''It is an exhilarating feeling for Staten Islanders,'' said Guy V. Molinari, the Staten Island borough president, in an interview yesterday. ''Even back four or five years ago, there were very few residents who believed the dump would close by the end of this year. And it is understandable because so many promises had been broken in the past about the dump.''  Fulfilling the promise to close Fresh Kills has been a costly one.  Sending trash to the landfill -- once considered the world's largest -- cost the city about $43 per ton. Exporting it to incinerators and landfills is costing an average of about $63 a ton, with one of the new Queens contracts costing $81 a ton.  The result is that the city's annual bill for collecting and disposing of about 12,000 tons of residential trash daily has jumped by about $220 million, to about $658 million, according to the city's Independent Budget Office. That increase is more than the city spends annually on the Department of Parks and Recreation and about half of what it spends on its university system.  ''A political decision was made to close the landfill,'' said Ronnie Lowenstein, director of the Independent Budget Office, adding that Fresh Kills, while perhaps despised by Staten Island residents, was capable of holding 20 to 30 years more of city trash.  ''It is important that people understand what that decision will cost,'' she said.  The decision also added a total of approximately 350,000 round trips a year by garbage trucks and tractor-trailers across the Goethals and George Washington Bridges and through the Holland and Lincoln Tunnels, according to an analysis by the Tri-State Transportation Campaign, a watchdog group based in New York City.  Much of the new truck traffic is carrying waste from the city to transfer stations in New Jersey and on Long Island.  Previously, that trash was dropped at marine transfer sites in each borough, then taken by barge to Fresh Kills. Starting today, the trash from Queens will follow a pattern similar to that already in place for the other boroughs.  Up to 2,855 tons a day will be driven by Sanitation Department trucks to four transfer stations in New Jersey: in Jersey City, Paterson, Totawa and Newark. Up to 150 additional tons a day will go to an incinerator in Hempstead, N.Y. And as much as 1,058 tons will go to transfer stations in Queens, before being shipped by tractor-trailer to distant landfills.  These figures exceed the 3,500-ton daily average, because the city has to plan for peak days and the possibility of problems with haulers or landfills.  The city is already using trucks to carry its residential garbage from the four boroughs other than Queens to four transfer stations in Brooklyn, four others in New Jersey and one in the Bronx. Most of that refuse is then sent by truck to distant landfills in states including Ohio, Pennsylvania, South Carolina and Virginia.  But the city has said it intends to use this truck-based disposal system for only three or four more years. It intends to then switch to a system that will rely largely on rail and perhaps barge, cutting down on the armada of trucks using the bridges and tunnels and traveling along Interstate 95 and other major highways.  The associate director of the Tri-State Transportation Campaign, Jonathan Orcutt, said the city should have timed the closing of Fresh Kills so it would have immediately started with a rail- and barge-based export system. Since that is now impossible, he said, city officials must ensure that the so-called interim export plan that relies on trucks is truly interim.  ''Once some system is in place, the next administration could just ignore the problem and leave it as it is,'' he said.  Giuliani administration officials, speaking on the condition that they not be identified, acknowledged some discomfort with the heavy stream of truck traffic that the trash export effort has produced.  But the deputy mayor for operations, Joseph J. Lhota, said that the city sends most of its trucks across the bridges and through the tunnels at night and in the early morning, when there is little traffic.  ''It will be done long before or long after the commuter rush,'' Mr. Lhota said.  Mr. Lhota also said the city is committed to moving quickly toward the long-term export plan, which now calls for transporting about 6,000 tons of city trash a day by barge from various sites around the city to Linden, N.J., where it would then be sent by rail to distant landfills.  ''That is our goal, to minimize the truck traffic,'' Mr. Lhota said.  Mr. Molinari said that once the final load of trash arrives at Fresh Kills -- sometime this spring -- a series of celebrations will start and will run through the Fourth of July.  ''It was an atrocity for us,'' Mr. Molinari said, adding that the parties will include a concert and fireworks. ''A terrible, terrible monstrosity we have had to live with is now nearly finished.''
Truck traffic on New York City's bridges and tunnels will be a bit heavier starting today, as New York City begins final step in its four-year effort to send residential trash from throughout five boroughs to mostly out-of-state landfills and incinerators rather than to huge Fresh Kills landfill on Staten Island; city officials say that first of seven contracts to dispose of average 3,500 tons of household garbage from Queens each day goes into effect Feb 5; other six contracts, with various haulers and landfill owners, will be phased in by middle of April (M)