Expected Length of Non-Empty Queue Calculator

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

✖The Expected Length of Non-empty Queue is the ratio of the mean service rate to the difference between the mean service rate and the mean arrival rate.ⓘ Expected Length of Non-Empty Queue [l]

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Formula

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Expected Length of Non-Empty Queue

Formula

`"l" = "μ"/("μ"-"λ"_{"a"})`

Example

`"10"="2000"/("2000"-"1800")`

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Expected Length of Non-Empty Queue Solution

STEP 0: Pre-Calculation Summary

Formula Used

Expected Length of Non-empty Queue = Mean_Service_Rate/(Mean_Service_Rate-Mean_Arrival_Rate)
l = μ/(μ-λ_a)
This formula uses 3 Variables

Variables Used

Expected Length of Non-empty Queue - The Expected Length of Non-empty Queue is the ratio of the mean service rate to the difference between the mean service rate and the mean arrival rate.
Mean_Service_Rate - Mean_Service_Rate is the number of customers served per unit time.
Mean_Arrival_Rate - Mean_Arrival_Rate is number of customers arriving per unit time.

STEP 1: Convert Input(s) to Base Unit

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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l = μ/(μ-λ_a) --> 2000/(2000-1800)

Evaluating ... ...

l = 10

STEP 3: Convert Result to Output's Unit

10 --> No Conversion Required

FINAL ANSWER

10 <-- Expected Length of Non-empty Queue

(Calculation completed in 00.004 seconds)

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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

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Expected Length of Non-Empty Queue Formula

Expected Length of Non-empty Queue = Mean_Service_Rate/(Mean_Service_Rate-Mean_Arrival_Rate)
l = μ/(μ-λ_a)

What is expected length of the non-empty queue?

The expected length of the non-empty queue is the ratio of the mean service rate to the difference between the mean service rate and the mean arrival rate. It signifies there are one or more customers waiting in the queue.

How to Calculate Expected Length of Non-Empty Queue?

Expected Length of Non-Empty Queue calculator uses Expected Length of Non-empty Queue = Mean_Service_Rate/(Mean_Service_Rate-Mean_Arrival_Rate) to calculate the Expected Length of Non-empty Queue, The expected length of non-empty queue is the ratio of the mean service rate to the difference between the mean service rate and the mean arrival rate. Expected Length of Non-empty Queue is denoted by l symbol.

How to calculate Expected Length of Non-Empty Queue using this online calculator? To use this online calculator for Expected Length of Non-Empty Queue, enter Mean_Service_Rate (μ) & Mean_Arrival_Rate (λ_a) and hit the calculate button. Here is how the Expected Length of Non-Empty Queue calculation can be explained with given input values -> 10 = 2000/(2000-1800).

FAQ

What is Expected Length of Non-Empty Queue?

The expected length of non-empty queue is the ratio of the mean service rate to the difference between the mean service rate and the mean arrival rate and is represented as l = μ/(μ-λ_a) or Expected Length of Non-empty Queue = Mean_Service_Rate/(Mean_Service_Rate-Mean_Arrival_Rate). Mean_Service_Rate is the number of customers served per unit time & Mean_Arrival_Rate is number of customers arriving per unit time.

How to calculate Expected Length of Non-Empty Queue?

The expected length of non-empty queue is the ratio of the mean service rate to the difference between the mean service rate and the mean arrival rate is calculated using Expected Length of Non-empty Queue = Mean_Service_Rate/(Mean_Service_Rate-Mean_Arrival_Rate). To calculate Expected Length of Non-Empty Queue, you need Mean_Service_Rate (μ) & Mean_Arrival_Rate (λ_a). With our tool, you need to enter the respective value for Mean_Service_Rate & Mean_Arrival_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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