Queueing Systems: Theory and Applications
The MMAP[K]/PH[K]/1 queues with a last-come-first-served preemptive service discipline
Queueing Systems: Theory and Applications
Probability in the Engineering and Informational Sciences
Single-Server Queues with Markov-Modulated Arrivals and Service Speed
Queueing Systems: Theory and Applications
A queueing model for multi-product production system under varying manufacturing environment
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and Its Applications - Volume Part IV
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This paper considers a stationary single-server queue with multiple arrival streams governed by a Markov chain, where customers are served on an LCFS preemptive-resume basis. Service times of customers from each arrival stream are generally distributed and service time distributions for different arrival streams may be different. Under these assumptions, it is shown that the stationary joint distribution of queue strings representing from which arrival stream each customer in the system arrived and remaining service times of respective customers in the system has a matrix product-form solution, where matrices constituting the solution are given in terms of the infinitesimal generator of a certain Markov chain. Compared with the previous works, the result in this paper is more general in the sense that general service time distributions are allowed, and it has the advantage of computational efficiency. Note also that the result is a natural extension of the classical result for the LCFS-PR M/G/1 queue. Further, utilizing the matrix product-form solution, we derive a new expression of the vector Laplace–Stieltjes transform of the stationary distribution of unfinished work in the work-conserving single-server queue with multiple arrival streams governed by a Markov chain, which is given by the sum of matrix-geometric series.