Expected Waiting Time In Queue - Erlang Service Times

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on

Jul 24, 2020, 6:28:07 PM

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on

Dec 30, 2013, 4:46:18 AM

W_{q} = [\frac{1 + k}{2 k}] \cdot [\frac{λ}{μ (μ - λ)}]

$W_q = [(1 + "k" ) / (2 "k" )] * [lambda / ( mu ( mu - lambda ))]$

Mean Service Rate

$"Mean Service Rate"$

k

Mean Arrival Rate

$"Mean Arrival Rate"$

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52d4f4b4-710d-11e3-84d9-bc764e202424

In a queuing model the fundamental relationship defining the expected waiting time in the queue, $W_{q}$ $W_q$ , is dependent on the mean service rate, $μ$ $mu$ , and the expected waiting time in the system, W.

Thus the fundamental relationship is: $W$ $W$ = $W_{q}$ $W_q$ + 1/ $μ$ $mu$

When the inputs are define by a Poisson distribution and service times are defined by an Elang distribution, $σ^{2}$ $sigma^2$ = 1/(k $mu^2'), in this case the expected waiting time in the queue,$ W_q`, is computed by this equation.

Inputs are:

`lambda' (mean arrival rate)
k
$mu$ (mean service rate)

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Expected Waiting Time In Queue - Erlang Service Times

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