Non-Empty Queue Probability 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%

✖Non-empty queue probability is the probability that the queue for the queuing system is non-empty.ⓘ Non-Empty Queue Probability [P_neq]

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Non-Empty Queue Probability Solution

STEP 0: Pre-Calculation Summary

Formula Used

Non-empty Queue Probability = (Mean_Arrival_Rate/Mean_Service_Rate)^2
P_neq = (λ_a/μ)^2
This formula uses 3 Variables

Variables Used

Non-empty Queue Probability - Non-empty queue probability is the probability that the queue for the queuing system is non-empty.
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

P_neq = (λ_a/μ)^2 --> (1800/2000)^2

Evaluating ... ...

P_neq = 0.81

STEP 3: Convert Result to Output's Unit

0.81 --> No Conversion Required

FINAL ANSWER

0.81 <-- Non-empty Queue Probability

(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!

< Operational and Financial Factors Calculators

Expected Number of Customers in Queue

LaTeX Go Expected Number of Customers in Queue = (Mean_Arrival_Rate^2)/(Mean_Service_Rate*(Mean_Service_Rate-Mean_Arrival_Rate))

Expected Number of Customers in System

LaTeX Go Expected Number of Customers in System = Mean_Arrival_Rate/(Mean_Service_Rate-Mean_Arrival_Rate)

Expected Length of Non-Empty Queue

LaTeX Go Expected Length of Non-empty Queue = Mean_Service_Rate/(Mean_Service_Rate-Mean_Arrival_Rate)

Uniform Series Present Sum of Money

LaTeX Go Annual_Devaluation_Rate = Rate_of_Return_Foreign_Currency+Rate_of_Return_USD

Non-Empty Queue Probability Formula

LaTeX Go

Non-empty Queue Probability = (Mean_Arrival_Rate/Mean_Service_Rate)^2
P_neq = (λ_a/μ)^2

What is Non-empty queue probability?

Non-empty queue probability is the probability that the queue for the queuing system is non-empty. It is given as the square of the ratio of the mean arrival rate to the mean service rate.

How to Calculate Non-Empty Queue Probability?

Non-Empty Queue Probability calculator uses Non-empty Queue Probability = (Mean_Arrival_Rate/Mean_Service_Rate)^2 to calculate the Non-empty Queue Probability, Non-empty queue probability denotes the favorable outcome from all outcomes that the queue for the queuing system is non-empty. Non-empty Queue Probability is denoted by P_neq symbol.

How to calculate Non-Empty Queue Probability using this online calculator? To use this online calculator for Non-Empty Queue Probability, enter Mean_Arrival_Rate (λ_a) & Mean_Service_Rate (μ) and hit the calculate button. Here is how the Non-Empty Queue Probability calculation can be explained with given input values -> 0.81 = (1800/2000)^2.

FAQ

What is Non-Empty Queue Probability?

Non-empty queue probability denotes the favorable outcome from all outcomes that the queue for the queuing system is non-empty and is represented as P_neq = (λ_a/μ)^2 or Non-empty Queue Probability = (Mean_Arrival_Rate/Mean_Service_Rate)^2. 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 Non-Empty Queue Probability?

Non-empty queue probability denotes the favorable outcome from all outcomes that the queue for the queuing system is non-empty is calculated using Non-empty Queue Probability = (Mean_Arrival_Rate/Mean_Service_Rate)^2. To calculate Non-Empty Queue Probability, 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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