A stationary distribution for the number of customers in the queue and mean queue length can be computed using [[probability generating function]]s.<ref>{{cite jstorjournal | last1 = Brun | first1 = Olivier | last2 =Garcia | first2 = Jean-Marie | year = 2000 | title = Analytical Solution of Finite Capacity M/D/1 Queues | journal = Journal of Applied Probability | volume = 37 | issue = 4 | pages = 1092-1098 | publisher = [[Applied Probability Trust]] | jstor = 3215497 | doi = 10.1239/jap/1014843086 | url = | format = | accessdate = }}</ref>
===Transient solution===
The transient solution of an M/D/1 queue of finite capacity N, often written M/D/1/N, was published by Garcia et al in 2002.<ref>{{cite jstorjournal | last1 = Garcia | first1 = Jean-Marie | last2 = Brun | first2 = Olivier | last3 = Gauchard | first3 = David | year = 2002 | title = Transient Analytical Solution of M/D/1/N Queues | journal = Journal of Applied Probability | volume = 39 | issue = 4 | pages = 853-864 | publisher = Applied Probability Trust | jstor = 3216008}}</ref>
