The persistent accumulation of unresolved legal cases, especially within the Indian judiciary, significantly hampers the timely delivery of justice. Manual methods of prioritizing petitions are often prone to inefficiencies and subjective biases further exacerbating delays. To address this issue, we propose LLMPR (Large Language Model-based Petition Ranking), an automated framework that utilizes transfer learning and machine learning to assign priority rankings to legal petitions based on their contextual urgency. Leveraging the ILDC dataset comprising 7,593 annotated petitions, we process unstructured legal text and extract features through various embedding techniques, including DistilBERT, LegalBERT, and MiniLM. These textual embeddings are combined with quantitative indicators such as gap days, rank scores, and word counts to train multiple machine learning models, including Random Forest, Decision Tree, XGBoost, LightGBM, and CatBoost. Our experiments demonstrate that Random Forest and Decision Tree models yield superior performance, with accuracy exceeding 99% and a Spearman rank correlation of 0.99. Notably, models using only numerical features achieve nearly optimal ranking results (R2 = 0.988, \r{ho} = 0.998), while LLM-based embeddings offer only marginal gains. These findings suggest that automated petition ranking can effectively streamline judicial workflows, reduce case backlog, and improve fairness in legal prioritization.