Quality of service (QoS) has been receiving wide attention in recent years in many research communities including networking, multimedia systems, real-time systems and distributed systems. In large distributed systems such as those used in defense systems, on-demand service and inter-networked systems, applications contending for system resources must satisfy timing, reliability and security constraints as well as user-perceived quality requirements. Allocating sufficient resources to different applications in order to satisfy various requirements is a fundamental problem in these situations. A basic yet flexible model for performance-driven resource allocations can therefore be useful in making appropriate tradeoffs. In this paper, we present an analytical model for QoS management in systems which must satisfy application needs along multiple dimensions such as timeliness, reliable delivery schemes, cryptographic security and data quality. We refer to this model as Q-RAM (QoS-based Resource Allocation Model). The model assumes a system with multiple concurrent applications, each of which can operate at different levels of quality based on the system resources available to it. Each application, in turn, may also need access to multiple resource types at each operating point of allocated resources. The goal of the framework is to allocate the resources to the various applications such that the overall system utility is maximized under the constraint that each application can meet its minimum needs. We identify resource profiles of applications which allow such decisions to be made efficiently and in real-time. We also identify application utility functions along different dimensions which are composable to form unique application requirement profiles. The resource allocation schemes sometimes lead to results that are not intuitive.