It is increasingly being recognized that a large pool of High Performance Computing (HPC) users requires interactive, on-demand access to HPC resources. How to provide these resources is a significant technical challenge that can be addressed from two directions. The first approach is to adapt existing batch queue based HPC systems to make them more interactive. The second approach is to start with existing interactive desktop environments (e.g., MATLAB®) and design a system from the ground up that allows interactive parallel computing. The Lincoln Laboratory Grid (LLGrid) project has taken the latter approach. The LLGrid system has been operational for over a year with a few hundred processors and roughly 70 users, having run over 13,000 interactive jobs and consumed approximately 10,000 processor days of computation. This paper compares the on-demand and interactive computing features of four prominent batch queuing systems: openPBS, Sun GridEngine, Condor, and LSF. It goes on to briefly describe the LLGrid system, and how interactive, on-demand computing was achieved on it by binding to a resource management system. Finally, usage characteristics of the LLGrid system are discussed.