Analysis of synchronous vacation retrial queue with non-preemptive customers

This paper deals with a retrial queue with non-preemptive customers and synchronous vacation. Customers arrive in the system, among which non-preemptive customers do not form any queue. If a customer in the first class discovers that there are no available servers, he will be dropped directly from the system without receiving service. A customer in the second class who is unable to receive service immediately may or may not wait for a period and retry his luck. Servers follow a vacation policy: some of the servers will go on vacation at the same time when they become idle, while the service is completed and system conditions satisfy the management policy. The matrix-geometric method is applied to calculate the stationary distribution. Some system performance measures are established to help determine the efficiency of the presented non-preemptive priority retrial queue. Numerical examples illustrate the influence of system parameters on some performance measures. Finally, the optimization problem is constructed to help the manager make decisions.