Modeling inference workloads for transformer-based neural networks poses unique challenges due to their dynamic memory footprints, head-of-line blocking caused by heavy-tailed request distributions, and memory-dependent preemption overhead arising from the need to load/unload cache state. In this paper, we introduce a new queuing model that captures the impacts of these features on system stability and scheduling design. We show that the Gittins-index policy, which minimizes mean response time in the standard M/G/1 setting, can incur substantial preemption overhead in our model. Motivated by this limitation, we propose the Multi-Level-Priority-Threshold (MLPT) policy, that limits preemption while preserving priority for short jobs. We characterize the mean response time under MLPT and provide empirical rules-of-thumb to solve the resulting threshold-optimization problem. Our key observation is that optimal scheduling is a balance between reducing the response times of shorter jobs and limiting the overhead incurred when preemption occurs. These results provide a theoretical framework for understanding scheduling in memory constrained queuing systems for inference tasks.

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