Is this with a WiFi connection ? If so, for a test, does a computer hardwired directly to the router / gateway device with an ethernet cable have the same problem ?

What do the modem's signal stats look like ? Try getting them here http://192.168.100.1 or here http://10.0.0.1

Please post the *Downstream Power Level*, the *Upstream Power Level*, and the *SNR* (Signal to Noise Ratio) numbers.

What is the exact make and model number of the modem ?

Is this a WiFi connection ?

See the attachement for all channels. 

Cable Modem

Motorola Corporation SB6141Serial #: 203D6607643B

Downstream power level  - QAM256 

Upstream power level - 43 dBmV

Signal to Noise Ratio - 33 dB

Yes, this is over a wifi connection.

O/k the SNR is too low / out of spec on some of the channels. And the downstream power is on the weak side. That can cause random disconnects, spontaneous re-booting of the modem, speed, packet loss, and latency problems.

In a self troubleshooting effort to try to obtain better connectivity / more wiggle room, check to see if there are there any excess/unneeded coax cable splitters in the line leading to the modem that can be eliminated/re-configured. Any splitters that remain should be high quality and cable rated for 5-1002 MHz, bi-directional, and no gold colored garbage types like GE, RadioShack, RCA, Philips, Leviton, Magnavox, and Rocketfish from big box stores like Home Depot, Lowes, Target, Wal-Mart etc. Splitters should be swapped with known to be good / new ones to test

If there aren't any unneeded splitters that can be eliminated and if your coax wiring setup can't be reconfigured so that there is a single two way splitter connected directly off of the drop from the street/pole with one port feeding the modem and the other port feeding the rest of the house/equipment with additional splits as needed, and you've checked all the wiring and fittings for integrity and tightness and refresh them by taking them apart then check for and clean off any corrosion / oxidation on the center wire and put them back together again, then perhaps it's best to book a tech visit to investigate and correct.

That's not the downstream power level. It's the modulation. And are there more channels ? Please post all up and down channels. BTW, that SNR at 33 dB is too low / out of spec.

And try the test that I suggested.

Could be but a router can't affect the modems signal stats. For a test, does a computer hardwired directly to the modem have the same problem ?

I do have a 5-1002 MHz antronix splitter. That is the only splitter. There doesn't seem to be anty corrosion and everything seems tight and secure. Is it possible that I have a bad router?

I connected my computer directly to the modem and I was getting 100 Mbps. Then when I went back to the router I am only getting 10 to 15 Mbps. I used the same ethernet cabel for both. I think it may be the router?

Yeah, you may want to consider upgrading to a newer model with more horsepower. That router has only 10/100 LAN ports.

WNDR3400v3 — N600 Wireless Dual Band Router 

There is a signal / line connection quality that needs to be addressed too. What is the exact make and model number of the router ?

Do you have any suggestions? I typically with stream netflix, do a little online gaming, and our household has 2 cell phones and one laptop connected to the wifi.

Here is an excellent site for researching routers;

https://www.smallnetbuilder.com/tools/charts/router/view

And you should consider getting a tech out to investigate that signal / connection problem. Bear in mind that if the premises facing techs can not find or fix a problem at your home, it is they who are responsible for escalating it to their line / network / maintenance dept. techs. The problem may lie beyond your home in the local neighborhood infrastructure somewhere but it is their S.O.P. to start at the home.

Good luck !