Comments on duality of queues with finite buffer size (Q1317020)

The issue of duality of queues has been studied by several authors, however, only for the infinite-buffer case. For finite buffer queueing systems, the developed duality principles are less useful. Therefore the concept of quasi-duality is introduced. Quasi-duality is defined, rather informally, in such a way that the \(G1/G2/1/K\) and the \(G2/G1/1/K\) queueing systems are quasi-dual, if the role of customers and non- customers, i.e., empty buffer spots, are reversed. Important to note here is that the above two queueing systems are not ``normal'' duals; they only behave the same if they are neither empty nor totally full. For some specific cases, i.e. the \(M/M/1/K\), the \(E2/M/1/K\) and the \(M/D/1/K\) queueing systems, the quasi-duals are discussed.