Performance approximations of Markov Modulated Poisson Process arrival queue with Markovian Service using matrix geometric approach

Abstract

Queue analysis of correlated work of the arrival and the service process are not available much in literature. This research paper applies matrix geometric approach to study the MMPP/MSP/1 queuing model under the quasi-birth death(QBD) process. Customers admitted in the system are having two different intensity of arrival followed by Markov Modulated Poisson Process(MMPP). MMPP is a versatile class of MAP and it is necessary to adapt the first characterization of the queuing model. In service mechanism Markov Service Process(MSP) is adopted. As like MMPP, MSP is also a versatile and can capture the correlation of the modulated arrivals. The methodology presented in this research work calculates the metric performances not depending on the series of infinite state of the system. The assumed model is formulated as QBD process to obtain the steady state probability of the system. The complexity model formulated involves structures matrices with appropriate dimension. Neut’s pioneered the matrix geometric approach to such complex models which involves the rate computation of rate matrix R. The rate matrix R is approximated to derive the performance metrics of the system and then compute the cost for the underlying Markov chain. To attain this approximation the sensitivity analysis is done with numerical results.

Keywords

• (mmpp)
• (msp)
• performance analysis
• quasi-birth-death process
• structured markov chain
• optimal cost