Sasaki, et al published results in 1995 on naturally mated queens four months after mating.  They concluded that sperm was well mixed in the spermatheca based on DNA fingerprinting worker larva.  They showed that sperm from several males were typically used for eggs laid each day and also that sperm from the same male was used at least a month apart.  In one case seven consecutive eggs were fertilized by sperm from seven different drones.
https://www.researchgate.net/publication/259078669_Sperm_Utilization_by_Honey_Bee_Queens_DNA_Fingerprinting_Analysis 

Frank, et  al report their results in 1999 on use of microsatellite marker identification of paternity in naturally mated queens.  I will quote the abstract: "Five microsatellite loci were used to determine paternities in six Apis mellifera colonies headed by naturally mated queens. The last inseminating males were identified by collecting and genotyping the mating sign left in the genital tract of each queen. Significant differences in paternity frequencies were observed between males, but the proportion of worker and queen offspring sired by the last inseminating drone did not differ significantly from those of other drones. Each male kept his rank of precedence for the different cohorts, although the variance in subfamily proportions decreased over time, most notably in the colony displaying the lowest level of polyandry. These results suggest that, if sperm competition exists in the honeybee, it does not significantly increase the fitness of the last inseminating drone. The spermatozoa of the different inseminating drones are not totally mixed before they reach the spermatheca, in particular when only few males mate with the queen."
https://www.sciencedirect.com/science/article/abs/pii/S0003347202930782  

Both of these papers show sperm is stored in a random, well mixed manner in the spermatheca for naturally mated queens.  Both of these papers are old enough that the methods used are pretty archaic by today's standards althou very good at the time of publication. So, it might be good if someone repeated these studies using a more reasonable number of markers.  More like say something well over 1000 instead of single digits or low double digits.  Unfortunately the Frank paper is behind a paywall so I do not know the experimental details.
Dick

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