Transient behaviour of three-heterogeneous servers queue with system disaster and server repair

Three-heterogeneous servers queue with system disaster, server failure and repair is investigated. The arrival of customers follows Poisson process and service time is exponentially distributed. Explicit expressions are derived for the transient-state probabilities using generating function, modified Bessel function and Laplace transform. Further, the steady-state system size probabilities are deduced and certain important performance measures are acquired. Finally, numerical interpretations are presented to depict the system behaviour