Analysis of a Batch Arrival Retrial Queue with Two-Phase Services, Feedback and Admission

Today, real-world problems modeling is the first step in controlling, analyzing, and optimizing them. One of the applied techniques for modeling some of these prob-lems is the queueing theory. Usually, the conditions such as lack of space, feedback, admission limits, etc. are the inseparable parts of these problems. This paper deals with modeling and analyzing the steady-state behavior of an MX∕G∕1 retrial queue-ing system with two phases of heterogeneous services and general retrial time. The arriving batches join the system with dependent admission due to the server state. If the customers find the server busy, they join the orbit to repeat their request. Although, the first phase of service is essential for all customers, any customer has three options after the completion of the i-th phase (i = 1, 2) . They may take the (i + 1)-th phase of service with probability θi , otherwise, return the orbit with prob-ability pi˜1 − 𝜃i° or leave the system with probability ˜1 − pi°˜1 − 𝜃i° . In this paper, after finding the steady-state distributions and the probability generating functions of the system and orbit size, some important performance measures are found. Then, the sensitivity analysis of performance measures and cost rate is done concerning arrival/retrial rates, feedback probabilities, and state-dependent admission in a tel-ecommunication system.