Queueing-Aware Optimization of Reasoning Tokens for Accuracy-Latency Trade-offs in LLM Servers

• URL: http://arxiv.org/abs/2601.10274v1
• Date: Thu, 15 Jan 2026 10:47:11 GMT
• Title: Queueing-Aware Optimization of Reasoning Tokens for Accuracy-Latency Trade-offs in LLM Servers
• Authors: Emre Ozbas, Melih Bastopcu,
• Abstract summary: We consider a single large language model (LLM) server that serves a heterogeneous stream of queries belonging to $N$ distinct task types.<n>For each task type, the server allocates a fixed number of internal thinking tokens, which determines the computational effort devoted to that query.<n>We formulate a constrained optimization problem that maximizes a weighted average accuracy objective penalized by the mean system time.
• Score: 4.3400407844814985
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider a single large language model (LLM) server that serves a heterogeneous stream of queries belonging to $N$ distinct task types. Queries arrive according to a Poisson process, and each type occurs with a known prior probability. For each task type, the server allocates a fixed number of internal thinking tokens, which determines the computational effort devoted to that query. The token allocation induces an accuracy-latency trade-off: the service time follows an approximately affine function of the allocated tokens, while the probability of a correct response exhibits diminishing returns. Under a first-in, first-out (FIFO) service discipline, the system operates as an $M/G/1$ queue, and the mean system time depends on the first and second moments of the resulting service-time distribution. We formulate a constrained optimization problem that maximizes a weighted average accuracy objective penalized by the mean system time, subject to architectural token-budget constraints and queue-stability conditions. The objective function is shown to be strictly concave over the stability region, which ensures existence and uniqueness of the optimal token allocation. The first-order optimality conditions yield a coupled projected fixed-point characterization of the optimum, together with an iterative solution and an explicit sufficient condition for contraction. Moreover, a projected gradient method with a computable global step-size bound is developed to guarantee convergence beyond the contractive regime. Finally, integer-valued token allocations are attained via rounding of the continuous solution, and the resulting performance loss is evaluated in simulation results.

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