Whittle, P. Partial balance and insensitivity. (English) Zbl 0561.60095 J. Appl. Probab. 22, 168-176 (1985). The problems of partial balance and insensitivity are revisited in the context of a discrete state continuous time Markov process \(X=(X_ t).\) I) Partial balance over a subset A of the state space means that for every \(x\in A\) the (equilibrium) probability flow from A to x equals the flow from x to A. II) Insensitivity of the steady state distribution of X ”to nominial sojourn time in A” states that the distribution of the nominal sojourn time in A may be changed without effecting the steady state if the mean sojourn time in A remains invariant. The author shows that property I) holds if and only if II) holds, and gives a multiset version of this theorem. The paper is part of a sequence of articles which consider insensitivity and partial (or local) balance. (See the references.) Its advantage is that the standard terminology of Markov processes is used. Reviewer: H.Daduna Cited in 2 ReviewsCited in 18 Documents MSC: 60K25 Queueing theory (aspects of probability theory) 90B22 Queues and service in operations research Keywords:partial balance; insensitivity; steady state distribution PDFBibTeX XMLCite \textit{P. Whittle}, J. Appl. Probab. 22, 168--176 (1985; Zbl 0561.60095) Full Text: DOI