Performance analysis and decomposition results for some dynamic priority schemes in 2-class queues

Many device to device communication networks can be modelled by multi-class tandem queues. In many applications, it is desired to have different quality of service for various classes. This can be achieved by implementing dynamic priority across classes. Performance analysis is an important aspect in such multi-class tandem queueing models for resource allocation. In this paper, we analyse two important, relatively complex and analytically intractable performance measures, tail probability and switching frequency, for two class queueing system with two different (relative and earliest due date based) dynamic priority schemes across classes. Such a two class queueing system can be used to model voice and data calls in communication networks. A simulator is built to analyse such queueing systems and various observations are made. Based on computational evidence, it is conjectured that two stage exponential queueing network with two classes of customers is decomposable as far as mean waiting times are concerned when relative priority is used across classes to schedule the customers. Based on further experiments, it is conjectured that departure processes with relative dynamic priority are indeed Poisson in two class exponential queue. We also conduct relevant statistical analysis in support of the conjectures.