A method of controlling access to a wireless Access Network "AN" by a wireless communication device (23, 31, 41), the method comprising the steps of: storing in a non-transitory memory in the wireless communication device (23, 31, 41), a Device Access Priority "DAP" level based on characteristics of the wireless communication device; when the wireless communication device has data to send, receiving by a radio receiver in the wireless communication device, a message from the AN containing a Network Access Priority "NAP" parameter, which defines a minimum priority level that the wireless communication device must meet to be allowed to initiate network access; determining by a processor in the wireless communication device, whether the stored DAP level is equal to or greater than the NAP parameter received from the AN; when the stored DAP level is determined to be less than the NAP parameter received from the AN, periodically repeating the receiving and determining steps until the stored DAP level is determined to be equal to or greater than the NAP parameter received from the AN; and when the stored DAP level is determined to be equal to or greater than the NAP parameter received from the AN, initiating network access by the wireless communication device, wherein the step of initiating network access by the wireless communication device includes the steps of: performing a Persistence Test in which the processor generates a random persistence value and determines that the device passed the Persistence Test when the generated random persistence value is equal to or larger than a persistence value assigned by the AN; and when the wireless communication device passes the Persistence Test, transmitting on an access channel by a radio transmitter in the wireless communication device, the data the device has to send storing in a non-transitory memory in the wireless communication device (23, 31, 41), a Device Access Priority "DAP" level based on characteristics of the wireless communication device; when the wireless communication device has data to send, receiving by a radio receiver in the wireless communication device, a message from the AN containing a Network Access Priority "NAP" parameter, which defines a minimum priority level that the wireless communication device must meet to be allowed to initiate network access; determining by a processor in the wireless communication device, whether the stored DAP level is equal to or greater than the NAP parameter received from the AN; when the stored DAP level is determined to be less than the NAP parameter received from the AN, periodically repeating the receiving and determining steps until the stored DAP level is determined to be equal to or greater than the NAP parameter received from the AN; and when the stored DAP level is determined to be equal to or greater than the NAP parameter received from the AN, initiating network access by the wireless communication device, wherein the step of initiating network access by the wireless communication device includes the steps of: performing a Persistence Test in which the processor generates a random persistence value and determines that the device passed the Persistence Test when the generated random persistence value is equal to or larger than a persistence value assigned by the AN; and when the wireless communication device passes the Persistence Test, transmitting on an access channel by a radio transmitter in the wireless communication device, the data the device has to send performing a Persistence Test in which the processor generates a random persistence value and determines that the device passed the Persistence Test when the generated random persistence value is equal to or larger than a persistence value assigned by the AN; and when the wireless communication device passes the Persistence Test, transmitting on an access channel by a radio transmitter in the wireless communication device, the data the device has to send