Quasi-Birth-and-Death Processes with Rational Arrival Process Components
نویسندگان
چکیده
In this paper we introduce the concept of a Quasi-Birth-and-Death process (QBD) with Rational Arrival Process components. We use the physical interpretation of a Rational Arrival Process (RAP), developed by Asmussen and Bladt, to consider such a Markov process. We exploit this interpretation to develop an analytic method for such a process, that parallels the analysis of a traditional QBD. We demonstrate the analysis by considering a queue where the arrival process and the sequence of service times are derived from two different RAPs that are not just Markovian Arrival processes. We also introduce an element of correlation between the arrival process and the sequence of service times.
منابع مشابه
Exhaustive vacation queue with dependent arrival and service processes
This paper presents a more general class of MAP/MAP/1 exhaustive vacation queue, in which the Markov modulated arrival and service processes are dependent. This model class requires the evaluation of the busy period of quasi birth death process with arbitrary initial level, which is a new analysis element. The model is analyzed by applying matrix analytic methods for the underlying quasi birth ...
متن کاملA Note on Quasi-stationary Distributions of Birth-death Processes and the Sis Logistic Epidemic
For Markov processes on the positive integers with the origin as an absorbing state, Ferrari, Kesten, Martinez and Picco [4] studied the existence of quasi-stationary and limiting conditional distributions by characterizing quasi-stationary distributions as fixed points of a transformation Φ on the space of probability distributions on {1, 2, . . .}. In the case of a birth-death process, one ca...
متن کاملTwo questions on linear QBD’s (quasi-birth-and-death) processes
Contents 1 Quasi birth and death processes 1 2 The QBD of the linear retrial/overflow model 3 3 The factorial moments 8 1 Quasi birth and death processes Motivation. Many important stochastic models involve mul-tidimensional random walks with discrete state space, whose coordinates split naturally into
متن کاملAnalysis of Queues with Markovian Service Processes∗
Markovian service process (MSP) is a model similar to the Markovian arrival process (MAP), where arrivals are replaced with service completions. The MSP can represent various queueing models such as vacation models, N -policy models and exceptional service models. We analyze MAP/MSP/1 queues and obtain a new sort of matrix-type factorization of the vector generating function for the stationary ...
متن کاملBirth-death Processes with Killing: Orthogonal Polynomials and Quasi-stationary Distributions
The Karlin-McGregor representation for the transition probabilities of a birth-death process with an absorbing bottom state involves a sequence of orthogonal polynomials and the corresponding measure. This representation can be generalized to a setting in which a transition to the absorbing state (killing) is possible from any state rather than just one state. The purpose of this paper is to in...
متن کامل