Optimal Control of a Two-Phase Heterogeneous Service Retrial Queueing System with Collisions and Delayed Vacations

This paper proposes a novel two-phase heterogeneous service retrial queueing system with collisions and delayed vacations. We consider services for two types of customers: ordinary customers (service completed in two phases) and priority customers (service completed in one phase). Collisions only occur in the first phase of service; if the collision does not happen, the server will proceed to the second phase of service. When the server turns to an idle state, it reserves a random period before taking formal vacations. We investigate two models for this system with and without orbit constraints and numerically analyze the sensitivity of the system performance metrics to validate the results and methodology. The expected total cost function is formulated. To prevent falling into the local optimal solution too fast, we utilize the canonical particle swarm optimization algorithm. Furthermore, we evaluate a bi-objective optimization problem to seek the balance of the expected total cost and the quality of service. Then, we apply the multi-objective evolutionary algorithm based on decomposition (MOEA/D) to obtain the Pareto front. Several numerical examples are presented for illustrative purposes.