Question

In: Operations Management

In a grocery store, there is one cashier counter. Customers arrive at the cashier counter according...

In a grocery store, there is one cashier counter. Customers arrive at the cashier counter according to a Poisson process. The arrival rate is 30 customers per hour. The service time is exponentially distributed. The mean service time is 1 minute 30 seconds.

What is the expected waiting time?

Expert Solution

Question: In a grocery store, there is one cashier counter. Customers arrive at the cashier counter according to a Poisson process. The arrival rate is 30 customers per hour. The service time is exponentially distributed. The mean service time is 1 minute 30 seconds.

Answer:

Given that:

Arrival Time () = 30 per hour

Service Time () = 1.3 minutes = 60 / 1.3 = 46.1538461538 = 46.15 per hour (rounded**)

Now:

The expected waiting time is:

Wq = / ( - )

Therefore:

Wq = 30 / 46.15 x (46.15 - 30)

Wq = 30 / 46.15 x 16.15

Wq = 30 / 745.3225

Wq = 0.04025103227 = 0.0403 hour (or) 2.418 minutes

**Note: Since you have not provided any rounding description, i have rounded "Service Time" to two decimals for this calculation. Refer accordingly.

keosha answered 1 year ago

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