SERVER COORDINATION IN QUEUEING SYSTEMS: WHEN AND HOW?

Abstract

Standard server assignment policies for multi-server queueing stations include the noncollaborative policy, where the servers work in parallel on different jobs; and the fully collaborative policy, where the servers work together on the same job. However, if each job can be decomposed into subtasks with no precedence relationships, then we consider a form of server coordination named task assignment where the servers work in parallel on different subtasks of the same job. We identify the task assignment policy that maximizes the long-run average throughput of a queueing station with finite internal buffers when blocked servers can be idled or reassigned to either replace or collaborate with other servers on unblocked subtasks. We then compare the server coordination policies and show that the task assignment is best when the servers are highly specialized; otherwise, the fully collaborative or noncollaborative policies are preferable depending on whether the synergy level among the servers is high or not. We also provide numerical results that quantify our previous comparison. Finally, we address buffer allocation in longer lines where there are precedence relationships between some of the tasks, and present numerical results that suggest our comparisons for one queueing station generalize to longer lines.