Abstract
We study the infinite-server system with batch arrivals ands different types of customers. With probabilityp i an arriving customer is of typei (i=1,..., s) and requires an exponentially distributed service time with parameterμ i (G GI/M 1 ...M s /∞). For theGI GI/M 1...M s /∞ system it is shown that the binomial moments of thes-variate distribution of the number of type-i customers in the system at batch arrival epochs are determined by a recurrence relation and, in steady state, can be computed recursively. Furthermore, forG GI/M 1...M s /∞, relations between the distributions (and their binomial moments) of the system size vector at batch arrival and random epochs are given. Thus, earlier results by Takács [14], Gastwirth [9], Holman et al. [11], Brandt et al. [3] and Franken [6] are generalized.
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Brandt, A. On the gi/m/∞ service system with batch arrivals and different types of service distributions. Queueing Syst 4, 351–365 (1989). https://doi.org/10.1007/BF01159473
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DOI: https://doi.org/10.1007/BF01159473