This paper discusses a two-state multiserver retrial queueing system with balking. Entering customer is admitted to join any idle server and receive his service immediately. On the other hand, if all the servers are busy, then the entering customer joins the orbit or balks from the system. Arrival of primary calls and repetition of repeating calls both follow Poisson distribution. Service times of each server follow exponential distribution. By solving the difference-differential equations recursively, we obtained transient probabilities of exact number of arrivals and exact number of departures at when all some or none servers are busy. Results for particular cases are also discussed.

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Objective: In this study we consider a two-state retrial queueing system with feedback having two identical parallel servers. Transient state probabilities for exact number of arrivals and departures from the system will be obtained when both, one or none of the servers is busy. Numerical and graphical solutions will also be obtained. Methods: The difference-differential equations governing the system are solved recursively, Laplace transform is then used to obtain the transient state probabilities for exact number of arrivals and departures from the system. Findings: Time dependent probabilities are obtained when both, one and none of the servers is busy. Numerical and Graphical solutions are also obtained using MATLAB programming. Novelty: In past research, models considered arrivals and departures from the orbit whereas in present model arrivals and departures from the system are studied along with the concept of feedback. Applications: This type of model is implemented in computer systems.

Objective: This study discusses a two-state multiserver retrial queueing system, where the customer may leave the system due to impatience. In this paper, we deal with the time dependent probabilities when all, some or none servers are busy. Method: For this model, we solved difference differential equations recursively and obtained the time dependent probabilities when all, some or none servers are busy. Findings: Time dependent probabilities of exact number of arrivals and exact number of departures at when all, some or none servers are busy are obtained. In this paper, some kind of verification and converting two state model into single state model are discussed. Some special cases of interest are also discussed. Novelty: In communication networks, multiple servers are used to reduce traffic congestion and improve system performance. The operation mode of a call center with repeated attempts provides an initial motivation for our study.