
For FullText PDF, please login, if you are a member of IEICE,
or go to Pay Per View on menu list, if you are a nonmember of IEICE.

Linear Transformations between Embedded Processes Associated with M/M/1 Queueing Systems
Toshikane ODA Aurel A. LAZAR
Publication
IEICE TRANSACTIONS on Communications
Vol.E75B
No.12
pp.13081314 Publication Date: 1992/12/25 Online ISSN:
DOI: Print ISSN: 09168516 Type of Manuscript: Special Section PAPER (Special Issue on Teletraffic) Category: Keyword: Markovian queueing systems, linear transformations, embedded Markov chains, arrival and departure theorems,
Full Text: PDF>>
Summary:
The embedded Markov processes associated with Markovian queueing systems are closely related, and their relationships are important for establishing an analytical basis for performance evaluation techniques. As a first step, we analyze the embedded processes associated with a general M/M/1 queueing system. Linear transformations between the infinitesimal generators and the transition probability matrices of embedded processes at arrival and departure times are explicitly derived. Based upon these linear transformations, the equilibrium distributions of the system states at arrival and departure times are obtained and expressed in terms of the equilibrium distribution at arbitrary times. The approach presented here uncovers an underlying algebraic structure of M/M/1 queueing systems, and establishes an algebraic methodology for analyzing the equilibrium probabilities of the system states at arrival and departure times for more general Markovian queueing systems.

