This article analyzes an \(M_1^X, M_2/G_1,G_2/1\) retrial queue with two-way communication under constant retrial policy. A server handles both inbound and outbound calls. The inbound calls arrive in batches according to a compound Poisson process. The server makes an outbound call that follows the Poisson process during its inactive period. The service duration of inbound and outbound calls follows two different arbitrary distributions, while retrial time follows an exponential distribution. Using the supplementary variable technique, the system of differential-difference equations is developed to directly compute the distribution of orbit length at random epoch. The execution of the waiting time distribution for an arbitrary call of an incoming batch constitutes the most challenging task in this study. We also conduct a comprehensive cost analysis to minimize the overall cost of system operation. Furthermore, a variety of performance metrics and numerical findings validate the proposed methodology.
