| This dissertation generalizes a popular class of single-server bulk-input-batch-service queues, with (N,r)-hysteretic control, gated service, and with or without multiple vacation policy. The gated service applies to a two-stage service policy, which lets new arriving customers choose to join the service batch during the first stage, not in excess of server capacity (R), and which “locks up the gate” during the second stage of service unconditionally. (N,r)-hysteresis refers to the combination of r-quorum and N-policy, i.e. the server stops processing customers when the queue length drops below r ≤ R and stays idle (case without vacation policy) or leaves the system for a multiple vacation sequence (case with multiple vacation policy); service is resumed upon respectively one of customers' arrival or one of server's returns from a vacation trip, if the queue accumulates to at least N customers.; The discrete and continuous time parameter queueing processes are analyzed by means of semi-regenerative techniques, along with the recently established results on functionals of a marked Poisson process observed by a renewal process. The latter results are proved in this dissertation. The steady state distribution is obtained in a closed analytical form. Other results and special cases include performance measures, conservation equation and busy period distribution. |
