Expected Waiting Time for Customers in Queue Calculator

✖The mean arrival rate is the mean number of arrivals per time period.ⓘ Mean Arrival Rate [λ_a]			+10% -10%
✖The Mean Service Rate is the mean number of customers served per time period.ⓘ Mean Service Rate [µ]			+10% -10%

✖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 [W_q]

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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))
W_q = λ_a/(µ*(µ-λ_a))
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

W_q = λ_a/(µ*(µ-λ_a)) --> 1800/(2000*(2000-1800))

Evaluating ... ...

W_q = 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)

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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!

< Time Estimation Calculators

Expected Waiting Time for Customers in Queue

LaTeX Go Expected Waiting Time for Customers in Queue = Mean Arrival Rate/(Mean Service Rate*(Mean Service Rate-Mean Arrival Rate))

Free Float

LaTeX Go Free Float = Early Finish Time-Early Start Time-Activity Time

Expected Waiting Time for Customers in System

LaTeX Go Expected Waiting Time for Customers in System = 1/(Mean Service Rate-Mean Arrival Rate)

Early Finish Time

LaTeX Go Early Finish Time = Early Start Time+Safety Stock

Expected Waiting Time for Customers in Queue Formula

LaTeX Go

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

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 W_q 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 (λ_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 W_q = λ_a/(µ*(µ-λ_a)) 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 (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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