Abstract:

We consider a single-server finite-buffer queue where the server can control a traffic signal, depending on the number of customers waiting in the queue. Hence, the server can decrease or increase the time limit of the traffic signal at each completion of the service depending on the real-time traffic density. In order to achieve this goal, we need to find the arbitrary-epoch joint distribution of the number of customers in the queue and queue length at service initiation of the customer being served at each instant. We develop relations between arbitrary and departure-epoch probabilities. We obtain Various performance measures of interest.