Exact and approximate numerical solutions of steady-state distributions arising in the queue GI/G/1
Queueing Systems: Theory and Applications - Numerical computations in queues
Waiting time, busy periods and output models of a server analyzed via Wiener-Hopf factorization
Performance Evaluation - Special issue on performance and control of network systems
Probability and Statistics with Reliability, Queuing and Computer Science Applications
Probability and Statistics with Reliability, Queuing and Computer Science Applications
Numerical approximations for the steady-state waiting times in a GI/G/1 queue
Queueing Systems: Theory and Applications
Markov chain representations of discrete distributions applied to queueing models
Computers and Operations Research
SMCtools '06 Proceeding from the 2006 workshop on Tools for solving structured Markov chains
Algorithmic analysis of the discrete time GIX/GY/1 queueing system
Performance Evaluation
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In this paper, we show that the discrete GI/G/1 system can be easily analysed as a QBD process with infinite blocks by using the elapsed time approach in conjunction with the Matrix-geometric approach. The positive recurrence of the resulting Markov chain is more easily established when compared with the remaining time approach. The G-measure associated with this Markov chain has a special structure which is usefully exploited. Most importantly, we show that this approach can be extended to the analysis of the GIX/G/1 system. We also obtain the distributions of the queue length, busy period and waiting times under the FIFO rule. Exact results, based on computational approach, are obtained for the cases of input parameters with finite support – these situations are more commonly encountered in practical problems.