Discrete-Time Geo/G/2 Queue under a Serial and Parallel Queue Disciplines

This article discusses the steady state analysis of a heterogeneous server queuing system called the Geo/G/2 queue. We supposed that arrivals occur according to a geometric process to receive ser- vice on server-1 according to a geometric service time distribution with mean rate μ or on server-2 accord- ing to a general distribution B(t) with mean rate μ2. There are two queue disciplines employed for service namely; the serial queue discipline (queue discipline- I) and the parallel queue discipline (queue discipline- II). Using the embedded method when the discipline is serial and the supplementary variable technique when it is parallel, we present an exact analysis of the arrival distribution. Furthermore, the actual waiting time expectations are derived and approximated. Our analysis can be applied in managing service systems in many areas of communication, telecommunications, business and computer systems where services are dis- crete in nature for instance, in the performance evalu- ation and design of buffers for statistical multiplexers, traffic concentrators, switch modules, networks.