- #1

Erenjaeger

- 141

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## Homework Statement

Anyone know anything about queueing theory? would really appreciate some help.

the question goes as follows:

The annual S&C Christmas sale is so popular that it is necessary to limit the number of customers who can be inside the store simultaneously; this limit is set at 60 people, with other customers having to queue on the street outside until somebody leaves the store. It is projected that when the store opens at 9am, there will already be 100 customers wanting to enter immediately, with further customers arriving thereafter as a Poisson process at rate 150 per hour until noon, and 50 per hour after that. Once a customer does get inside, the time they spend there is thought to be exponentially distributed with mean 30 minutes.

(a) Describe this queueing system in Kendall notation.

## Homework Equations

not really any relevant equations I don't think, not even a precalc question but i didnt know where to post it

## The Attempt at a Solution

From the question I can see that λ=150 customers / hour initially after the people waiting get in and λ=50 customers / hour after noon. also μ = 1/0.5 = 2 customers / hour / server

and i can see that the queue is an M/M/something queue C being the number of servers but I am not sure how to work that out.

by the way λ and μ are arrival rate and service rate respectively.