Editing Queueing theory (section)

=== Simple two-equation queue ===

A common basic queueing system is attributed to [[Agner Krarup Erlang|Erlang]] and is a modification of [[Little's Law]]. Given an arrival rate ''λ'', a dropout rate ''σ'', and a departure rate ''μ'', length of the queue ''L'' is defined as:

: <math>L = \frac{\lambda - \sigma}{\mu}</math>.

Assuming an exponential distribution for the rates, the waiting time ''W'' can be defined as the proportion of arrivals that are served. This is equal to the exponential survival rate of those who do not drop out over the waiting period, giving:

: <math>\frac{\mu}{\lambda} = e^{-W{\mu}}</math>

The second equation is commonly rewritten as:

: <math>W = \frac{1}{\mu} \mathrm{ln}\frac{\lambda}{\mu}</math>

The two-stage one-box model is common in [[epidemiology]].<ref>{{Cite journal|last=Hernández-Suarez|first=Carlos|date=2010|title=An application of queuing theory to SIS and SEIS epidemic models|journal=Math. Biosci.|volume=7|issue=4|pages=809–823|doi=10.3934/mbe.2010.7.809|pmid=21077709|doi-access=free}}</ref>