Stability Analysis of a Basic Collaboration System via Fluid Limits

In this work, the fluid limit approach methodology is applied to find a sufficient and necessary stability condition for the Basic Collaboration (BC) system with feedback allowed, which is a generalization of the so-called W -model. In this queueing system, some customer classes need cooperation of a subset of (non-overlapping) servers. We assume that each customer class arrives to the system following a renewal input with general i.i.d. inter-arrival times, and general i.i.d. service times are also assumed. Priority is given to customer classes that can not be served by a single server but need a cooperation.