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Statistical procedures for estimating branch flows and total network flow
Author(s) -
Wells Charles E.,
Evans James R.
Publication year - 1989
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/net.3230190407
Subject(s) - flow network , cash flow , flow (mathematics) , computer science , mathematical optimization , variance (accounting) , quadratic equation , function (biology) , maximum flow problem , mathematics , geometry , accounting , evolutionary biology , business , biology
The problem fo estimating branch flows and total network flow in a directed acyclic network is important in diverse applications, such as: (1) in the measurement of rainfall and water run off and (2) in cash control as cash receipts move through an accounting system. In this paper, a variety of network flow estimation problems are examined, where the measurement errors of the observed branch flows may be correlated. Procedures are presented which produce branch flow estimates that conserve flow when observations of flow are available on all network branches and which produce total network flow estimates when observations of flow are available on only a subset of network branches. The latter procedure uses observed flows through proper cut sets. Also included is a discussion of a tractable method of computing biased total network flow estimates. These biased estimates have the potential advantage of having a relatively small variance. All of the estimation procedures presented derive estimates from the solution of appropriately formaulated mathematical programs whose objective function is a quadratic form. An example is included to illustrate the ease of use of the proposed estimation procedures.