Analysis of the GI/Geo/<i>c</i> Queue with Working Vacations

Abstract

Working vacation queue models are well applied in the modeling and analysis of the router in optical networks. The GI/Geo/c queue with working vacations is studied in this paper. Through establishing two-dimensional Markov chain and using matrix-geometric solution method, the stability condition is derived. Adopting UL-type RG-factorization of irreducible Markov chain, the stationary distribution is given. Based on these, the probability distribution of queue-length and PGF of waiting time are obtained in the end.

Analysis of $GI^{[X]}/D$-$MSP/1/\infty$ queue using $RG$-factorization

“…While the LUtype RG-factorization is a key technique for calculating the transient performance measures such as the first passage time, the waiting-time and the sojourn time. In this connection, readers are referred to Li et al [22], Wang et al [38], Jiang and Liu [20], Zhang and Hou [40], Avram and Chedom [6], Gao and Liu [14], and Yu and Alfa [39], who have used the RG-factorization.…”