A scheduler in accord with the invention schedules available bit rate (ABR) traffic over an asynchronous transfer mode (ATM) link in such a manner as to provide circuits having the ABR traffic service a minimum cell rate (MCR) that may be greater than zero. The scheduler uses static scheduling information to schedule traffic for high priority services, such as constant bit rate service. The static information also specifies transmit opportunities for an ABR circuit, in a manner analogous to that for CBR traffic. The statically scheduled transmit opportunities provide a negotiated minimum cell rate that is greater than zero, for the ABR circuit. The scheduler maintains dynamic scheduling information, which it uses to schedule traffic in otherwise available transmit times. For example, the scheduler may use the dynamic information to create a work list of virtual circuit connections for ABR service. During any cell transmit time that is not used by a higher priority service (e.g. CBR or MCR), the scheduler goes to the work list to find a circuit with a cell ready for transmission and initiates transmission of the cell for that circuit. The ABR circuit having a non-zero MCR receives service from the statically scheduled opportunities and from the dynamically scheduled opportunities.