Controlling the delay trade-off between packet flows using multiple reserved places

We analyse a discrete-time queueing model with packet arrivals that are either delay-sensitive (type 1) or delay-tolerant (type 2). The prominent feature of this model is its reservation-based queueing discipline, which reduces the queueing delay perceived by the 1-packets at the cost of allowing higher delays for the 2-packets. A total of NN reserved places are introduced in the queue. Whenever a 1-packet enters the queue, it takes the position of the most advanced reservation and creates a new one at the end of the queue. The amount of delay differentiation between 1- and 2-packets can thus be controlled smoothly by the parameter NN. We obtain the probability-generating function, the mean value and the tail distribution of the delay experienced by 1- and 2-packets.