Discrete-time limited 1-slot G/G/1 vacation queues and asymmetric polling systems

We study the discrete-time limited 1-slot G/G/1 vacation queueing models and asymmetric polling systems. We assume that the time is slotted and the switchover time is nonzero. The switchover time and the customer service time are functions of integral multiples of the slot size. The number of arrivals at each station is independently and generally distributed. The probability generation functions (PGFs) of the queue length and the waiting time distributions are explicitly derived. The closed form formulas of the mean queue length and the mean waiting time are obtained as well