I'm not sure why there should
be a queue at the turbolift. I mean, these people are supposedly moving fairly predictably - "commuting" to their workstations for each shift, mainly. The computer might have a fairly good idea of where the lifts are needed and when, and would predict all but the plot-dictated movements of our adventurous main characters. For those, it would keep a suitable reserve of lifts and routes available.
Thus, the system would only hiccup when something really
unexpected happened. Such as Saavik pressing "hold" in ST2, meaning the Chief Medical Officer would have to do a rare wait.
There would probably also exist "contingency" plans for things like evacuation or red alert or hostile boarding or diplomatic reception, with the computer always staying one step ahead of the lift users.