OLYMPIA — Initiative promoter Tim Eyman’s latest measure, which aims to smooth traffic jams and head off open-ended tolls on state road projects, should make the fall ballot.

Eyman, who submitted his last big batch of signed initiative petitions to Secretary of State Sam Reed on Monday, said the Initiative 985 campaign has now turned in about 299,000 signatures.

That should be enough to virtually guarantee the measure makes the ballot. About 225,000 valid voter signatures are needed to qualify, with sponsors shooting for thousands more to compensate for any signatures that are ruled invalid.

Eyman’s measure is a multifaceted approach to altering state and local traffic policy, and follows up State Auditor Brian Sonntag’s audit about traffic jams around the state.

If approved by voters, the initiative would send portions of the money flowing from vehicle sales taxes, certain tolls, red-light cameras and other state transportation projects into a “Reduce Traffic Congestion Account.”

State lawmakers would decide how to divide that money among three top priorities: opening up car pool lanes during off-peak travel times, synchronizing traffic lights and boosting roadside assistance crews.

Once those targets are met, the money would have to go to additional programs aimed at easing traffic jams. Sonntag would be given oversight of the new account and its programs.

Eyman said that while his measure isn’t likely to be the star attraction on this fall’s initiative ballot, he believes it will garner support from drivers across the state, particularly in light of the traffic frustration that Sonntag found in canvassing for audit suggestions.

“It’s a chance for us to say to the Legislature, ‘Hey — if you don’t adopt Sonntag’s recommendations, the people will do it for you,’” Eyman said. “It’s kind of a swift kick in the shins.”

There is no organized opposition campaign.

Eyman has taken out a $250,000 line of credit against his Mukilteo home to help finance the campaign, after the loss of a major financial backer. Eyman said he’s spent about $150,000 from the loan, and could come close to using the rest. But he predicted that supporters would help retire the debt after the campaign is over.

Two other initiatives are considered likely to qualify for the ballot this year: I-1000, which would set up an assisted-suicide program for terminally ill people, and I-1029, which would require long-term care workers to pass a certification exam and complete more training.