Triggered batch movement in queueing networks
One considers both in discrete and continuous time a network consisting of \(N\) nodes, each of them is associated with a queue of customers (negative queue lengths are also allowed). There is an external source (labelled node 0) representing the outside of the network. Customers enter the network by being emitted from node 0 and leave by being absorbed by node 0. State changes of the network occur by batches of customers represented by the nonnegative vector \(a = (a_1, a_2, \dots, a_N)\) being released/served from the \(N\) queues of the network, a second batch \(a'\) may (or may not) be released by being ``triggered'' by \(a\), and, if it is, a third batch \(a''\) is deposited. It is shown that a product form equilibrium distribution holds; a telecommunication network example presents a possible application of the described system.
scientific article; zbMATH DE number 851507
scientific article