Fajardo, Val AndreiDrekic, Steve2017-06-142017-06-142016-10-01http://dx.doi.org/10.1080/15326349.2016.1193753http://hdl.handle.net/10012/12007This is an Accepted Manuscript of an article published by Taylor & Francis in Stochastic Models on June, 24, 2016, available online: http://dx.doi.org/10.1080/15326349.2016.1193753.We consider a single-server queueing system which attends to N priority classes that are classified into two distinct types: (i) urgent: classes which have preemptive resume priority over at least one lower priority class, and (ii) non-urgent: classes which only have non-preemptive priority among lower priority classes. While urgent customers have preemptive priority, the ultimate decision on whether to interrupt a current service is based on certain discretionary rules. An accumulating prioritization is also incorporated. The marginal waiting time distributions are obtained and numerical examples comparing the new model to other similar priority queueing systems are provided.enAccumulating priorityLaplace–Stieltjes transformMixed priority queueServer discretion rulesWaiting time distributionArticle