All three accidents could have been avoided — if the Green Line were equipped with an automated system to track and control trains to prevent train-to-train collisions and derailments when drivers speed or miss track signals that look like traffic lights.

That technology also would have prevented many of the lesser-known incidents on the Green Line, Boston’s only rapid-transit line without at least some form of computerized or mechanical accident-prevention system. Those lower-profile episodes include at least 54 of the 56 times trolley operators missed signals between 2000 and 2010, seven of which ended in derailments, according to a new study prepared for the T.

The catch? The T estimates it would cost $645 million to $721 million and require nine years to design, install, and test a modern collision avoidance-system for the Green Line. That is a staggering sum for an agency with at least $3 billion in unmet repair and replacement needs.

For roughly the same price, the T could replace nearly its entire bus fleet or complete much of the long-delayed Green Line extension to Somerville.

Investing in what is known as positive train control — an umbrella term referring not to one specific technology but different means of tracking and controlling train movements to prevent accidents — means spending resources that could go elsewhere. That money could be used to speed travel times, expand capacity, add service, or enhance reliability or comfort for the 1.3 million weekday riders who rely on an increasingly congested MBTA.

“Our customers expect safety, but they also expect service improvements as well, which is really the challenge we have,” Secretary of Transportation Richard A. Davey said.

Though most light rail lines lack the technology, the Green Line has been singled out by the National Transportation Safety Board, which investigated the 2008 and 2009 crashes.

And state officials are loath to repeat another passenger-injuring, headline-grabbing, service-disrupting crash — even as they emphasize that the Green Line completes hundreds of thousands of trips and ferries millions of riders without incident.

Davey, a daily Green Line commuter, indicated that overhauling the line with anticrash technology is a matter of when, not if, even if it means bumping other worthy projects to make room in the T’s infrastructure budget.

“We’re definitely thinking about what kind of financial bandwidth we have in the next five to 10 years and what are our priorities,” he said. “We absolutely have to get to” positive train control.

But some analysts caution that such thinking could be reactive, seeking to reassure customers at the expense of arguably more deserving improvements. Even automated systems can fail, said former state transportation secretary Fred Salvucci .

Instead, he said, the transportation agency could invest in new vehicles and the power systems needed to run more three-car trains, which could reduce breakdowns and make passenger boarding at crowded downtown stations less chaotic. That in turn could make boardings safer and “dwell times” — the time a train sits at each station — more predictable, reducing rear-end collisions.

“If someone’s got half a billion dollars to put into the Green Line, which I hope is the case, you ought to be really careful about where to put it, to improve performance,” said Salvucci, who now teaches at the Massachusetts Institute of Technology. “Performance and safety are linked.”

Vukan Vuchic, a University of Pennsylvania professor who has worked as a consultant for large transit agencies and written about automation and safety, said a collision prevention system can mean slower and less frequent service, and no technology yet can eliminate all accidents.

“It sounds good when you are on the side of safety, it’s true. But whatever you do, you have to see the trade-offs,” Vuchic said.

After the 2008 fatal crash in Newton, when an operator suffering from an apparent “micro-sleep” episode died after slamming into another train at 38 miles an hour, National Transportation Safety Board investigators noted the absence of technology that “would have intervened to stop the train and prevent the collision.”