Random access coverage is assured while at the same time supporting high uplink data rates in a same service area served by a base station. A set of radio resources are shared by multiple mobile terminals for transmitting uplink to the base station including requests for access to service from the base station and transmissions for active connections with the base station. A first repeating time period and a second different repeating time period are defined. Uplink transmission grants are scheduled for active connections that permit use of a greater amount of the radio resources during the first repeating time period. Uplink transmission grants are also scheduled for active connections that permit use of a smaller amount of those resources during the second repeating time period. At least some random access requests to the base station are controlled to occur only during the second repeating time period.