Tyrone Simms needed work, and Ogden Allied Aviation Services had several positions at Dulles International Airport mopping floors, cleaning kitchens and emptying garbage at $4.50 an hour.

Simms, a high school graduate from Northwest Washington, reasoned that the pay was good enough but he would never be able to afford daily transportation costs: a bus ride from his home to downtown and a $6 Metro Flyer ticket from there to Dulles.

Yet today Simms, 19, is a full-time employe of Ogden Allied, a company he says is "wonderful and everyone is so supportive." And the biggest way Ogden Allied showed its support, Simms said, was to help pay for a private van to transport him and other workers from the District to its far-flung suburban location.

What happens to Simms every day is occurring all over the the District. Suburban employers who once shunned District workers are finding them a valuable commodity in a labor market that has absorbed nearly every available worker living in the suburbs. They are trying, with increasing success and with urging from city employment specialists, to attract District residents by paying travel expenses and offering bonuses to workers willing to venture there.

Those efforts have come at the same time that more jobs have opened up in the District through a small but healthy economic growth.

As a result, the District unemployment rate -- traditionally nearly three times that of the suburbs and as high as 8 percent until recently -- has sunk to its lowest level in 15 years.

A year ago, the District unemployment rate in August stood at 7.6 percent. This August it was 6.1 percent. From January to August this year alone, the rate has dropped 1.9 percentage points, according to figures released Friday by the city's employment service office.

The rate for black men, which contributes heavily to the city's unemployment rate, also has shown comparable improvement, according to city statistics.

For young black men such as Simms, the change is dramatic. Four years ago, more than half of all 16- to 19-year-old black males and a quarter of those 20 to 24 years old who wanted jobs could not find them. Last year, the figure toppled to 31 percent for teen-agers and 16 percent for young adults. Overall in 1983, 11.7 percent of black men were unemployed. In 1986, the figure sank to 7.7 percent.

"I had no problems working out in Virginia," Simms said. "I could get up at 3:30 a.m. to get to work by 6 a.m. But I didn't have transportation. And without that, I was in a bad way. Now I'm able to work and save up money to buy a car."

Employment patterns in the region began changing about two years ago as rapid development in the suburbs brought in new businesses and skilled, educated people to work in middle- to high-income jobs. Yet the number of unskilled workers needed for service jobs to accompany such expansion could not be easily found in an affluent, high-cost area.

Even once-reliable sources of entry-level labor had diminished. The teen-age population in the suburbs declined faster than in the District, increasing the gap, labor experts said.

As a consequence, old biases -- by prospective employes unwilling to cross the Potomac River to work and prospective employers wary of hiring unskilled workers from the inner city -- have had to crumble under market demands, according to those familiar with labor needs.

"There's nothing like a shortage to force your eyes open," said Michael Gilbert, executive director of the D.C. Private Industry Council, a nonprofit community business group that trains economically disadvantaged workers in the District and matches them with jobs.

"There's no question that historically there had been a reluctance by employers to hire from the inner city. But now the labor market is so tight, they're willing to look at people they have never considered before."

"We can't afford to say to anybody, 'We don't need you,' " said Janice Cotter, human resources director for Host International, a division of Marriott, located at Dulles. "And we're trying to do what we can to have every person brought out from the District stay and bring others."

Statistics on the number of District residents working in the suburbs were not available. But labor market experts and business groups said they have noticed a sharp increase in District residents working in other jurisdictions. District officials said they have placed 6,300 people in suburban jobs since 1985 through a regional jobs program, but that figure does not include placements by businesses and other private groups.

Officials with the D.C. Department of Employment Services believe movement toward the suburbs is strong, though, based on data compiled during the past year. District residents obtained 25 percent of the new jobs in the region though they make up 17 percent of the labor force, according to city statistics.

"They're not just getting their share of District jobs," said Richard Groner, chief of the District's labor information division. "They're getting more of their share in the suburbs."

This brightening employment picture for District job seekers has evolved through no single force. In the past two years, the District has made unprecedented attempts to match employers around the region with employes and to subsidize travel costs -- an average of $157 a person for no longer than 10 weeks -- for any worker who needs an incentive to cross the District line.

District civic groups such as the Community Family Life Services Inc., headed by the Rev. Thomas Knoll, responded to service companies' pleas for workers in 1985 by starting a fledgling van pool to Dulles. Today, the group transports about 60 people a day in two shifts.

Defense contractor Tracor Inc. in Rockville, for example, began footing the bill to computerize job openings sent to Virginia and Maryland government employment agencies, and is gearing up to do the same in the District, an expense they say is repaid in quicker responses. Chambers of commerce such as one in Upper Montgomery County are planning seminars and special mailings to reach minorities who might be willing to go the distance for a job.

"Historically, we've been looking at D.C. as a city unto itself," said Edmund Cronin, president of the Greater Washington Board of Trade.

"What we're really seeing now is the culmination of the region with the city as its heart. It's just we've tended to think of this area as a city and two states unlike, say, a Chicago, which is seen as the base for a region of development."

Said Jon Gerson, executive director of the Gaithersburg and Upper Montgomery Chamber of Commerce: "We're trying very hard to make certain that populations that earlier might have been discouraged feel very positive about working here. We're looking at the D.C. market as a rich resource of entry-level workers. It almost has to be. Because there's no way that someone who earns $5 an hour can afford to live in this {Montgomery County} community."

Employers agree that transportation is the biggest barrier to getting workers into the suburbs.

But the need for adequate, low-cost child care also has played a significant role in eliminating some prospective workers, a problem the District and private employers are trying to solve.

For example, Miriam Mason, a mother of two from Southeast Washington, had never thought about looking over the District line for a job. One of her children is 4 years old. The other, age 9, was born with Down's syndrome, a genetic disorder. Mason wanted to find work but could not afford the kind of day care required for her youngsters.

Then she heard about an Urban League training program that would teach data processing and would, with District funds, pay for an at-home sitter and for travel to the suburbs. "The money gave me enough time to get on my feet," Mason said. "I didn't have enough money to keep going back and forth for job interviews in the suburbs."

Mason interviewed with Vitro Corp., a defense contractor that employs 4,000 in the Washington area and is the largest private employer in Montgomery County. She was hired at $6.50 an hour six weeks ago to review security clearances in the company's Silver Spring office.

It is a job she said she could afford to take only because of the District subsidy program that would pay part of her travel costs for 10 weeks. She takes two buses and the subway for the 1 1/2-hour ride to work.

"It's given me a little time to get my first and second checks and save some," Mason said. "And I certainly wouldn't have gone out on my own to these places for work. I would have looked in the District because of the bus fare. And in the District, there's so much competition for jobs, I was afraid I wouldn't get hired for a job I wanted."

Of the 6,300 workers placed by the District in suburban companies, nearly 1,000 received some kind of transportation subsidy to work in jobs located predominantly in Montgomery, Fairfax and Arlington counties and in Alexandria.

But employers are not relying solely on the District or government employment agencies to find workers who will come to the suburbs. They are also taking the initiative to boost benefits and provide transportation.

Host International, which operates all food service outlets at Dulles airport, has a never-ending problem finding workers, officials said. During the past year, management there has tried to appeal to the cost-conscious worker by offering a car pool subsidy of $10 a day for anyone who drives and brings in coworkers, free parking, and a free van pool from the District supplied by Knoll's Community Family Life Services.

Host also pays $50 to an employe who refers a part-time worker who stays more than 90 days. If the referral is a full-time employe, the bonus jumps to $100. A recent promotion last month offered $5 to any employe who had a prospect fill out an application. If the new worker stayed at least 30 days, the employe received another $10.

Britches of Georgetown is opening two stores in Virginia and Maryland and now operates a processing warehouse in Herndon. The competition for retail and warehouse workers has pushed the company to consider a van pool from the District and to continually assess its employe benefit plan.

In just the past couple of years, spokesmen said, the company has added dental insurance and attendance bonuses, improved medical coverage to attract workers and upgraded in-house employe training and career development.

Ogden Allied, the company that hired Simms, began cooperating in the van pool supplied by the community group after determining that it was more expensive to hire temporaries than full-time workers who would have to be bused to Dulles from the District. The cost of $6.03 an hour -- $4.50 plus benefits -- was well spent in comparison to the $7.50-an-hour price Ogden Allied would have paid to a temporary agency to place a worker, a spokesman said. "We found we have better control," said Mark Goodwin, general manager for in-flight services. "When you have the same people day in and day out, you can instill discipline, there's less damage and the person begins to feel part of the company."

For Tyrone Simms, the unexpected foray into the suburbs has led to a job that he said he hopes will lead to advancement both in position and salary. "This job is so much better than what I'd be doing at a fast-food restaurant," Simms said. "If companies who want workers would just make the investment of providing vans, they would get returns many times over. Because there are people who want to work."