Optimal and Sensitivity Analysis of Vacation Queueing System withF-Policy and Vacation Interruption

In this article, the investigation on a randomized arrival control policy for the prospective customers in the finite capacity queueing system with working vacation and vacation interruption is done. The impatience behavior of the customers is also considered in modeling and assumptions to the studied problem to make it more realistic. In the investigated queueing model, at the epoch when the number of customers in the system reaches system's capacity, newly arriving customers are not allowed to join the system for service and referred as lost customers. As the length of the queue decreases to a pre-specified threshold valueF, the server commences a start-up for allowing to join the customers according to an exponential distribution and starts allowing newly arriving customers to join the system for service. The steady-state probability distribution and vector representation of various system performance measures are derived using matrix-analytic approach. The cost optimization problem is also formulated, and the particle swarm optimization algorithm is implemented to determine the optimal decision parameters to achieve the minimal expected cost. Finally, some numerical results in tables and graphs are provided for the illustrative and comparative purpose which help the system analyst in decision making from the performance and economic perspective.