Expected Number of Customers in System 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 System is the estimated number of customers in a queuing system.ⓘ Expected Number of Customers in System [L_s]

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Expected Number of Customers in System Solution

STEP 0: Pre-Calculation Summary

Formula Used

Expected Number of Customers in System = Mean_Arrival_Rate/(Mean_Service_Rate-Mean_Arrival_Rate)
L_s = λ_a/(μ-λ_a)
This formula uses 3 Variables

Variables Used

Expected Number of Customers in System - The Expected Number of Customers in System is the estimated number of customers in a 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_s = λ_a/(μ-λ_a) --> 1800/(2000-1800)

Evaluating ... ...

L_s = 9

STEP 3: Convert Result to Output's Unit

9 --> No Conversion Required

FINAL ANSWER

9 <-- Expected Number of Customers in System

(Calculation completed in 00.020 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

Expected Number of Customers in System Formula

LaTeX Go

Expected Number of Customers in System = Mean_Arrival_Rate/(Mean_Service_Rate-Mean_Arrival_Rate)
L_s = λ_a/(μ-λ_a)

What is the expected number of customers in the system?

The expected number of customers in the system is the estimated number of customers in a queuing system. This number includes the number of customers waiting in the queue as well. It is given as the ratio of the mean arrival rate to the difference between the mean arrival rate and the mean service rate.

How to Calculate Expected Number of Customers in System?

Expected Number of Customers in System calculator uses Expected Number of Customers in System = Mean_Arrival_Rate/(Mean_Service_Rate-Mean_Arrival_Rate) to calculate the Expected Number of Customers in System, The expected number of customers in system is the estimated number of customers in a queuing system. Expected Number of Customers in System is denoted by L_s symbol.

How to calculate Expected Number of Customers in System using this online calculator? To use this online calculator for Expected Number of Customers in System, enter Mean_Arrival_Rate (λ_a) & Mean_Service_Rate (μ) and hit the calculate button. Here is how the Expected Number of Customers in System calculation can be explained with given input values -> 9 = 1800/(2000-1800).

FAQ

What is Expected Number of Customers in System?

The expected number of customers in system is the estimated number of customers in a queuing system and is represented as L_s = λ_a/(μ-λ_a) or Expected Number of Customers in System = Mean_Arrival_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 System?

The expected number of customers in system is the estimated number of customers in a queuing system is calculated using Expected Number of Customers in System = Mean_Arrival_Rate/(Mean_Service_Rate-Mean_Arrival_Rate). To calculate Expected Number of Customers in System, 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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