Workloads and waiting times in single-server systems with multiple customer classes

One of the most fundamental properties that single-server multi-class service systems may possess is the property of work conservation. Under certain restrictions, the work conservation property gives rise to a conservation law for mean waiting times, i.e., a linear relation between the mean waiting times of the various classes of customers. This paper is devoted to single-server multi-class service systems in which work conservation is violated in the sense that the server's activities may be interrupted although work is still present. For a large class of such systems with interruptions, a decomposition of the amount of work into two independent components is obtained; one of these components is the amount of work in the corresponding systemwithout interruptions. The work decomposition gives rise to a (pseudo)conservation law for mean waiting times, just as work conservation did for the system without interruptions.