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This paper considers a Markov decision model for profit maximization of a cloud computing service provider catering to customers submitting jobs with firm real-time random deadlines. Customers are charged on a per-job basis, receiving a full refund if deadlines are missed. The service provider leases computing resources from an infrastructure provider in a two-tier scheme: long-term leasing of basic infrastructure, consisting of heterogeneous parallel service nodes, each modeled as a multi-server queue, and short-term leasing of external servers. Given the intractability of computing an optimal dynamic resource allocation and job routing policy, maximizing the long-run average profit rate, the paper addresses the design, implementation and testing of low-complexity heuristics. The policies considered are a static policy given by an optimal Bernoulli splitting, and three dynamic index policies based on different index definitions: individually optimal (IO), policy improvement (PI) and restless bandit (RB) indices. The paper shows how to implement efficiently each such policy, and presents a comprehensive empirical comparison, drawing qualitative insights on their strengths and weaknesses, and benchmarking their performance in an extensive study. (C) 2018 Elsevier Ltd. All rights reserved.