Delay analysis of a place reservation queue with heterogeneous service requirements

We study the delay performance of a queue with a reservation-based priority scheduling mechanism. The objective is to provide a better quality of service to delay-sensitive packets at the cost of allowing higher delays for the best-effort packets. In our model, we consider a discrete-time single-server queue with general independent arrivals of class 1 (delay-sensitive) and class 2 (best-effort). The scheduling mechanism makes use of an in-queue reservation for a future arriving class-1 packet. A class-1 arrival takes the place of the reservation in the queue, after which a new reservation is created at the tail of the queue. Class-2 arrivals always take place at the end of the queue. Past work on place reservation queues assumed independent and identically distributed transmission times for both packet classes, either deterministically equal to one slot, geometrically distributed or with a general distribution. In contrast, we consider heterogeneous service requirements with class-dependent transmission-time distributions in our analysis. The key element in the analysis method for class-dependent transmission times is the use of a new Markovian system state vector consisting of the total amount of work in the queue in front of the reservation and the number of class-2 packets in the queue behind the reservation, at the beginning of a slot. Expressions are obtained for the probability generating functions, the mean values and the tail probabilities of the packet delays of both the delay-sensitive and the best-effort class. Numerical results illustrate that reservation-based scheduling mitigates the problem of packet starvation as compared to absolute priority scheduling