The random N-policy

A vacation queueing system, where the server idles until a random number N of customers accumulates in a queue is investigated. Following the arrival of the N-th customer, the server serves exhaustively the queue and then a new idling period commences. The vacation queuing system is a generalization of the conventional N-policy queue with N a constant number. The steady state distribution of the queue size and the waiting time of a customer are derived in transform forms for both the FIFO and LIFO service disciplines