Someone in Arlington last week instinctively dialed 911 to report the murder-suicide of a mother and daughter and was connected to the Alexandria police. The caller hung up.

Within seconds, Alexandria had transmitted the information to Arlington and within minutes officers were at the scene. For police in both jurisdictions, the call was proof that 911 works, in spite of the territory's jumble of overlapping geographical zones.

Today at noon, after weeks of real and rigged tests, months of installation delays and years of intraregional disputes, 911 goes into full effect in Northern Virginia. At long last, residents of Fairfax, Arlington, Alexandria, Falls Church, Herndon, Vienna and the city of Fairfax have only to dial a simple, three-digit number to be connected to the emergency services they need.

Fearing a rash of curious callers, officials in all jursidictions stress that 911 is strictly reserved for police, fire and rescue emergencies. Routine calls everywhere should be made to nonemergency numbers listed in the phone book, although dispatchers are expecting to see an increase in calls -- possibly as high as 35 percent -- with the introduction of the new system.

Northern Virginia is the last link in the Washington area's 911 network. Residents of the District of Columbia have been dialing 911 since 1971; the same service has been available in Prince George's County since 1973 and in Montgomery since 1974. Even rural Prince William County, Va., has been hooked into 911 for fire and rescue services since the mid-70s and last July, Loudoun County went ahead with its own system.

In most of Northern Virginia inauguration of the 911 system has been frought with problems ever since Arlington proposed the idea in June 1978.

The project hit a major stumbling block in 1980 when the Alexandria City Council told its neighbors it would only participate in a costly "enhanced" 911 system, a computerized operation that would automatically have routed calls made in Alexandria to Alexandria departments, calls made in Arlington to Arlington departments, and so on.

Last fall, Alexandria agreed to go along with a "basic 911" -- the system that goes into effect today -- with the understanding that the region will consider the more sophisticated service some time in the future.

The basic 911 posed problems for Northern Virginia's eight political entities that never existed in Maryland. Since jurisdictional boundaries do not conform to the phone company's phone center zones, the system will require some juggling -- as in the case of the phone tip on last week's murder-suicide.

In Arlington, for instance, an estimated 26,000 residents will find their 911 calls picked up in Alexandria or in Fairfax and relayed by another three-digit code back to Arlington.

In all, there will be four communications centers -- Fairfax, Arlington, Alexandria and Loudoun -- accepting 911 calls. The smaller communities of Fairfax City, Vienna, Falls Church and Herndon still will advertise their old police emergency numbers, although any emergency phoned in on 911 quickly will be routed to the proper departments.

All this has taken a rare amount of cooperation, preparation and training, but there is agreement that it is worth while. Among the most enthusiastic about the system is Fairfax Supervisors Chairman John F. Herrity, who recalled for the Alexandria City Council last year that when he had a heart attack it took his family several minutes to figure out which of the 13 Northern Virginia emergency numbers to call to get help.