Approximation in non-product form finite capacity queue systems

In this paper a class of finite length Markovian queueing models is studied that, in general, does not exhibit a product form solution. Good approximations can be derived for the marginal queue size distributions in this case, and hence measures such as the average response time can be calculated. However, because no product form exists, expressions for the joint queue size distribution are much more costly to derive, hence many performance measures of interest cannot be easily computed. An approximation for the joint queue size distributions is explored here, which improves on a naive product form assumption by considering various boundary cases. The approximations are explored numerically by example.