Matrix-Geometric Solution for Two Node Tandem Queueing Systems with Phase-Type Servers Subject to Blocking and Failures
Abstract
A two node tandem queueing system with phase-type servers and Bernoulli arrivals is considered in discrete-time when servers are subject to blocking and failures. The invanant probability vector of the the underlying finite state Quasi-Birth-and-Death process is shown to admit a matrix- geometric representation for all values of the arrival rate wavelength. The corresponding rate matrix is given explicitly in terms of the modA parameters and the resulting closed-form expression provides the basis for an efficient calculation of the invariant probability vector. The cases wavelength = 1 and wavelength < 1 are studied separately and the irreducibilty of the underlying Markov chain is discussed for each case. The continuous-time formulation is bnefly discussed and only major differences with the discrete-time results are pointed out. Some numerical examples are also provided.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1987
- Accession Number
- ADA452456
Entities
People
- Armand M. Makowski
- Levent Guen
Organizations
- University of Maryland