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)
Ls = λa/(μ-λa)
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
Ls = λa/(μ-λa) --> 1800/(2000-1800)
Evaluating ... ...
Ls = 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 00.004 seconds)

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
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13 Basics of Industrial Engineering Calculators

Single Exponential Smoothing
Go Smooth_Averaged_Forecast_for_Period_t = Smoothing Constant*Previous observed Value+(1-Smoothing Constant)*Previous Period Forecast
New Number in Simplex Table
Go New Number of Simplex Table = Old Number of Simplex Table-Key Row of Simplex*Key Column of Simplex/Key Number of Simplex
Expected Number of Customers in Queue
Go Expected Number of Customers in Queue = (Mean_Arrival_Rate^2)/(Mean_Service_Rate*(Mean_Service_Rate-Mean_Arrival_Rate))
Probability of Customers Exceeding Number
Go Probability of Customers Exceeding Number = Mean_Arrival_Rate*Exceeded Number Queuing Theory/Mean_Service_Rate
Number of Kanbans
Go No. of Kanban = (Demand_per_Year*Lead Time*(1+Safety_Factor))/Container Size
Expected Number of Customers in System
Go Expected Number of Customers in System = Mean_Arrival_Rate/(Mean_Service_Rate-Mean_Arrival_Rate)
Expected Length of Non-Empty Queue
Go Expected Length of Non-empty Queue = Mean_Service_Rate/(Mean_Service_Rate-Mean_Arrival_Rate)
Gross Margin Return on Investment
Go Return_on_Investment_(ROI) = Gross_Profit/((Opening Stock-Closing Stock)/2)*100
Perfect Order Measurement
Go Perfect Order Measurement = ((Total Orders-Error Orders)/Total Orders)*100
Uniform Series Present Sum of Money
Go Annual_Devaluation_Rate = Rate_of_Return_Foreign_Currency+Rate_of_Return_USD
Point r on Line
Go Point r on Line = Point a+Lambda*Point b
Non-Empty Queue Probability
Go Non-empty Queue Probability = (Mean_Arrival_Rate/Mean_Service_Rate)^2
Standard Error (Pooled)
Go Standard Error = (Mean Square Error^0.5)/Observations

Expected Number of Customers in System Formula

Expected Number of Customers in System = Mean_Arrival_Rate/(Mean_Service_Rate-Mean_Arrival_Rate)
Ls = λa/(μ-λa)

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 Ls 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 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 Ls = λa/(μ-λa) 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 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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