Discrete time queues and matrix-analytic methods. (With comments and rejoinder) (Q1871416)

The paper is expository dealing with discrete time analysis of queues using matrix-analytic methods. In the present moment, there are many practical situations (e.g. telecommunication systems) based more on digital technology than analog one. On the other hand, sometimes it is easier to study discrete time analysis than continuous one, however, the paper provides both the advantages and disadvantages of discrete time analysis. The paper presents several queueing systems as discrete time quasi-birth-death processes and then shows how to use matrix-geometric method which in many situations gives much simpler approach. Finally, the paper is accompanied by discussions given by J. Garcia-Vidal, A. Gómez-Corral, W. K. Grassmann, Qi-Ming He, Wei Li, B. Van Houdt, Quiang Ye.