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G/G/1 queue
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<p>In <a href="/facts/Queueing_theory/8NDl56EM">queueing theory</a>, a discipline within the mathematical <a href="/facts/Probability_theory/mFBn51rE">theory of probability</a>, the G/G/1 queue represents the queue length in a system with a single server where interarrival times have a general (meaning arbitrary) distribution and service times have a (different) general distribution. The evolution of the queue can be described by the <a href="/facts/Lindley_equation/jyfVbf5M">Lindley equation</a>. </p><p>The system is described in <a href="/facts/Kendall%2527s_notation/zz5PJ7vs">Kendall's notation</a> where the <i>G</i> denotes a general distribution for both interarrival times and service times and the 1 that the model has a single server. Different interarrival and service times are considered to be independent, and sometimes the model is denoted GI/GI/1 to emphasise this. The numerical solution for the GI/G/1 can be obtained by discretizing the time. </p>