Semi-explicit solutions for M/PH/1-like queuing systems

Abstract A large class of queuing systems have a stationary probability vector of matrix-geometric form. The essential step in the computation algorithm is the evaluation of a matrix R , the unique nonnegative solution of a matrix quadratic equation. The matrix R is usually determined by successive approximations. An explicit form of R is proposed, for systems that resemble the M/PH/1 queue.