Tree Structured Qbd Markov Chains and Tree-like Qbd Processes

On the Generality of Binary Tree-like Markov Chains

In this paper we show that an arbitrary tree-like Markov chain can be embedded in a binary tree-like Markov chain with a special structure. When combined with [7], this implies that any tree structured QBD Markov chain can be reduced to a binary tree-like process. Furthermore, a simple relationship between the V , Rs and Gs matrices of the original and the binary tree-like Markov chain is estab...

Explorer Quasi - Birth - Death Processes , Tree - Like QBDs , Probabilistic 1 - Counter Automata , and Pushdown Systems

We begin by observing that (discrete-time) QuasiBirth-Death Processes (QBDs) are equivalent, in a precise sense, to (discrete-time) probabilistic 1-Counter Automata (p1CAs), and both Tree-Like QBDs (TLQBDs) and Tree-Structured QBDs (TS-QBDs) are equivalent to both probabilistic Pushdown Systems (pPDSs) and Recursive Markov Chains (RMCs). We then proceed to exploit these connections to obtain a ...

Analysis of a QBD process that depends on background QBD processes

We define a class of Markov chains that are called recursive foreground-background quasi-birthand-death (RFBQBD) processes, and describe approximate (nearly exact) analyses of an RFBQBD process. An RFBQBD process consists of a foreground QBD process whose transitions depend on the level of a background QBD process, where the transitions of the background QBD process may depend on the level of a...

Quasi-birth-and-death Markov processes with a tree structure and the MMAP[K]/PH[K]/N/LCFS non-preemptive queue

This paper studies a multi-server queueing system with multiple types of customers and last-come-®rst-served (LCFS) non-preemptive service discipline. First, a quasi-birth-and-death (QBD) Markov process with a tree structure is de®ned and some classical results of QBD Markov processes are generalized. Second, the MMAP[K]/PH[K]/N/LCFS non-preemptive queue is introduced. Using results of the QBD ...

Stability and Performance of Stack Algorithms for Random Access Communication Modeled as a Tree Structured Qbd Markov Chain