Solving Structured Markov Chains and Applications to Performance Analysis of Communication Networks

by

Nail Akar
Bilkent University 

The Birth and Death (BD) process, M/G/1 and G/M/1 queues are fundamental queueing systems and all three systems are explored in almost every queueing textbook. The introduction of an additional dimension (i.e., phase process) generalizes the above queueing systems to certain structured Markov chains called the Quasi-Birth-and-Death (QBD) process, and M/G/1 and G/M/1 type Markov chains, respectively. These structured Markov chains play a crucial role in the performance analysis of computer and communication networks. This talk surveys through these queueing systems and their applications from a "communication networks" perspective. Moreover, the so-called "invariant subspace" approach to solve such Markov chains is outlined and several extensions and new directions are explored.