In a real-time distributed transactional system, customers generate transactions, which should be executed on different servers. Transactions are scheduled according to EDF discipline. To get the global view of the system, the consensus algorithm has been considered. In this paper, a mathematical model is developed to obtain the average stay time of a transaction within the system. This model introduces a bulk arrival M/G/1 station with K classes of customers where bulks are considered according to FIFO discipline, customers are scheduled according to EDF within a group. and the algorithm operating is taken into account according to the Head Of Line discipline The response time distribution is also computed. This has allowed us to determine the optimal minimal interconsensus for a given consensus duration, the deadline miss probability and the minimum value to attribute to a transaction deadline in order to guarantee a given probability that the transaction does not miss its deadline.