Transient analysis of two heterogeneous servers queueing system with differentiated vacations subject to system disaster, server repair

This research paper examines the dynamic behavior of a heterogeneous two-server queuing model that incorporates differentiated vacation periods. Additionally, the model accounts for the possibility of a disaster occurring during busy periods and vacations, with immediate initiation of the repair process. The motivation for this study stems from the two types of power-saving mechanisms found in IEEE 802.16E. The paper presents explicit expressions, obtained using generating functions, for the time-dependent probabilities of system size, expressed in terms of modified Bessel functions. To further validate the theoretical findings, numerical illustrations have been included.