Waiting time of M/D1,∞/1 queue

In this paper, we consider a single-server infinite capacity queue with Poisson arrival. The server takes all waiting customers as a batch into service, and the service time of the kth customer in a batch is a + b × k, where a and b are the set-up time and the individual service time for each customer, respectively. The steady-state mean and variance of waiting time of an arbitrary customer are obtained. Simulation results confirm our analysis.