We construct a stochastic fluid process with an underlying piecewise deterministic Markov (PDMP) akin to the one used in construction of rational arrival (RAP) Asmussen and Bladt (1999) which we call RAP-modulated process. As opposed classic Markov-modulated driven by jump process, PDMP has continuous state space is matrix parameters may not be related intensity matrix. Through novel techniques...

The purpose of this paper is to study the classification problem of discrete time and continuous time Markov processes of matrix M/G/1 type with a tree structure. We begin this paper by developing a computational method to find whether a Markov process of matrix M/G/1 type with a tree structure is positive recurrent, null recurrent, or transient. The method is then used to study the impact of t...

We address the transient analysis of networks of queues with exponential service times. Such networks can easily have such a huge state space that their exact transient analysis is unfeasible. In this paper we propose an approximate transient analysis technique based on decomposing the queues of the network using a compact and approximate representation of the departure process of each queue. N...

We consider a uid queue receiving its input from the output of a Marko-vian queue with nite or innnite waiting room. The input rate of the uid queue is characterized by a Markov modulated rate process. We derive a new approach for the computation of the stationary buuer content. This approach leads to a numerically stable algorithm for which the precision of the result can be given in advance. ...

Motivated by the fault tolerance for manufacturing, we investigate a renewal input bulk arrival queue with fault-tolerant server, in which server can keep working low service rate even if partial failure occurs. Only when there are no customers system, be removed. To explore performance measures of queue, more generic and simpler algorithm based on right shift operator method solving difference...

Queues with Markovian arrival and service processes, i.e., MAP/MAP/1 queues, have been useful in the analysis of computer and communication systems and di erent representations for their stationary sojourn time and queue length distribution have been derived. More speci cally, the class of MAP/MAP/1 queues lies at the intersection of the class of QBD queues and the class of semi-Markovian queue...

Abstract Two GI/M/1 type Markov chains associated with the queue length are often used in analyzing the discrete time MAP/PH/K queue. The first Markov chain is introduced by tracking service phases for servers; a method we call TPFS. The transition probability matrix of the Markov chain can be constructed in a straightforward manner. The second Markov chain is introduced by counting servers for...

Abstract This paper considers a FIFO single-server queue with service interruptions and multiple batch Markovian arrival streams. The server state (on and off), the type of arriving customers and their batch size are assumed to be governed by a continuous-time Markov chain with finite states. To put it more concretely, the marginal process of the server state is a phase-type alternating Markov ...

Key properties of multimedia traac are characterized by the great diversity of correlation and burstiness. Construct the multimedia traac by heterogeneous 2-state Markov chains as in 1] 2]. Here we allow each 2-state MC to be deened on diierent transition intervals, representing the diversity of peak access rate from individual sources. Upon time renormalization, the queue is modeled by a multi...

We present a non-equilibrium analysis and control approach for the Active Queue Management (AQM) problem in communication networks. Using simplified fluid models we carry out a bifurcation study of the complex dynamic queue behavior to show that non-equilibrium methods are essential for analysis and optimization in the AQM problem. We investigate an ergodic theoretic framework for stochastic mo...