No latency measured increasing request number

I am performing a capacity test in my local network using an Apache Server on an Ubuntu Virtual Machine, running JMeter on a physical Ubuntu machine.

Increasing the request rate I can easily observe the maximum throughput and describe how it saturates starting from a given request rate, I see no increase in average time. If I try to access a very heavy page (3 MB text + 10 MB image + 50 MB video), I can even try hundreds of samples for minute but I see no increase in latency comparing it to the average response time measured with much less requests. I am starting thinking that the local network is the issue.

How can I setup the experiment to observe an increase on response time?

The reason you don't see increase in average time even when accessing a very heavy page is that JMeter doesn't try by default to download all images,

You can change default behavior in HTTP Request Advanced tab check the option Retrieve All Embedded Resources

Retrieve All Embedded Resources from HTML Files Tell JMeter to parse the HTML file and send HTTP/HTTPS requests for all images, Java applets, JavaScript files, CSSs, etc. referenced in the file.

This way JMeter will download all relevant files for your HTML.

You can adjust and check Parallel downloads if it'll become too much slower.