### A Simple Approximation to the Average Queue Size in the Time-Dependent M/M/1 QueueA Simple Approximation to the Average Queue Size in the Time-Dependent M/M/1 Queue

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 Author Rider, Kenneth Lloyd Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©1976 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Abstract The time-dependent equations for the M/M/1 queue can be reduced to a single equation for the expected queue size, but the equation is dependent on $\textit{P}0(\textit{t}),$ the probability of no jobs in the system. An exact equation for the behavior of $\textit{P}0(\textit{t})$ under special conditions is derived and an approximation relating $\textit{P}0(\textit{t})$ to $\textit{Q}(\textit{t}),$ the expected queue size at time $\textit{t},$ is derived for the case when the change in queue size is slow compared to the service rate. It is found that the approximation affords a significant improvement over the use of a steady state approximation to the time-dependent queue and is simpler to use than the exact equations. ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 1976-04-01 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 23 Issue Number 2 Page Count 7 Starting Page 361 Ending Page 367

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Source: ACM Digital Library