Abstract
This contribution avoids frequently used transform and inversion problems by a decomposition of the transition state model in the original domain. First, the relevant differential‐recurrence backward equation system valid for the M/M/1 processor sharing (PS) is converted to a sum of a service component and an arrival–departure component. The first one yields a pure differential equation system, which can be solved exactly and proves to be uniformly valid for M/G/1 PS systems. The second component vanishes for small and large processor utilisations but contributes to shorter response times otherwise. Thus, the PS service component defines an estimate of the true response time distribution. Second, the higher order moments of the estimates form simple upper bounds of their true much more complicated counterparts where the first moments agree. Partly simulative case studies subject to M, D, H2, heavy‐tailed service time distributions, and PS with permanent customers confirm the new estimation. Third, reference values of the arrival–departure component provide an approximate solution of the differential‐recurrence equation system. This significantly improves the accuracy of the estimates for moderate utilisations. Finally it is shown that the remaining inaccuracies of the estimates are far below expectable forecast errors for high economic loads and otherwise the approximation significantly supports PS system engineering for moderate loads too. Copyright © 2007 John Wiley & Sons, Ltd.