Metaheuristic optimization and strategic behavior of Markovian vacation queue with retrial policy: application to virtual call center

This research investigation is concerned with social optimization and customers' strategic behavior for a double orbit retrial queueing model with vacation, aiming to enhance the performance of virtual call centers. In many call center scenarios, if the server is busy, the arriving customer moves to premium/ordinary orbit, i.e., becomes a repeated customer; otherwise, if the server is accessible, the arriving customer joins the system to receive the required service. Once the service is completed, the server will look into the premium orbit to check whether there is any customer who needs service. If no new customer from premium/ordinary orbit or outside arrives and the system is empty, then the server takes a vacation. The customer's decision to wait or balk from the system depends on the server's status and the reward for receiving the service. By using a probability generating function and iterative approach, the long-run probability distribution of the queue size and other metrics, viz. equilibrium thresholds, entering probability, etc., have been obtained. Moreover, the social welfare function is analyzed based on two given information levels. The optimal solution is presented by solving the social welfare maximization problem using particle swarm optimization and harmony search techniques. The impact of different parameters on the performance metrics in Virtual Call Centers (VCC) is examined.