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Expected Number of Customers in Queue Formula

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The Expected Number of Customers in Queue is the number of customers that are waiting for their queue in the queuing system. Check FAQs

L q = \frac{{λ a}^{2}}{μ \cdot (μ - λ a)}

L_q - Expected Number of Customers in Queue?λ_a - Mean_Arrival_Rate?μ - Mean_Service_Rate?

Expected Number of Customers in Queue Example

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Here is how the Expected Number of Customers in Queue equation looks like with Values.

Here is how the Expected Number of Customers in Queue equation looks like with Units.

Here is how the Expected Number of Customers in Queue equation looks like.

8.1 = \frac{1800^{2}}{2000 \cdot (2000 - 1800)}

8.1 = \frac{1800^{2}}{2000 \cdot (2000 - 1800)}

8.1 = \frac{1800^{2}}{2000 \cdot (2000 - 1800)}

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Expected Number of Customers in Queue Solution

Follow our step by step solution on how to calculate Expected Number of Customers in Queue?

FIRST Step Consider the formula

L q = \frac{{λ a}^{2}}{μ \cdot (μ - λ a)}

Next Step Substitute values of Variables

∴

L q = \frac{1800^{2}}{2000 \cdot (2000 - 1800)}

Next Step Prepare to Evaluate

∴

L q = \frac{1800^{2}}{2000 \cdot (2000 - 1800)}

LAST Step Evaluate

∴

L q = 8.1

Expected Number of Customers in Queue Formula Elements

Variables

Expected Number of Customers in Queue

The Expected Number of Customers in Queue is the number of customers that are waiting for their queue in the queuing system.

Symbol: L_q

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Expected Number of Customers in Queue

Mean_Arrival_Rate

Mean_Arrival_Rate is number of customers arriving per unit time.

Symbol: λ_a

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Mean_Arrival_Rate

Mean_Service_Rate

Mean_Service_Rate is the number of customers served per unit time.

Symbol: μ

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Mean_Service_Rate

Other formulas in Operational and Financial Factors category

Go Expected Number of Customers in System

L s = \frac{λ a}{μ - λ a}

Go Expected Length of Non-Empty Queue

l = \frac{μ}{μ - λ a}

Go Uniform Series Present Sum of Money

f c = i fc + i u.s

Go Standard Error (Pooled)

E std = \frac{{MSE}^{0.5}}{n t}

How to Evaluate Expected Number of Customers in Queue?

Expected Number of Customers in Queue evaluator uses Expected Number of Customers in Queue = (Mean_Arrival_Rate^2)/(Mean_Service_Rate*(Mean_Service_Rate-Mean_Arrival_Rate)) to evaluate the Expected Number of Customers in Queue, The expected number of customers in queue is the number of customers that are waiting for their queue in the queuing system. Expected Number of Customers in Queue is denoted by L_q symbol.

How to evaluate Expected Number of Customers in Queue using this online evaluator? To use this online evaluator for Expected Number of Customers in Queue, enter Mean_Arrival_Rate (λ_a) & Mean_Service_Rate (μ) and hit the calculate button.

FAQs on Expected Number of Customers in Queue

What is the formula to find Expected Number of Customers in Queue?

The formula of Expected Number of Customers in Queue is expressed as Expected Number of Customers in Queue = (Mean_Arrival_Rate^2)/(Mean_Service_Rate*(Mean_Service_Rate-Mean_Arrival_Rate)). Here is an example- 8.1 = (1800^2)/(2000*(2000-1800)).

How to calculate Expected Number of Customers in Queue?

With Mean_Arrival_Rate (λ_a) & Mean_Service_Rate (μ) we can find Expected Number of Customers in Queue using the formula - Expected Number of Customers in Queue = (Mean_Arrival_Rate^2)/(Mean_Service_Rate*(Mean_Service_Rate-Mean_Arrival_Rate)).

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Expected Number of Customers in Queue Formula

Expected Number of Customers in Queue Example

Expected Number of Customers in Queue Solution

Expected Number of Customers in Queue Formula Elements

Other formulas in Operational and Financial Factors category

How to Evaluate Expected Number of Customers in Queue?

FAQs on Expected Number of Customers in Queue

Variable Name