A Complete Time Geo/G/1 Retrial Queue Analyzation with a Second Optional Service Available

Abstract

A discrete time Geo/G/1 retrial queuing model with a single vacation and a second discretionary service was covered in this work. In this paradigm, every client receives comprehensive primary vital service from the system, and those who visit during peak hours stop being persistent. A small percentage of clients want a second optional service once first one is finished. Additionally, the system has an idle of unsystematic distance. After this vacation, the server only begins to function if a customer is present; otherwise, it remains idle until at least one customer is present. While service and vacation periods are generally dispersed, arrival times are geometrically distributed in this approach. By creating function technique we obtain PGF and also we derived an analytical expression for mean queue length.