Strategic behaviour on M/M/1 retrial queue with discouragement and working vacation
摘要
This study investigates the performance of the Markovian single server retrial queue with working vacation policy. Some customers may opt not to enter the system or join the retry pool to wait for their turn if the server is occupied. If customers are unwilling to stay in the retry pool for a longer length of time, they may abandon (renege) the system. For mathematical formulation, the differential difference equations are constructed, and queue length distributions are established. By taking the customers’ discouraging behaviour into account, joining strategies have been proposed. To examine the customers’ discouraging behaviour, the joining policy based on non-cooperative strategies and cooperative strategies are suggested. The mixed equilibrium strategies are obtained by constructing the social profit function associated with reward function. The sensitivity of several parameters for various performance indices are examined. Using the particle swarm optimization technique, the optimal decision parameters and respective minimum cost are determined by taking numerical example.