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Service rate is an important, recently introduced, performance metricassociated with distributed coded storage systems. Among other interpretations,it measures the number of users that can be simultaneously served by thestorage system. We introduce a geometric approach to address this problem. Oneof the most significant advantages of this approach over the existingapproaches is that it allows one to derive bounds on the service rate of a codewithout explicitly knowing the list of all possible recovery sets. Toillustrate the power of our geometric approach, we derive upper bounds on theservice rates of the first order Reed-Muller codes and simplex codes. Then, weshow how these upper bounds can be achieved. Furthermore, utilizing theproposed geometric technique, we show that given the service rate region of acode, a lower bound on the minimum distance of the code can be obtained.

A Geometric View of the Service Rates of Codes Problem and its Application to the Service Rate of the First Order Reed-Muller Codes