Abstract
An important property of most infinite server systems is that customers are independent of each other once they enter the system. Though this non-interacting property (NIP) has been instrumental in facilitating excellent results for infinite server systems in the past, the utility of this property has not been fully exploited or even fully recognized. This paper exploits theNIP by investigating a general infinite server system with batch arrivals following a Markov renewal input process. The batch sizes and service times depend on the customer types which are regulated by the Markov renewal process. By conditional approaches, analytical results are obtained for the generating functions and binomial moments of both the continuous time system size and pre-arrival system size. These results extend the previous results on infinite server queues significantly.
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Liu, L., Templeton, J.G.C. TheGr X n/G n/∞ system: System size. Queueing Syst 8, 323–356 (1991). https://doi.org/10.1007/BF02412259
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DOI: https://doi.org/10.1007/BF02412259