STATIONARY QUEUE-LENGTH DISTRIBUTION IN A QUEUING SYSTEM WITH LIMITED CAPACITY, BATCH ARRIVAL, AND PHASE-TYPE SERVICE TIME

The queueing system GI/GI/1/r with batch arrival, input and service-lime distribution functions of phase type is considered. The batch size is random, but limited by the system capacity, and when it is greater than the number of unoccupied places in the queue, the remainder of the batch is lost. The matric-recurrent computational algorithm for the stationary distribution is obtained, as well as the Laplace-Stieltjes transformation of the stationary waiting-time distribution.