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A lower bound on the reliability exponent of the memoryless exponential server timing channel with noiseless feedback is provided. The lower bound depends on whether fixed or random transmission time, as well as on whether fixed block-length or variable block-length codes are considered (with block-length denoting the number of recorded departures). On the other hand, we show that E. Arikan's one-way sphere-packing bound for fixed transmission time codes (see IEEE Trans. Inform. Theory, vol.IT-48, no.6, p.1681-9, 2002) applies as well to fixed transmission time codes for the case at hand. As for random transmission time variable block-length codes, a lower bound on the zero error capacity is obtained.