Single server unreliable queueing model with removable service station

This investigation deals with a single server queueing model with a removable service station under steady‐state conditions. The server is in a controllable position, i.e., the organiser can turn the single server on at any arrival epoch or turn off at any service completion. The number of arrivals follows a Poisson process and the service time follows an exponential distribution. The arrival rates of the customers depend on the various states of the system at any time t. The transient analysis for the queue size distribution has been provided by solving a set of governing equations characterising the model in terms of Laplace transform of state probabilities. Several system characteristics are evaluated by using queue size distribution.