No abstract

No abstract

No abstract

Completeness of some scheduling policies with mean waiting time performance measure is used quiet extensively in literature for dynamic control of multi-class queues due to its wide range of applications in computers, communication networks and manufacturing systems. For a single class queue, we introduce the idea of 2-moment completeness of a parametrized class of policies that also have to be non pre-emptive, non anticipative and work conserving. Significance of this idea lies in the importance of variance (or second moment) of waiting time in any queuing system. Some parametrized classes of policies are identified and shown to be 2-moment complete for M/M/1 queues. Some well known queue disciplines viz random order of service (ROS), Random Assigned Priority (RAP), etc., turn out to be 2-moment incomplete. We introduce a parametrized priority scheme that also turns out to be 2-moment incomplete. Further, few preemptive and anticipative scheduling disciplines are shown to have second moment beyond the achievable region of non pre-emptive, non anticipative and work conserving scheduling policies. Some optimal control problems are discussed to illustrate the possible applications of 2-moment complete parametrized set of policies.

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.