This paper proposed a new system of two-class priority polling based on multi-times gated service policy. A queuing model of the polling system is constructed

in which the number of waiting customers in each site is set together as random variables of the system state. Moreover

iterative equations are set up by taking second-order partial derivatives of the generating function

and then the integral mathematical analytical expressions of the key indexes are derived via simultaneous solution

concerning the mean queue length

the mean waiting time of the key queue and common queues

and the mean polling period time of the server. Finally

computer simulations are conducted on the system and it is found that theoretical and simulation results are identical. The analysis shows that this new polling system satisfies the demand of service diversity and flexible service in the process of resource allocation in a periodic system

and demonstrates that the polling control protocol has wider applications.