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]

⎘ Copy

👎

Formula

✖

Expected Waiting Time for Customers in Queue

Formula

`"W"_{"q"} = "λ"_{"a"}/("µ"*("µ"-"λ"_{"a"}))`

Example

`"0.0045"="1800"/("2000"*("2000"-"1800"))`

Calculator

LaTeX

Reset

👍

Download Time Estimation Formulas PDF PDF Image

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)

You are here -

Home » Engineering » Mechanical » Industrial Engineering » Time Estimation » Expected Waiting Time for Customers in Queue

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))

Standard Normal Variation

Go Standard Normal Variation = (Normal Variate-Expected Value)/Standard Deviation

PERT Expected Time

Go PERT Expected Time = (Optimistic Time+4*Most Likely Time+Pessimistic Time)/6

Time Taken for Manufacturing Model with Shortage

Go Time taken for Manufacturing Model with Shortage = EOQ Manufacturing Model with Shortage/Demand per Year

Independent Float

Go Independent Float = Early Finish Time-Late Start Time-Activity Time

Total Float

Go Total Float = Late Finish Time-(Early Start Time+Activity Time)

Free Float

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

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

Go Time taken for Purchase Model with Shortage = EOQ Purchase Model/Demand per Year

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

Go Late Finish Time = Late Start Time+Duration of Activity

Early Finish Time

Go Early Finish Time = Early Start Time+Safety Stock

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))
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.

Home

FREE PDFs

🔍 Search