The 12-year-old Grand Design for Washington's 101-mile subway system will creep 3.52 miles closer to fulfillment next Saturday when Metro opens three more stations including the eastern terminus of the Blue Line, Addison Road.

The new stations, one in the District of Columbia and two in Prince George's County, will serve primarily residential areas that have seen better days. Yet in these areas a large number of residents depend heavily on public transportation and the new stations are expected to add thousands of subway riders.

With the opening of the Addison Road extension at a cost of $179 million, the operating subway system will be 37 miles long with 40 stations. So far, it has cost an average of $68 million a mile to build Metro for a total of about $2.5 billion.

The new extension will run from the present Stadium-Armory station east along the elevated tracks through the RFK Stadium parking lot, then will separate from the existing Orange Line tracks and dive under Benning Road just after crossing the Anacostia River.

The line will be in tunnel almost all of the way, but will emerge from the side of a hill just before the open-air Addison Road terminal.

The new District of Columbia station, Benning Road, is located on the northeast corner of Benning Road and East Capital Street NE. The middle of the three new stations, Capitol Heights, is immediately east of the District-Prince George's County line, on the southeast corner of Southern Avenue and East Capitol Street. The Addison Road station itself is south of Central Avenue, just east of Addison Road.

The passenger platforms are in the center of all the stations. The Benning Road and Capitol Heights stations display the traditional Metro vaulted arch underground construction. The Addison Road station is the first outdoor station in the system that has a station-long skylight over the center of the platform.

When the line opens for paying customers next Sunday, experienced Blue Line riders accustomed to boarding trains marked Stadium-Armory will instead board trains that say Addison Road (assuming the destination signs work). National Airport, a 3 1/2-year-old temporary terminus, will be the final destination for trains at the other end of the Blue Line for at least another 20 months.

The opening of the Addison Road segment is expected by Metro to boost subway ridership by about 15,000 trips per weekday, up from its present 181,000.

The segment should also improve the daily operation for all riders on the Blue and Orange lines, which share the same track between Stadium-Armory and Rosslyn.

Many of the new riders will get there by bus, many will walk from the garden apartment and town houses near the stations, and many more will drive. There will be a total of 800 parking places at the Capitol Heights and Addison Road stations, although no all-day parking is provided at the Benning Road station. Some car drivers who now use the Orange Line lots at New Carrollton, Landover and Cheverly are expected to shift to the Blue Line stations.

The biggest new lot, at Addison Road, is 2 1/2 difficult miles from the Beltway's Central Avenue exit. Central Avenue is being widended from two to four lanes and the official completion date for that project is late December. An enormous amount of work remains to be done, however, and the drive today is serpentine and slow.

Bus routes will be changed Jan. 4 to improve connections with the three new stations, but neither the District nor Prince George's County is planning major cutbacks in existing bus service along the East Capitol Street-Benning Road corridor. Such cutbacks were made particularly in Virginia and Maryland, after earlier openings.

In the District, the decision to subsidize some duplicative bus and subway service is attributable to the fact the subway charges more than the bus for rush-hour trips of longer than three miles, and many of the city's poorest residents live in the areas served by the Benning Road and Capitol Heights stations. The bus fare is the same for all rides within the District of Columbia. The District has reduced some duplicative bus service, but citizen complaints have resulted in the maintenance of other duplicative lines, particularly those serving areas east of the Anacostia.

The District government will pay Metro an extra subsidy of 10-cents-per-ride for passengers boarding or leaving the Benning Road station, the same discount it now offers those who use the Orange Line D.C. stations of Deanwood and Minnesota Avenue, which are also east of the Anacostia. The fare-collecting system Metro uses automatically figures the fare and the discount and then deducts the proper amount from a rider's farecard.

Metro's Transit Police, as in the past, will stress high-visibility patrolling at the new stations and along the new stretch of line for the first few weeks of operation. Seven patrolmen have been added to the Transit Police force, to bring its authorized strength to 279.

According to Metro officials, Blue Line trains will no longer have to turn around in the elevated storage track near the Stadium parking lot, an awkward process that sometimes causes delays on both lines. Instead the trains will be able to proceed directly to the Addison Road station where crossover switches were designed for end-of-the-line operation.

Metro will need 250 subway cars during rush hour to operate this system, and that is about the maximum number available at any one time. Metro seems to have recovered from chronic car shortages it was suffering in the summer, but there is still a shortage of qualified subway car mechanics at Metro.

The original order of 300 cars will be supplemented next year with the first of 90 new cars. Metro's next opening -- the Red Line extension from DuPont Circle north under Connecticut Avenue to Van Ness Center -- is tentatively scheduled for April 1982 but is dependent on the arrival of the first of those new cars.

Addison Road will be the last Metro station to open east of the Anacostia River for at least six years, under the present construction schedule. The other line that is scheduled to cross the river, the Green line from Greenbelt to Rosecroft Raceway through Anacostia, is last on the construction schedule as area politicians strive to settle touchy issues about routing and station location.

In addition to having 37 mile in operation, Metro has another 29 miles and 22 stations under construction, and 14.5 miles and 10 stations in design. However, as always, the future of Metro's construction program is clouded in a continuing series of sometimes petty regional disputes and the ever-present question of how much the federal government will be willing to help, since it pays 80 percent of the bill for new subway construction. It is estimated, using perhaps optimistic projections for inflation, that Metro will cost a total of $8.2 billion and be completed in 1990. That schedule assumes fairly heavy spending in the next few years but, as Metro keeps pointing out to the federal Office of Management and Budget, the longer it takes, the more it will cost.