Random \(N\)-policy Geo/G/1 queue with startup and closedown times (Q1952941)

Summary: This study investigates a random \(N\)-policy Geo/G/1 queue with startup and closedown times. \(N\) is newly determined every time a new cycle begins. When random \(N\) customers are accumulated, the server is immediately turned on but is temporarily unavailable to the waiting customers. It needs a startup time before starting providing service. After all customers in the system are served exhaustively, the server is shut down by a closedown time. Using the generating function and supplementary variable technique, analytic solutions of system size, lengths of state periods, and sojourn time are derived.