Investigation of one class of batch service systems

Single-channels systems are considered with finite lengths and batch servicing of all requests in the queues by the time the server is switched on ($\vec{M_n}/G/1/\vec{x_n}$ systems). The service costs are independent of the number of requests in the batch. The requests arriving in the system during the service are lost. Explicit expressions are obtained for stationary probabilistic states of the system as are characteristics of service performance.