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This paper brings out relations among the moments of various orders of the waiting time of the 1st customer and a randomly selected customer of an arrival group for bulk arrivals queueing models, and as well as moments of the waiting time (in queue) for M/G/1 queueing system. A numerical study of these relations has been developed in order to find the (β1,β2) measures of waiting time distribution in a comutable form. On the basis of these measures one can look into the nature of waiting time distribution of bulk arrival queues and the single server M/G/1 queue.