A class of queueing networks which consist of single-server fork-join nodes with infinite buffers is examined to derive a representation of the network dynamics in terms of max-plus algebra. For the networks, we present a common dynamic state equation which relates the departure epochs of customers from the network nodes in an explicit vector form determined by a state transition matrix. We show how the matrix may be calculated from the service time of customers in the general case, and give examples of matrices inherent in particular networks.
|Title of host publication||Proceedings of 1996 Summer Computer Simulation Conference, Portland, OR, July 21-25, 1996|
|Editors||V. W. Ingalls, J. Cynamon, A. Saylor|
|Publisher||Society for Computer Simulation International|
|Publication status||Published - 1996|
Scopus subject areas
- Management Science and Operations Research
- Algebra and Number Theory