In this paper, we propose and investigate the characteristics of a fair queueing with service envelopes (FQSE) algorithm-a hierarchical fair-share scheduling algorithm for access networks based on a remote scheduling system such as Ethernet passive optical networks (EPON) or cable TV network. FQSE is designed to overcome the limiting factors of a typical remote scheduling system such as large control-plane delay, limited control-plane bandwidth, and significant queue switch-over overhead. The algorithm is based on a concept of service envelope-a function representing the fair allocation of resources based on a global network condition called satisfiability parameter (SP). We define properties of cousin-fairness and sibling-fairness and show the FQSE to be cousin-fair. FQSE is unique in that it is the only hierarchical algorithm that is simultaneously cousin-fair. Furthermore, we show the necessary techniques to adapt FQSE to variable-sized packet-based networks. We analyze FQSE performance in EPON serving 1024 independent queues and demonstrate FQSE's ability to provide guaranteed bandwidth to each queue and to share the excess bandwidth fairly.