Expected Number of Customers in Queue Calculator

✖Mean_Arrival_Rate is number of customers arriving per unit time.ⓘ Mean_Arrival_Rate [λ_a]			+10% -10%
✖Mean_Service_Rate is the number of customers served per unit time.ⓘ Mean_Service_Rate [μ]			+10% -10%

✖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 [L_q]

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Formula

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Expected Number of Customers in Queue

Formula

`"L"_{"q"} = ("λ"_{"a"}^2)/("μ"*("μ"-"λ"_{"a"}))`

Example

`"8.1"=(("1800")^2)/("2000"*("2000"-"1800"))`

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Expected Number of Customers in Queue Solution

STEP 0: Pre-Calculation Summary

Formula Used

Expected Number of Customers in Queue = (Mean_Arrival_Rate^2)/(Mean_Service_Rate*(Mean_Service_Rate-Mean_Arrival_Rate))
L_q = (λ_a^2)/(μ*(μ-λ_a))
This formula uses 3 Variables

Variables Used

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.
Mean_Arrival_Rate - Mean_Arrival_Rate is number of customers arriving per unit time.
Mean_Service_Rate - Mean_Service_Rate is the number of customers served per unit time.

STEP 1: Convert Input(s) to Base Unit

Mean_Arrival_Rate: 1800 --> No Conversion Required
Mean_Service_Rate: 2000 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L_q = (λ_a^2)/(μ*(μ-λ_a)) --> (1800^2)/(2000*(2000-1800))

Evaluating ... ...

L_q = 8.1

STEP 3: Convert Result to Output's Unit

8.1 --> No Conversion Required

FINAL ANSWER

8.1 <-- Expected Number of Customers in Queue

(Calculation completed in 00.004 seconds)

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Credits

Created by Suman Ray Pramanik

Indian Institute of Technology (IIT), Kanpur

Suman Ray Pramanik has created this Calculator and 50+ more calculators!

Verified by Akshada Kulkarni

National Institute of Information Technology (NIIT), Neemrana

Akshada Kulkarni has verified this Calculator and 900+ more calculators!

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Expected Number of Customers in Queue

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Expected Number of Customers in Queue Formula

Expected Number of Customers in Queue = (Mean_Arrival_Rate^2)/(Mean_Service_Rate*(Mean_Service_Rate-Mean_Arrival_Rate))
L_q = (λ_a^2)/(μ*(μ-λ_a))

What is expected number of customers in the queue?

The expected number of customers in the queue is the number of customers that are waiting for their queue in the queuing system. From the set of customers waiting for service, we choose the one to be served next either by FIFO (first-in-first-out) - also known as FCFS (first-come-first-served) or by LIFO (last-in-first-out) randomly. This is often called the queue discipline.

How to Calculate Expected Number of Customers in Queue?

Expected Number of Customers in Queue calculator uses Expected Number of Customers in Queue = (Mean_Arrival_Rate^2)/(Mean_Service_Rate*(Mean_Service_Rate-Mean_Arrival_Rate)) to calculate 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 calculate Expected Number of Customers in Queue using this online calculator? To use this online calculator for Expected Number of Customers in Queue, enter Mean_Arrival_Rate (λ_a) & Mean_Service_Rate (μ) and hit the calculate button. Here is how the Expected Number of Customers in Queue calculation can be explained with given input values -> 8.1 = (1800^2)/(2000*(2000-1800)).

FAQ

What is 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 and is represented as L_q = (λ_a^2)/(μ*(μ-λ_a)) or Expected Number of Customers in Queue = (Mean_Arrival_Rate^2)/(Mean_Service_Rate*(Mean_Service_Rate-Mean_Arrival_Rate)). Mean_Arrival_Rate is number of customers arriving per unit time & Mean_Service_Rate is the number of customers served per unit time.

How to calculate 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 is calculated using Expected Number of Customers in Queue = (Mean_Arrival_Rate^2)/(Mean_Service_Rate*(Mean_Service_Rate-Mean_Arrival_Rate)). To calculate Expected Number of Customers in Queue, you need Mean_Arrival_Rate (λ_a) & Mean_Service_Rate (μ). With our tool, you need to enter the respective value for Mean_Arrival_Rate & Mean_Service_Rate and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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