Annotated Bibliography of Blocking Systems.

Abstract : Queueing systems subject to blocking have been studied by researchers from different research communities. Due to the wide applicability of these models there is an exhaustive list of related papers. This annotated bibliography summarizes 55 of these papers by briefly describing the model, the performance measure, and the basic methodology used and/or results obtained in each paper. The literature considers two distinct blocking policies for transfer lines with finite buffers: immediate blocking and nonimmediate blocking. The papers are classified into two major classes depending on whether the servers are reliable or subject to breakdowns. In the first class, Systems with Reliable Servers, each node in the network is attended by reliable servers. As long as there is a job to process and the server is not blocked, it can always give service according to some known service distribution. In the second class, Systems with Failure-Type Servers, each node is attended by unreliable servers (i.e., servers subject to failures that are non-deterministic in both occurrence and duration). Some models assume operational failures (i.e., a server can only fail when working on a job). Others assume that the failures are time-dependent only and independent from the state of the server. This class of models can be further divided into two subclasses according to the assumptions imposed on the service times: deterministic processing times and random processing times. A common assumption to all the models surveyed is that the last node server(s) is never blocked. All models assumes a single job class and, unless otherwise mentioned, it is assumed that a single server that operates according to the first-come-first-served queueing discipline is in attendance at each node. Operational failures are specifically mentioned in the model description, while failure type is not mentioned for time-dependent failures. The papers in each class are presented in historical order.