Consider c distinct M$/$M$/1$ queues, each with average service rate $$ and average arrival rate $\backslash$lambda $.$ Let $\backslash$rho

denote the utilization of a single server. Next, consider merging the arrivals from the c distinct M$/$M$/1$

queues into a single M$/$M$/$c queue. Let $\backslash$rho Merged denote the utilization of the resource pool of servers

in the M$/$M$/$c queue. The number $\backslash$rho Merged is less than the number $\backslash$rho $.$