We establish functional large deviation principles (FLDPs) for waiting times and departure times in single-server queues with unlimited waiting space. We apply the extended contraction principle to show that these processes obey FLDPs in the function space D whenever the arrival and service processes obey FLDPs. However, the rate function for the departure process is complicated for non-deterministic service times. We exhibit the rate function in the case of deterministic interarrival times. We also establish an FLDP for inverse processes, which we apply to establish FLDPs for the arrival counting process and the arrival times in a superposition of independent arrival processes. We combine the results to obtain an FLDP for waiting times in the Σ_(i=1)~k GI_i/GI/1 queue.
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机译：我们为具有无限等待空间的单服务器队列中的等待时间和离开时间建立了功能性大偏差原理（FLDP）。我们应用扩展收缩原理来表明，只要到达和服务过程服从FLDP，这些过程就服从功能空间D中的FLDP。但是，对于不确定的服务时间，出发过程的费率函数很复杂。在确定的到达间隔时间的情况下，我们展示出速率函数。我们还为逆过程建立了FLDP，我们将其用于为到达计数过程和到达时间（独立到达过程的叠加）建立FLDP。我们将结果组合起来，以获得Σ_（i = 1）〜k GI_i / GI / 1队列中等待时间的FLDP。
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