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Expected Waiting Time for Customers in Queue Formula

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The Expected Waiting Time for Customers in Queue is the expected time a customer has to wait for their queue in the queuing system. Check FAQs

W q = \frac{λ a}{µ \cdot (µ - λ a)}

W_q - Expected Waiting Time for Customers in Queue?λ_a - Mean Arrival Rate?µ - Mean Service Rate?

Expected Waiting Time for Customers in Queue Example

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Here is how the Expected Waiting Time for Customers in Queue equation looks like with Values.

Here is how the Expected Waiting Time for Customers in Queue equation looks like with Units.

Here is how the Expected Waiting Time for Customers in Queue equation looks like.

0.0045 = \frac{1800}{2000 \cdot (2000 - 1800)}

0.0045 = \frac{1800}{2000 \cdot (2000 - 1800)}

0.0045 = \frac{1800}{2000 \cdot (2000 - 1800)}

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Expected Waiting Time for Customers in Queue Solution

Follow our step by step solution on how to calculate Expected Waiting Time for Customers in Queue?

FIRST Step Consider the formula

W q = \frac{λ a}{µ \cdot (µ - λ a)}

Next Step Substitute values of Variables

∴

W q = \frac{1800}{2000 \cdot (2000 - 1800)}

Next Step Prepare to Evaluate

∴

W q = \frac{1800}{2000 \cdot (2000 - 1800)}

LAST Step Evaluate

∴

W q = 0.0045

Expected Waiting Time for Customers in Queue Formula Elements

Variables

Expected Waiting Time for Customers in Queue

The Expected Waiting Time for Customers in Queue is the expected time a customer has to wait for their queue in the queuing system.

Symbol: W_q

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Expected Waiting Time for Customers in Queue

Mean Arrival Rate

The mean arrival rate is the mean number of arrivals per time period.

Symbol: λ_a

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Mean Arrival Rate

Mean Service Rate

The Mean Service Rate is the mean number of customers served per time period.

Symbol: µ

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Mean Service Rate

Other formulas in Time Estimation category

Go Early Finish Time

EFT = EST + S

Go Expected Waiting Time for Customers in System

W s = \frac{1}{µ - λ a}

Go Free Float

FF 0 = EFT - EST - t activity

Go Independent Float

IF 0 = EFT - LST - t activity

How to Evaluate Expected Waiting Time for Customers in Queue?

Expected Waiting Time for Customers in Queue evaluator uses Expected Waiting Time for Customers in Queue = Mean Arrival Rate/(Mean Service Rate*(Mean Service Rate-Mean Arrival Rate)) to evaluate the Expected Waiting Time for Customers in Queue, The expected waiting time for customers in queue is the expected time a customer has to wait for their queue in the queuing system. Expected Waiting Time for Customers in Queue is denoted by W_q symbol.

How to evaluate Expected Waiting Time for Customers in Queue using this online evaluator? To use this online evaluator for Expected Waiting Time for Customers in Queue, enter Mean Arrival Rate (λ_a) & Mean Service Rate (µ) and hit the calculate button.

FAQs on Expected Waiting Time for Customers in Queue

What is the formula to find Expected Waiting Time for Customers in Queue?

The formula of Expected Waiting Time for Customers in Queue is expressed as Expected Waiting Time for Customers in Queue = Mean Arrival Rate/(Mean Service Rate*(Mean Service Rate-Mean Arrival Rate)). Here is an example- 0.0045 = 1800/(2000*(2000-1800)).

How to calculate Expected Waiting Time for Customers in Queue?

With Mean Arrival Rate (λ_a) & Mean Service Rate (µ) we can find Expected Waiting Time for Customers in Queue using the formula - Expected Waiting Time for Customers in Queue = Mean Arrival Rate/(Mean Service Rate*(Mean Service Rate-Mean Arrival Rate)).

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Expected Waiting Time for Customers in Queue Formula

Expected Waiting Time for Customers in Queue Example

Expected Waiting Time for Customers in Queue Solution

Expected Waiting Time for Customers in Queue Formula Elements

Other formulas in Time Estimation category

How to Evaluate Expected Waiting Time for Customers in Queue?

FAQs on Expected Waiting Time for Customers in Queue

Variable Name