Maximum number of nodes connected when the link has a large buffer

Question

A link of capacity 100 Mbps is carrying traffic from a number of sources. Each source generates an on-off traffic stream;when the source is on, the rate of traffic is 10 Mbps, and when the source is off, the rate of traffic is zero. The duty cycle,which is the ratio of on-time to off-time, is 1 : 2Assuming that all sources are synchronized and that the link is provided with a large buffer, the maximum number of sources that can be multiplexed so that there is no data loss is_____.

My solution manual claims that the max. no of nodes connected can be found out by dividing total link capacity from expected bandwidth utilization.

I dont understand why we need to take the expected bandwidth. Why can't we simply use the maximum bandwidth utilization?

Thanks in advance!

Answer 1

You can have ten of them going at once. If they're on a third of the time and you decree that, for instance, ten operate for twenty seconds, then the next ten, then the next ten, then you can have thirty of them total.

If you just focused on the max you'd think that you could only have ten (which would be the case if you weren't able to synchronize them, and thus couldn't rule out that they might all try to talk at once.)

By averaging over the available time you can get the same result without having to speculate about how exactly to schedule them. Over its uptime, each node transmits at an average of 3+1/3 Mbps. Dividing 100 MBps by this number gives 30.