A tutorial on some new methods for performance evaluation of queueing networks

In the 1970´s, Baskett, Chandy, Muntz and Palacios, Kelly, and others, generalized the earlier results of Jackson (1957) and obtained explicit solutions for the steady-state distributions of some restricted queueing networks. These queueing networks are called “product-form networks,” due to the structure of their explicit solutions. The class of such tractable networks is quite small, however. For example, if customers require different mean service times on different revisits to the same server, or if customers on a later visit are given higher priority, then very little is known concerning whether the network is even stable or what form the steady-state distribution has if it exists. Recently, some new methods have been developed for establishing the stability of a system and for obtaining bounds on key performance measures such as mean delay, mean number in system, or mean throughput. Since they are based on the well-developed computational tool of linear programming, these methods can be widely employed in diverse applications in communication networks, computer systems, and manufacturing systems. We provide a tutorial exposition of some of these recent developments