ssume there are two priority classes for a queuing system. In addition, assume that customers

in the first priority class arrive at a Poisson rate of $\backslash$lambda $,$ while customers in the second priority class

arrive at a Poisson rate of $\backslash$mu $.$ Assume the arrival processes are independent of each other. Prove

that the overall arrival process $($the arrival of customers without respect to their priority$)$ is a

Poisson process with arrival rate $\backslash$lambda $+\backslash$mu