Queueing Systems With Random Volume Internal and External Calls

In the present paper we investigate a single-server BM/.G/1 /∞ queuing system with non-homogeneous calls of two following types: 1) external calls served by the system under consideration, 2) internal calls arrive only when an external call is served and interrupt the service process. The external calls appear according to a stationary Poisson process with bulk arrivals. Calls of each from above-mentioned types are characterized by some random volume. Service time of the call arbitrarily depends on its volume. Two schemes of calls service organization are analyzed. The non-stationary and stationary total calls volume distribution is determined in terms of Laplace and Laplace-Stieltjes transforms. The stationary first moment of total calls volume distribution is calculated for each scheme.