Expected Waiting Time for Customers in Queue Solution

STEP 0: Pre-Calculation Summary
Formula Used
Expected Waiting Time for Customers in Queue = Mean Arrival Rate/(Mean Service Rate*(Mean Service Rate-Mean Arrival Rate))
Wq = λa/(µ*(µ-λa))
This formula uses 3 Variables
Variables Used
Expected Waiting Time for Customers in Queue - The Expected Waiting Time for Customers in Queue is the expected time a customer has to wait for their queue in the queuing system.
Mean Arrival Rate - The mean arrival rate is the mean number of arrivals per time period.
Mean Service Rate - The Mean Service Rate is the mean number of customers served per time period.
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
Wq = λa/(µ*(µ-λa)) --> 1800/(2000*(2000-1800))
Evaluating ... ...
Wq = 0.0045
STEP 3: Convert Result to Output's Unit
0.0045 --> No Conversion Required
FINAL ANSWER
0.0045 <-- Expected Waiting Time for Customers in Queue
(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
Akshada Kulkarni has verified this Calculator and 900+ more calculators!

16 Time Estimation Calculators

Expected Waiting Time for Customers in Queue
Go Expected Waiting Time for Customers in Queue = Mean Arrival Rate/(Mean Service Rate*(Mean Service Rate-Mean Arrival Rate))
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Total Float
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Free Float
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Expected Waiting Time for Customers in System
Go Expected Waiting Time for Customers in System = 1/(Mean Service Rate-Mean Arrival Rate)
Time Taken for Purchase Model with No Shortage
Go Time taken for Purchase Model no Shortage = Economic Order Quantity/Demand per Year
Time Taken for Purchase Model with Shortage
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Total Float given Finish Time
Go Total Float given Finish Times = Late Finish Time-Early Finish Time
Standard Deviation given Optimistic and Pessimistic Time
Go Standard Deviation = (Pessimistic Time-Optimistic Time)/6
Independent Float given Slack
Go Independent Float given Slack = Free Float-Slack of Event
Late Finish Time
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Early Finish Time
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Total Float given Start Time
Go Total Float = Late Start Time-Early Start Time

Expected Waiting Time for Customers in Queue Formula

Expected Waiting Time for Customers in Queue = Mean Arrival Rate/(Mean Service Rate*(Mean Service Rate-Mean Arrival Rate))
Wq = λa/(µ*(µ-λa))

What is expected waiting time for customers in the queue?

The expected waiting time for customers in the queue is the expected time a customer has to wait for their queue in the queuing system. Often the queue discipline "choose the customer with the lowest service time" results in the smallest value for the time (on average) a customer spends queuing.

How to Calculate Expected Waiting Time for Customers in Queue?

Expected Waiting Time for Customers in Queue calculator uses Expected Waiting Time for Customers in Queue = Mean Arrival Rate/(Mean Service Rate*(Mean Service Rate-Mean Arrival Rate)) to calculate the Expected Waiting Time for Customers in Queue, The expected waiting time for customers in queue is the expected time a customer has to wait for their queue in the queuing system. Expected Waiting Time for Customers in Queue is denoted by Wq symbol.

How to calculate Expected Waiting Time for Customers in Queue using this online calculator? To use this online calculator for Expected Waiting Time for Customers in Queue, enter Mean Arrival Rate a) & Mean Service Rate (µ) and hit the calculate button. Here is how the Expected Waiting Time for Customers in Queue calculation can be explained with given input values -> 0.0045 = 1800/(2000*(2000-1800)).

FAQ

What is Expected Waiting Time for Customers in Queue?
The expected waiting time for customers in queue is the expected time a customer has to wait for their queue in the queuing system and is represented as Wq = λa/(µ*(µ-λa)) or Expected Waiting Time for Customers in Queue = Mean Arrival Rate/(Mean Service Rate*(Mean Service Rate-Mean Arrival Rate)). The mean arrival rate is the mean number of arrivals per time period & The Mean Service Rate is the mean number of customers served per time period.
How to calculate Expected Waiting Time for Customers in Queue?
The expected waiting time for customers in queue is the expected time a customer has to wait for their queue in the queuing system is calculated using Expected Waiting Time for Customers in Queue = Mean Arrival Rate/(Mean Service Rate*(Mean Service Rate-Mean Arrival Rate)). To calculate Expected Waiting Time for Customers in Queue, 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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