A queueing model with server breakdowns, repairs, vacations, and backup server

Srinivas R. Chakravarthy, Kettering University
Shruti, Birla Institute of Technology and Science, Pilani
Rakhee Kulshrestha, Birla Institute of Technology and Science, Pilani


© 2019 The Authors Queueing models wherein having a backup server during the absences (caused by vacations and breakdowns) of the main server have found many applications in practice. Such services offered by a backup server can be viewed as the (main) server working during a vacation or during a breakdown period. A backup server offering services can be thought of as the main server working (at a reduced rate) on vacations/repairs. Using Neuts’ versatile point process for the arrivals and modeling the service times with phase type distributions, we propose a model that generalizes some of the previously published ones on working-vacation-breakdown-repair queues. We carry out the steady-state analysis and report interesting illustrative numerical examples. We also prove decomposition results for the rate matrix and the mean number in the system under some special cases.