Abstract <p>A single-channel queueing system with a Poisson incoming flow, general distribution of the service, infinite number of places in the queue, and vacations of the servicing device is considered in the report. During vacations, a server cannot service requests. The server can go on vacation both at the moments when the system is idle and at the moments of completion of service of requests. The main result, which will be presented during the report, is the distribution of the number of requests in the system in a non-stationary mode for some distributions of the device’s departure for vacation.</p>