Why is the exponential distribution chosen to model service time in Queuing theory ?


1 Answer 1


The exponential distribution incorporates the assumption that the hazard rate is not dependent on the time spent in the queue.

The hazard rate is the instantaneous rate of an event (via Wikipedia page on Survival analysis):

\begin{equation} \lambda(t) = \lim_{dt\rightarrow 0}{\frac{\Pr(t\le T < t+dt)}{dt \cdot (1-F(t))}} = \frac{f(t)}{1-F(t)} \end{equation}

For an exponential distribution $f(t) = b \exp(-b t)$ and $1-F(t)=\exp(-b t)$, therefore $\lambda(t)=b$, i.e., constant.

  • $\begingroup$ Thank you for your answer. So (as far as I understood )the exponential distribution is chosen to model service time just because the event rate is constant ? $\endgroup$ Commented Jun 9, 2015 at 16:32
  • $\begingroup$ @user3914897 That's probably the reason, but I suspect it's not so realistic. The time between arrival of customers might be realistically modeled as exponentially distributed, but service times are quite a different matter. $\endgroup$ Commented Oct 11, 2019 at 15:01
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    $\begingroup$ It's all to do with the Markov property isn't it? Non exponential queues are modelled as M/G/n queues (much more complicated) $\endgroup$ Commented May 18, 2021 at 8:39

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