Open tandem networks with blocking analysis – two approaches

The paper describes an analytical study of open twonode (tandem) network models with blocking. Here, a specific tandem configuration is chosen: the first node is treated as an infinite server (IS - often referred to as the ample-server), meaning that any incoming task can find at least one empty line for service in this node, and the second node has several parallel lines that can serve input task streams simultaneously. Between these two nodes there is a buffer with finite capacity. In this type of network, if the buffer is full, the accumulation of new tasks by the second node is temporarily suspended (blocking factor) and tasks must wait at the first node until the transmission process is resumed. In this paper, the two-node model is investigated using two different methods. The first is the multi-step exact algorithm, involving a numerical part for solving a set of linear equations, and the second is an approximate algorithm using a product form solution. The numerical part is used for solving a system of linear equations and for calculating the state probability vector. Finally, after comparing both algorithms, some recommendations as to when each method can be used are given.