# Some questions in Queueing Theory

1. Dec 11, 2013

### sigh1342

1. The problem statement, all variables and given/known data
In$$M/M/1/FCFS/c/\infty$$
Wiki say offered load is equal to the expected number in the system, and I found offered load is equal to the ρ=λ/μ, where λ is the average arrive rate. And the μ is the average service time. And I don't know which one is true , and I can't find the information about effective load.
Thank you . :^)
2. Relevant equations

3. The attempt at a solution

2. Dec 11, 2013

### Ray Vickson

Please clarify: some authors use the notation A/B/C/D?E/F is slightly different order, so you need to tell us what the $c$ stands for. My guess is that you have an infinite calling population but a finite queue capacity; is that correct?

You need to show your work; it is not enough to just say you don't know what to do. In particluar, if the 'c' means that a total of c customers can be accommodated (one in service and c-1 waiting) then some 'arriving' customers will not enter the system because it is full. In particular, you need to be careful when using such results as $L = \bar{\lambda} W,$ etc.

3. Dec 11, 2013

### haruspex

I believe the definition of offered load is mean arrival rate * mean service time, so λ/μ. Looks to me that for a queue of finite capacity the effective load is based on the effective arrival rate, which discounts arrivals when the queue is full. See e.g. http://www.engr.sjsu.edu/udlpms/ISE 265/set4 queuing theory.ppt.
However, care must be taken in using this. You can't simply treat a queue of limited capacity as being an infinite queue with a reduced offered load.