Steady state behavior of multiple variant hiatus queues with a waiting server at each stage

This paper considers an infinite buffer single server Markovian queueing system with multiple variant hiatus (vacation) policy. After every busy period ends, the server remains wait in the system to new arrival customers for a random period of time. If no arrival occurs in this waiting time, the server takes a vacation. After completion of the vacation, if any customers waiting in the system the server immediately starts the service process. Otherwise, the server remains wait in the system to new arrival customers for a random period of time. If no arrival occurs in this waiting time, the server proceeds to another vacation. The server continues this policy till the server takes the maximum number of J (a pre-determined threshold value) vacations. After completing maximum number of random vacations, the server stays dormant in the system and waits for the new customers. Steady state analysis of the model is carried out by using a probability generating function approach. The stability condition of the model and stochastic decomposition results are discussed. Moreover, the optimality of the cost model is numerically derived by using particle swarm optimization and Newton–Raphson method. A comparative analysis is also done between these two techniques. Numerical illustrations are included to study the influence of system parameters on some important performance measures of the queueing model. Finally, we present some managerial insights.