Performance of a Single Server Queue Supported by an Intermittent Server

International audienceThis chapter concerns the situation of a queue with one regular single server supported by an additional intermittent server who, in order to decrease the mean response time, i) leaves the back office to join the first server when the number of customers reaches the threshold K, ii) leaves the front office when he has no more customers to serve. This study produces a closed form solution for the steady state probability distribution and for different metrics such as expected response times for customers or expectation of busy periods. Then, for a given value of K, the influence of the intermittent server on the response time is exhibited. The consequences on the primary task of the intermittent server are investigated through metrics such as mean working and pseudo-idle periods. Finally, a cost function is proposed from which an optimal value of the threshold K is obtained