Discrete-time bulk-service queue with two heterogeneous servers

This paper analyzes a discrete-time bulk-service queueing system with two heterogeneous servers, i.e., two batch servers working with different service rates. The interarrival times of customers and service times of batches are assumed to be independent and geometrically distributed. Applications can be found in a wide variety of real systems including servers formed with different types of processors as a consequence of system updates, nodes in telecommunications network with links of different capacities, nodes in wireless systems serving different mobile users. We obtain closed-form expressions for the steady-state probabilities at arbitrary epoch with the help of displacement operator method and derive the outside observer’s observation epoch probabilities and waiting time distribution measured in slots. Computational experiences with a variety of numerical results in the form of tables and graphs are discussed. Moreover, some queueing models discussed in the literature are derived as special cases of our model. Finally, it is shown that in the limiting case the results obtained in this paper tend to the continuous-time counterpart.