The <i>Geo</i>/<i>G</i>^{<i>a</i>,<i>Y</i>}/1/<i>N</i> Queue Revisited

Abstract

We not only present an alternative and simpler approach to find steady-state distributions of the number of jobs for the finite-space queueing model Geo/Ga,Y/1/N using roots of the inherent characteristic equation, but also correct errors in some published papers. The server has a random service capacity Y, and it processes the jobs only when the number of jobs in the system is at least ‘a’, a threshold value. The main advantage of this alternative process is that it gives a unified approach in dealing with both finite- and infinite-buffer systems. The queue-length distribution is obtained both at departure and random epochs. We derive the relation between the discrete-time Geo/Ga,Y/1/N queue and its continuous-time analogue. Finally, we deal with performance measures and numerical results.

Keywords

• batch service
• roots
• discrete-time queue
• discrete renewal theory
• finite buffer capacity