This question is about networking issues of one public internet access.
The service I am using is an internet access for the public, spread on the main places of a city, for examples in libraries.
I experience bad functioning, even in places very well covered with the wifi signal, because of the high number of users (?) but I think the problem is another.
When it kind of works it is like intermittent, it gives me some data at full speed then stops, and it's bad when applying to certain forms that can timeout because many seconds can pass before I have data again.
Video are often stuttering because of this.
I suspect this is a trick so they have a lot more users than they can handle, so to get paid for accordingly.
I would like to run some tool to assess how the network is working, so to understand whether a sort of fraud to users and to the community is perpetrated, or serious negligence is involved.
I already contacted them and described the problems. They say no one complains, but I experienced this with different OS's, like Windows, Linux, Android.
Do you have any suggestions?

If it's free, I guess you just have to put up with what they give you.

There are online service testing sites, just google for them.

Indeed - how can it be service fraud if you are complaining about a free service ?.
Whenever on a free service (even on a phone) I use VPN -so by definition it's even slower. Depends on what you consider valuable.

Have bolded two lines in what you posted for emphasis only. As said, you're using a FREE service, provided by the city/town/wherever-you-are, and you're complaining about it not being fast enough for you. Yes, a high number of users WILL cause a slowdown, no matter what. There are such things as QOS, meaning that low priority things (say, VIDEOS??) are throttled back to allow others to use the service as well. Basic network management.

And could you please explain how this is 'fraud' or 'serious negligence', when it's FREE???? More users = more network congestion. I'm sure if you'd PAY for a service, you'd get faster speeds, or if you wanted to volunteer your time, efforts, and money towards helping them with a solution, they'd welcome it. Both will solve your issue.
You mention videos...what else? Lots of things (like bittorrent) are massively throttled, and will work as described, mainly due to QOS and having to provide this service to many people, for free. Since it's doing it on Linux, Windows, and Android, that means there's nothing to do about it, past paying for a faster connection just for you, or using what's available and adjusting your expectations accordingly.

Thank you for your response.
I have to say that the service is slow and disconnecting even with a few users (early in the morning for example) and for normal website navigation, like forums.
The videos are not slowered, the fact is that the connection is intermittent with long pauses that often causes timeout in certain sites, yielding a timeout error or similar.
The service is free but is mantained by a technical department or outsourced, I do not know.
It is not so unlikely here that public or private enterprises could be cheating. It just my idea and I did not mean a fraud in the real sense of the word, but more like a sort of convenient negligence.
However the service is going to cost a lot for sure to the community and the tax payers, so it has to work. I agree that videos could be un-prioritized but they are not. I cannot risk losing an important data-transaction because of it.
I need tools because at least I can inform the "customer unions" (with evident data), often very powerful to make things change about services or products. And yourself will be able to examine the data, I can put here.
The department always answers to complaints in the same way: "you are wrong, no one else is complaining". I ensure you none has checked the connection and the service after my communication, and will not check or fix until a "union" is informed.
So which tools could I use for proofing?

So it's free, regardless of the quality....so again, how is this 'fraud'??
Then if you have 'important data-transactions', why aren't you paying for a more reliable connection?? Seems like an easy fix..I wouldn't run my business on a free service.
No thanks...not interested in examining data logs for a service in some other country/city/state. I have enough real work to do.
What is this 'union'??? If there IS a union, have you asked others, besides the tech support people? When you have problems in your public space, do you ever ask the people around you, "Hey, are you having Internet problems right now??"

And you're still leaving out things like what browser(s), extensions and add ons you're using, etc. There are a myriad of tools you can use to check internet connectivity and speed, but without knowing the OS you're running (you mention three), how often you're connected to it (not much point in 24/7 monitoring if you're connected 3 hours a day at the library), or other such details, it's hard to make a recommendation past what you can find with your own internet search. Running a simple ping test to Google.com would give you a log of ping times, dropped/successful packets, etc., but it proves nothing. Could be a flaky/old network card in your system, or an old Android phone. FAR too many variables.

Asking other people, who by the way nowadays mainly rely on their private 3G/4G connection is not useful, unless it is a real poll.
However it's the next thing to do. Checking the connection in a more technical manner is the first step I think to gather some information.
I do not understand how you do not agree that a public service has to work as intended, at least according to minimum common-sense standard like not causing me a disconnection while I am paying something online or applying to a job offer.
It's not a free service like you can find in the wifi list like "free internet access", it is an important official service and it does not work.
Linux also is free, still I have some reasonable expectations. Not every time I open a thread I get answers like "it's free so do not complain".
I think that such a public service like internet connection in libraries is important for many users.
I run UbuntuStudio 18.10 at present time.
I know ping but I hoped there were dedicated tools performing suitable network interrogations to assess what is going on.

And until you ask what they're using, how exactly are you going to know???
Great...again, there are lots of tools you can use, from browser extensions, shell scripts, etc. What you have NOT done yet is provide actual details about your system, how often you use it in these spaces, what you're using, hardware, etc., that would let anyone make any sort of halfway informed suggestion.
So back to "how is it fraud if it's free"?? Again, if you want better reliability, then pay for it. Simple. Otherwise, manage your expectations. This is like saying, "I pay for the public transportation in my city, and sometimes the bus is late, or it goes slow!!" No kidding....things happen, and it's a shared service. If you want door-to-door service on your terms, that's when you either call a taxi or buy a car.
Yep...with reasonable expectations. It's not there to give you 100%, full-bore 433Mb/s speed 100% of the time, but to be shared among everyone who's there. With security policies in place, proxy servers, and other such items that slow things down.
Again, you were told that you can write a bash script to collect ping data. Use curl to check sites like google (which are ALWAYS up), to see how they respond. Simple:
Loop through that, output results to log file, along with time/date/ping/whatever-else you want, and there's your data. Load a browser extension (search for them), or run a network speed test (going to Google.com and putting in "speedtest" gives you theirs as the very first hit).

I explained to you that the service interrupts itself even when it is delivering enough data to stream a video, the problem is that they slice the connection among many users the wrong way, not slowering down but interrupting, that is very bad because it causes timeouts and disconnections.
This is why I suspect they are trying to officially serve more users than they really do, indeed they provide a failing service to each user, even if the total number of users partially served is very high.

...except you said initially, "Video are often stuttering because of this.". But now video is fine?
What do you actually expect anyone here to be able to tell you??? You have been given suggestions to track this nefarious fraud down, as you asked for. You don't seem to want to ask anyone else in person if they're having problems, don't want to pay for a better connection, but somehow expect things to be different?

And based on what you just posted, you're admitting that this free service is actually **SERVING MORE PEOPLE THAN IT WAS DESIGNED TO**, and you're still wondering why it's slow? Since you say you 'suspect' what they're doing, that must mean you are a networking expert...perhaps you should offer them your services to fix the problem.

Free services here in The Netherlands officially acknowledge that they will not have the capacity to handle "many" streaming video connections, they're meant to check your mail, use a route planner or such. If you want more then that, pay for it.
I.e. my service provider (wired, wifi and modile) charges me 71 Euros a month, but for that I can rely on a very dependable service, signal AND speed.

@ehartman it's not about videos, I said clearly that sometimes it is not possible to use common websites too. The video example is explanatory because I see the buffering going on (youtube), then stopping, then going on again, and this is bad because causes timeouts and disconnections for other websites. Moreover, it depends on the time, sometimes it's worse, sometime it is better. But it is clear that they are stopping suddenly the service at intervals. And they say it's not true.
This is the best way I can explain.

Then either:

• Take the suggestions offered, do some research and get "them" to address the issue
• Volunteer your networking expertise to "them" to fix the issue yourself, or to find out what's really going on.
• PAY FOR SOMETHING BETTER

Pick one. There isn't a magic "make my free internet work faster" app you can load for ANY OS. If what you claim is true, you can easily gather data with just pings/curl as suggested, and present it to "them".

@TBOne I think you deserve respect for I see your reputation is high, but please do not alter what I say, we all have understood you do not agree, now let others chime in and express their suggestions or ignore the question. Thank you for your contribution.

How, exactly, does my posting hinder anyone else from doing so???

Your options remain as stated. Choose one and move forward.