ARMONK, N.Y. — International Business Machines Corp. said Wednesday it agreed to acquire Micromuse Inc., which makes software that manages video and voice traffic on computer networks, for about $865 million in cash.

Under the definitive agreement, Armonk-based IBM is paying shareholders $10 for each Micromuse share, almost a 40 percent premium to its closing price of $7.21 on Tuesday. Micromuse shares surged $2.71, or 37.6 percent, to close at $9.92 on the Nasdaq Stock Market. The stock had previously traded in a 52-week range of $3.97 to $8.13.

San Francisco-based Micromuse's software is used to monitor and manage network traffic by about 1,800 clients such as Time Warner Inc.'s America Online, E-Trade Financial Corp., Verizon Communications Inc. and other corporate and government customers.

Consumers ultimately benefit when telecommunications carriers and other companies are able to use Micromuse's software to detect and diagnose problems, said Steve Mills, a senior vice president for IBM's software products.

Such tools are increasingly crucial, he said, as Internet technologies become the basis for phone calls, voice mail services and even video programs.

"There's a clear growth in network convergence," he said. "It's an important space for our customers, and it's an area where we've had gaps."

The acquisition boosts IBM's software portfolio as the company increasingly turns its focus to business services. Revenue from Micromuse's customers grew 10 percent to $160.8 million in fiscal 2005.