Alexandria is using its new computerized traffic signals to look out for Number One while tweaking the nose of an old adversary: the driver who just happens to be passing through town.

Last month, by special order of the City Council, signals began serving up extra green at off-peak hours for east-west streets, where drivers tend to be taxpaying constituents running errands to Old Town, picking up youngsters from play groups or heading out on the town.

The decision means that motorists passing through town in a north-south direction on such roads as Washington Street--the through route favored by Fairfax County motorists and truck drivers--will have to spend more time at red lights during the off peak.

"The north-south traffic is largely for the convenience of outsiders, not Alexandrians," said council member Carlyle Ring, reflecting a common perception in the city.

In its $4 million signal system, which went into full operation last year, the city has a new and persuasive means of enforcing who gets priority. From City Hall, the master computer can control precisely what lights at 130 key intersections are doing at any given time.

The council's move is the latest round in a long tussle over traffic with the Virginia Department of Highways and Transportation, which took a lead role in designing the signal system. "The state, I think, basically looked at the project as an opening up of Alexandria," council member Donald Casey said.

City officials believe state highway planners have traditionally viewed Alexandria as a collection of through routes for Fairfax County commuters and commercial traffic and tend to give insufficient thought to pollution, noise and the rights of residents.

Following a trend around the country, Alexandria is the first area government to install a major computer system. The theory is that computers give better synchronization and can shift timings to fit changing traffic patterns during the day, leading to smoother flow and fuel savings.

When it went into full operation last year, the usual computer bugs made trouble and they continue. But Alexandrians were enraged to find out that even when things worked right, cross-town drivers hit red at just about every light while north-south got what seemed to be permanent green.

City Hall was bombarded with phone calls and letters. This was one civic concern with which council members had personal experience, however.

"After the last council meeting, I drove down King Street and hit six lights," Casey said. Some even took to jotting down the location of bad lights as they drove and reporting back.

State planners say they stressed north-south traffic because that is where the flow is heaviest.

"We don't take into account whether it's a resident or nonresident vehicle," said W.C. Nelson of the highways department. " . . . We're trying to handle most effectively the traffic that's on the street."

The council, however, did care who was behind the wheel. So, in November, when the state handed over control of the system to the city, the stage was set for action.

Rush-hour patterns, which heavily favor north-south, were retained. But in the off-peak hours, the computer now uses a program that gives less green to that direction. At Washington and King streets, for example, the old program gave Washington green 75 percent of the time and King 25 percent of the time, according to city traffic engineer Charles Kenyon. That has changed to 55 percent Washington and 45 percent King.

It also has put 12 intersections onto a flashing sequence at off-peak hours, with the flashing red, which means stop, facing north and south. Cross-town drivers get flashing yellow, which means proceed with caution but proceed.

City traffic technicians first had to visit eight of those intersections to reverse some wires. The system's designers had never conceived of flashing red at north-south drivers and the signals simply couldn't do it.

Many residents appear to welcome the changes, although some believe that more substantive action is needed. Others feel nervous at the flashing yellow. By law, "you've got the right of way, but you can't count on somebody giving you the right of way," said resident Pam St. Clair.

Gauging the reaction of out-of-towners is more difficult. The sentiment of Marcos Smyth, who lives just outside of Alexandria and drives through on a commute to Rockville, may be typical. Old timing or new timing, he said, "during rush hour, it just bottlenecks and backs up real bad."

North-south drivers do continue to get most of the green but less than before. Some council members look to some future date when the city might make more drastic use of its new tool, deliberately creating delays to try to choke off flow on major arteries, such as Rte. 1 and Washington Street.

"We own these streets and we maintain them," Casey said. " . . . If we decide to close them, we close them and that's it."