Fluid approximation and its convergence rate for GI/G/1 queue with vacations
The author considers a GI/G/1 queue with vacations, where vacations take place after completing the service of all customers in the buffer. If during a vacation new customers enter, they are served after the end of vacation, if not, another vacation begins. In order to establish the fluid approximation and exponential convergence rate, the approach is to identify a simple lower bound and a simple upper bound and show that both bounds converge to the same limit after fluid scaling under some assumptions. A fluid model is developed for the queue length, the busy time and the workload process. The fluid approximation turns out to be the same as that for the GI/G/1 queue. Different from the rate of convergence for the GI/G/1 queue, the exponential rate of convergence for the GI/G/1 queue with vacations holds only for large \(N\).
scientific article; zbMATH DE number 5865239
scientific article