Random N-Policy GeoG1 Queue with Startup and Closedown Times

Abstract EN

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.