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==Stationary distribution==
The number of jobs in the queue can be written as [[M/G/1 queue|M/G/1 type Markov chain]] and the stationary distribution found for state ''i'' (written π<sub>''i''</sub>) in the case ''D'' = 1 to be<ref name=":1">{{cite journal| url = http://kashiwa.nagaokaut.ac.jp/members/nakagawa/ronbun/029.pdf | journal = Journal of the Operations Research Society of Japan | volume = 48 | year = 2005 | issue = 2 | pages = 111–122 | title = On the Series Expansion for the Stationary Probabilities of an M/D/1 queue | first = Kenji | last = Nakagawa | doi=10.15807/jorsj.48.111| doi-access = free }}</ref>
:<math>\begin{align}\pi_0 &= 1-\lambda \\
\pi_1 &= (1-\lambda)(e^\lambda - 1)\\
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