Differentiability and analyticity of queues in light traffic

Several methods have been proposed to approximate performance measures of queueing systems based on their light traffic derivatives, e,g., the MacLaurin expansion, the Pade approximation, and interpolation with heavy traffic limits. To apply these methods, it requires that the performance measures he differentiable and analytic when the arrival rates equal to zero. In this paper, we study these issues for the GI/GI/1 queue. We present conditions under which the mean steady-state system time of a job is differentiable and analytical when the arrival rate to the queue equals to zero