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


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 ? $\endgroup$ – user3914897 Jun 9 '15 at 16:32

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