# Aggregate Rate and Poisson Process in Aloha

I'm having a hard time understanding what is mean't by the aggregrate rate $\lambda$ and what it means for throughput in unslotted and slotted Aloha protocols. The more I seem to read about poission process the more confused I get.

I understand that the probability a packet is transmitted in a time interval $\delta t$ is $\lambda \times \delta t$ where you have $N$ senders and $Y$ is the aggregate rate from all $N$ senders.

However I don't understand what is mean't by aggregate rate. It's quite a perculiar phrase. Does it mean the probability that any of the $N$ senders will try to transmit, or is the number of packets to be sent by $N$ senders over the time?

Next we're then told that the individual rate for a sender is $\lambda / N$. Because I'm so confused by what is mean't by rate it's hard to begin to think about what this even means.

## 1 Answer

The dictionary definition of aggregate might be helpful: https://www.wordnik.com/words/aggregate

You have $N$ senders. Each sender sends packets on a network at some rate, say, $\lambda/N$. Now think about all the packets that are sent over that network, without regard to who sent it. What's the rate at which such packets appear on the network? That's a total over all packets. The aggregate rate will be something like $\lambda$.

It might also be helpful to refresh your understanding of what a rate is. A rate is an amount divided by a time period: e.g., the number of packets sent by Alice per unit time interval. The aggregate rate is also a count divided by a time period, but in this case, the count is of a different quantity: it's a count of all packets, not a count of the packets sent by Alice. So, the number of packets sent (in total, from anyone) per unit time interval is a rate. That is what your book is calling the aggregate rate.

• So if you said that a sender sends packets on a network with a rate of $1/N$ that is $1/N$ packets per time interval per sender, with a total rate of $1$ packets per time interval for all senders. Can you deduce from that since the rate is $1/N$ per sender, then each sender sends a packet in that time interval of probability $1/N$, or is that wrong? – George Robinson Nov 7 '14 at 17:51