Taylor series solution of a single server queueing model with feedback

In multi-access systems, scheduling mechanism often require a proper feedback policy. In this article, we compute transient state probabilities of the classical single server Markovian queueing system with feedback. The method demonstrated in present study involves direct and practical steps for deriving explicit expression for queue size distribution. The present method avoids involvement of any special function (e.g., Bessel function), transformation (e.g., Laplace transform) or/and complex analysis. The resulting Taylor series for queue size distribution are proved to converge for all time under arbitrary initial condition. This approach is easy to understand and to extend for a more advanced queueing system otherwise another solution technique is very complicated when compared to this technique. For example, if we use Laplace technique then Rouch theorem will be used to find the roots and it is very difficult to obtain the roots by using any other method.