Invariance of workload in queueing systems

In multi‐server systems, invariance of workload is a key step in establishing conservation and strong conservation laws. Although several articles have dealt with the issue, invariance of workload has been either assumed, asserted without proof, or the proof given is unsatisfactory, except when service times are exponential. In this article we consider a multi‐server queueing system with a work‐conserving, non‐preemptive, and non‐anticipative scheduling rule and give a proof for the invariance of the workload in queue and in system for all such rules. We also show that invariance of workload holds for a subclass of strict priority rules.