Throughput and bottleneck analysis of tandem queues with nested sessions

Various types of systems across a broad range of disciplines contain tandem queues with nested sessions. Strong dependence between the servers has proved to make such networks complicated and difficult to study. Exact analysis is in most of the cases intractable. Moreover, even when performance metrics such as the saturation throughput and the utilization rates of the servers are known, determining the limiting factor of such a network can be far from trivial. In our work, we present a simple, tractable and nevertheless relatively accurate method for approximating the above mentioned performance measurements for any server in a given network. In addition, we propose an extension to the intuitive slowest server rule for identification of the bottleneck, and show through extensive numerical experiments that this method works very well.