Probability of Customers Exceeding Number Calculator

✖Mean_Arrival_Rate is number of customers arriving per unit time.ⓘ Mean_Arrival_Rate [λ_a]			+10% -10%
✖Exceeded Number Queuing Theory is the number that has been exceeded by the given number of customers in a queuing system.ⓘ Exceeded Number Queuing Theory [k]			+10% -10%
✖Mean_Service_Rate is the number of customers served per unit time.ⓘ Mean_Service_Rate [μ]			+10% -10%

✖The Probability of Customers Exceeding Number is the probability of the number of customers in the system exceeding a certain number.ⓘ Probability of Customers Exceeding Number [P_ex]

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Probability of Customers Exceeding Number Solution

STEP 0: Pre-Calculation Summary

Formula Used

Probability of Customers Exceeding Number = Mean_Arrival_Rate*Exceeded Number Queuing Theory/Mean_Service_Rate
P_ex = λ_a*k/μ
This formula uses 4 Variables

Variables Used

Probability of Customers Exceeding Number - The Probability of Customers Exceeding Number is the probability of the number of customers in the system exceeding a certain number.
Mean_Arrival_Rate - Mean_Arrival_Rate is number of customers arriving per unit time.
Exceeded Number Queuing Theory - Exceeded Number Queuing Theory is the number that has been exceeded by the given number of customers in a queuing system.
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
Exceeded Number Queuing Theory: 13 --> No Conversion Required
Mean_Service_Rate: 2000 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P_ex = λ_a*k/μ --> 1800*13/2000

Evaluating ... ...

P_ex = 11.7

STEP 3: Convert Result to Output's Unit

11.7 --> No Conversion Required

FINAL ANSWER

11.7 <-- Probability of Customers Exceeding Number

(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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Probability of Customers Exceeding Number Formula

LaTeX Go

Probability of Customers Exceeding Number = Mean_Arrival_Rate*Exceeded Number Queuing Theory/Mean_Service_Rate
P_ex = λ_a*k/μ

What is Probability of customers exceeding a number?

The Probability of customers exceeding a number is the probability of the number of customers in the system exceeding a certain number. it is given as the product of the exceeded number and the ratio of the mean arrival rate to the mean service rate.

How to Calculate Probability of Customers Exceeding Number?

Probability of Customers Exceeding Number calculator uses Probability of Customers Exceeding Number = Mean_Arrival_Rate*Exceeded Number Queuing Theory/Mean_Service_Rate to calculate the Probability of Customers Exceeding Number, The Probability of Customers Exceeding Number is the probability of the number of customers in the system exceeding a certain number. Probability of Customers Exceeding Number is denoted by P_ex symbol.

How to calculate Probability of Customers Exceeding Number using this online calculator? To use this online calculator for Probability of Customers Exceeding Number, enter Mean_Arrival_Rate (λ_a), Exceeded Number Queuing Theory (k) & Mean_Service_Rate (μ) and hit the calculate button. Here is how the Probability of Customers Exceeding Number calculation can be explained with given input values -> 11.7 = 1800*13/2000.

FAQ

What is Probability of Customers Exceeding Number?

The Probability of Customers Exceeding Number is the probability of the number of customers in the system exceeding a certain number and is represented as P_ex = λ_a*k/μ or Probability of Customers Exceeding Number = Mean_Arrival_Rate*Exceeded Number Queuing Theory/Mean_Service_Rate. Mean_Arrival_Rate is number of customers arriving per unit time, Exceeded Number Queuing Theory is the number that has been exceeded by the given number of customers in a queuing system & Mean_Service_Rate is the number of customers served per unit time.

How to calculate Probability of Customers Exceeding Number?

The Probability of Customers Exceeding Number is the probability of the number of customers in the system exceeding a certain number is calculated using Probability of Customers Exceeding Number = Mean_Arrival_Rate*Exceeded Number Queuing Theory/Mean_Service_Rate. To calculate Probability of Customers Exceeding Number, you need Mean_Arrival_Rate (λ_a), Exceeded Number Queuing Theory (k) & Mean_Service_Rate (μ). With our tool, you need to enter the respective value for Mean_Arrival_Rate, Exceeded Number Queuing Theory & 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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