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In a G/GI/c loss system with balking, reneging, or limited waiting space, deleting some of the arriving customers can either increase or decrease the fraction of the remaining arrivals who get served, depending on how customers are deleted. We present a model in which the random deletion of arrivals independently and with some fixed probability can never decrease the fraction of the remaining arrivals who get served.doi:10.1017/s0021900200002552 fatcat:scktoxtw4ze2tnn4w5enppz32i