Before revision:  Since (n, k) fork-join queues are prevalent in modern popular distributed systems such as Cassandra, MapReduce and Spark ,  estimating the sojourn time of such queues is  critical for the performance measurement and resource plan of these systems .
After revision:  Since (n, k) fork-join queues are prevalent in modern popular distributed systems such as Cassandra, MapReduce and Spark , estimating the sojourn time of such queues is thus critical for the performance measurement and resource plan of these systems .