Details

Autor(en) / Beteiligte

• GRASSMANN, Winfried K
• DREKIC, Steve

Titel

An analytical solution for a tandem queue with blocking

Ist Teil von

• Queueing systems, 2000, Vol.36 (1-3), p.221-235

Ort / Verlag

Dordrecht: Kluwer

Erscheinungsjahr

2000

Quelle

SpringerLINK Contemporary (Konsortium Baden-Württemberg)

Beschreibungen/Notizen

• The model considered in this paper involves a tandem queue with two waiting lines, and as soon as the second waiting line reaches a certain upper limit, the first line is blocked. Both lines have exponential servers, and arrivals are Poisson. The objective is to determine the joint distribution of both lines in equilibrium. This joint distribution is found by using generalized eigenvalues. Specifically, a simple formula involving the cotangent is derived. The periodicity of the cotangent is then used to determine the location of the majority of the eigenvalues. Once all eigenvalues are found, the eigenvectors can be obtained recursively. The method proposed has a lower computational complexity than all other known methods. [PUBLICATION ABSTRACT]