, ▁a ▁D / M / 1 ▁queue ▁represents ▁the ▁queue ▁length ▁in ▁a ▁system ▁having ▁a ▁single ▁server , ▁where ▁arrival s ▁occur ▁at ▁fixed ▁regular ▁intervals ▁and ▁job ▁service ▁requirements ▁are ▁random ▁with ▁an ▁exponential ▁distribution . ▁The ▁model ▁name ▁is ▁written ▁in ▁K end all ' s ▁notation . ▁Ag ner ▁Kr ar up ▁Er lang ▁first ▁published ▁a ▁solution ▁to ▁the ▁station ary ▁distribution ▁of ▁a ▁D / M / 1 ▁and ▁D / M / k ▁queue , ▁the ▁model ▁with ▁k ▁servers , ▁in ▁ 1 9 1 7 ▁and ▁ 1 9 2 0 . ▁ ▁Model ▁definition ▁ ▁A ▁D / M / 1 ▁queue ▁is ▁a ▁st ochastic ▁process ▁whose ▁state ▁space ▁is ▁the ▁set ▁{ 0 , 1 , 2 , 3 , ... } ▁where ▁the ▁value ▁corresponds ▁to ▁the ▁number ▁of ▁customers ▁in ▁the ▁system , ▁including ▁any ▁currently ▁in ▁service . ▁▁▁ ▁Ar rival s ▁occur ▁determin ist ically ▁at ▁fixed ▁times ▁ β ▁apart . ▁ ▁Service ▁times ▁are ▁expon entially ▁distributed ▁( with ▁rate ▁parameter ▁ μ ). ▁ ▁A ▁single ▁server ▁serves ▁customers ▁one ▁at ▁a ▁time ▁from ▁the ▁front ▁of ▁the ▁queue , ▁according ▁to ▁a ▁first - come , ▁first - ser ved ▁discipline . ▁When ▁the ▁service ▁is ▁complete ▁the ▁customer ▁leaves ▁the ▁queue ▁and ▁the ▁number ▁of ▁customers ▁in ▁the ▁system ▁reduces ▁by ▁one . ▁ ▁The ▁buffer ▁is ▁of ▁infinite ▁size , ▁so ▁there ▁is ▁no ▁limit ▁on ▁the ▁number ▁of ▁customers