Control of a M/IG/1 with service times modeled by a diffusion-threshold process

A parts queueing system is studied where the arrival of parts is according to a Poisson process and a diffusion-threshold process is proposed for modeling the service times. A work rate is the control variable; it is shown to affect the service time probability distribution in an explicit way. The sojourn time for a part is found to be monotone decreasing as a function of this work rate under some reasonable conditions. A class of optimization problems minimizing the weighted sum of the sojourn time and control effort is formulated.