO (First-In First-Out) manner. This way, it is possible for a 1-packet to jump over already queued 2-packets, resulting in the desired prioritisation of type 1 over type 2 packets. The amount of stochastic delay difference between 1- and 2-packets can be controlled smoothly by the parameter N. As a result of our analysis, we obtain the probability generating function, the mean value and the tail distribution of the delay experienced by both 1- and 2-packets. In each case, fast computational algorithms are provided, as well as some numerical examples.