*Article* **The** *Geo***/***Ga***,***Y***/1/***N* **Queue Revisited**

**Mohan Chaudhry 1 and Veena Goswami 2,\***


**\*** Correspondence: veena@kiit.ac.in

**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*,*<sup>Y</sup>*/1/*<sup>N</sup>* 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*,*<sup>Y</sup>*/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

**MSC:** 60K25; 68M20; 90B22
