Large language models (LLMs) have revolutionized natural language processing, yet their high computational demands pose significant challenges for real-time inference, especially in multi-user server speculative decoding and resource-constrained environments. Speculative decoding has emerged as a promising technique to accelerate LLM inference by using lightweight draft models to generate candidate tokens, which are subsequently verified by a larger, more accurate model. However, ensuring both high goodput (the effective rate of accepted tokens) and fairness across multiple draft servers cooperating with a central verification server remains an open challenge. This paper introduces GOODSPEED, a novel distributed inference framework that optimizes goodput through adaptive speculative decoding. GOODSPEED employs a central verification server that coordinates a set of heterogeneous draft servers, each running a small language model to generate speculative tokens. To manage resource allocation effectively, GOODSPEED incorporates a gradient scheduling algorithm that dynamically assigns token verification tasks, maximizing a logarithmic utility function to ensure proportional fairness across servers. By processing speculative outputs from all draft servers in parallel, the framework enables efficient collaboration between the verification server and distributed draft generators, streamlining both latency and throughput. Through rigorous fluid sample path analysis, we show that GOODSPEED converges to the optimal goodput allocation in steady-state conditions and maintains near-optimal performance with provably bounded error under dynamic workloads. These results demonstrate that GOODSPEED provides a scalable, fair and efficient solution for multi-server speculative decoding in distributed LLM inference systems.