The equilibrium joint state probabilities of interacting Markov processes are obtained in a hierarchical way, by finding the reversed process of the interaction in terms of the reversed processes of the components. From a reversed process, a product-form solution for the joint state probabilities follows directly. The method uses a Markovian process algebra formalism and generalizes the recent ...

The equilibrium joint state probabilities of interacting Markov processes are obtained in a hierarchical way, by finding the reversed process of the interaction in terms of the reversed processes of its components. From a reversed process, a product-form solution for the joint state probabilities follows directly. The method uses a Markovian process algebra formalism and generalizes the recent ...

We consider a stochastic fluid flow model with a single server and K infinite capacity buffers. The input to the k-th buffer is a Markovian on-off process that transmits fluid at a constant rate pk while it is on and at rate 0 while it is off. The fluid is emptied from the buffers by a single server at a constant rate μ according to a static priority service discipline in which class 1 fluid ha...

Motivated by the need to study traffic incident management, we consider a Markovian infinite server queue that is subjected to randomly occurring shocks. These shocks affect the service of all servers to deteriorate, i.e., increase the service time of all servers, and might also cause other shocks, thus causing further service deterioration. There are a finite number of service levels, zero cor...

This paper provides a performance evaluation of the TETRAPOL random access protocol. The results are based on a Markovian model which is also presented. The Markovian model is used to derive quality of service parameters, e.g. mean throughput, waiting probability, and mean random access delay. The analytical results are compared to results based on stochastic simulation. Our prototypic implemen...

A decision process in which rewards depend on history rather than merely on the current state is called a decision process with non-Markovian rewards (NMRDP). In decisiontheoretic planning, where many desirable behaviours are more naturally expressed as properties of execution sequences rather than as properties of states, NMRDPs form a more natural model than the commonly adopted fully Markovi...

This article describes the batch Markovian arrival process (BMAP), a point process that is characterized by Markov-modulated batch arrivals of random size. The BMAP is a generalization of many well-known processes including the Markovian arrival process (MAP), the Poisson process, and the Markov-modulated Poisson process. It provides a common framework for modeling arrival processes in a variet...

We consider a queueing system with two types of servers and two types of customers. General-use servers can provide service to either customer type while limited-use servers can be used only for one of the two. Though the apparent Markovian state space of this system is five-dimensional, we show that an aggregation results in an exact two-dimensional representation that is also Markovian. Matri...