Wavering

You need a fire-flow bypass. During the fire, flow is through the 8" bypass. Normally, the bypass will be closed and flow will be through the 3" likely a venturi meter.

The bypass needs to be automated.

Please tell us which side of the booster this valve pit is (suction or discharge).

Suction side of the booster. The water originates in a tower. It goes down to the municipal valve pit where it passes through either the 3" or 8" valve depending upon demand. Then it travels through an industrial park, branches off to residential areas and ends in a dead end at my booster station.

Here is how I understand your problem

When the demand increases, and the pressure drops, your booster station's fire-pump engages and demands more from the city pit, the city pit opens its large valve and provides allot of pressure which in turn shuts off your pump. The flow is reduced so the city pit shuts down to the smaller valve, the demand is not met, so the cycle repeats, over and over again.

In other words the city pit is providing more water then your booster pump can handle, or your booster pump is engaging too soon for too small of a demand change.

You may want to have your pressure sensors and relays re-calibrated until the demand or pressure drop is is greater, or slightly delay pump engagement.

Best fix would be to add a pressure regulating tank, or water tower between the source and your booster station.$$$

There are a number of solutions to attenuate pressure waves in the system. Typically you would employ a pressure tank or a release valve in a situation like yours. These systems absorb or attenuate the pressure wave as it travels through the system. another thing to consider is that the 8 inch valve is just opening too fast, and maybe it can be slowed down in response time (or a different valve system may be employed that repsonds a little slower). This would mean you build pressure slower, but you would not have the huge pressure surge.

Have you tried installing a hydraulic accumulator on the pipeline?