The queue M/G/1 with Markov modulated arrivals and services
Mathematics of Operations Research
Markov-modulated PH/G/1 queueing systems
Queueing Systems: Theory and Applications
Performance '93 Proceedings of the 16th IFIP Working Group 7.3 international symposium on Computer performance modeling measurement and evaluation
Analysis of a nonpreemptive priority queue with SPP arrivals of high class
Performance Evaluation
Queueing Systems: Theory and Applications
The BMAP/G/1 QUEUE: A Tutorial
Performance Evaluation of Computer and Communication Systems, Joint Tutorial Papers of Performance '93 and Sigmetrics '93
The Nonpreemptive Priority Map/G/1 Queue
Operations Research
Matrix-geometric solutions of M/G/1-type Markov chains: a unifying generalized state-space approach
IEEE Journal on Selected Areas in Communications
The M/G/1 FIFO Queue with Several Customer Classes
Queueing Systems: Theory and Applications
Single-Server Queues with Markov-Modulated Arrivals and Service Speed
Queueing Systems: Theory and Applications
Queueing Systems: Theory and Applications
Multiclass Markovian fluid queues
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 the queue length distribution in a class of FIFO single-server queues with (possibly correlated) multiple arrival streams, where the service time distribution of customers may be different for different streams. It is widely recognized that the queue length distribution in a FIFO queue with multiple non-Poissonian arrival streams having different service time distributions is very hard to analyze, since we have to keep track of the complete order of customers in the queue to describe the queue length dynamics. In this paper, we provide an alternative way to solve the problem for a class of such queues, where arrival streams are governed by a finite-state Markov chain. We characterize the joint probability generating function of the stationary queue length distribution, by considering the joint distribution of the number of customers arriving from each stream during the stationary attained waiting time. Further we provide recursion formulas to compute the stationary joint queue length distribution and the stationary distribution representing from which stream each customer in the queue arrived.