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Model parallelism is conventionally viewed as a method to scale a single large deep learning model beyond the memory limits of a single device. In this paper, we demonstrate that model parallelism can be additionally used for the statistical multiplexing of multiple devices when serving multiple models, even when a single model can fit into a single device. Our work reveals a fundamental trade-off between the overhead introduced by model parallelism and the opportunity to exploit statistical multiplexing to reduce serving latency in the presence of bursty workloads. We explore the new trade-off space and present a novel serving system, AlpaServe, that determines an efficient strategy for placing and parallelizing collections of large deep learning models across a distributed cluster. Evaluation results on production workloads show that AlpaServe can process requests at up to 10× higher rates or 6× more burstiness while staying within latency constraints for more than 99% of requests.