Queueing Systems: Theory and Applications - Special issue of queueing systems, theory and applications
A tandem Jackson network with feedback to the first node
Queueing Systems: Theory and Applications
Retrial networks with finite buffers and their application to internet data traffic
Probability in the Engineering and Informational Sciences
Accessible bibliography on retrial queues
Mathematical and Computer Modelling: An International Journal
A new computational algorithm for retrial queues to cellular mobile systems with guard channels
Computers and Industrial Engineering
Queues in tandem with customer deadlines and retrials
Queueing Systems: Theory and Applications
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We consider systems of tandem blocking queues having a common retrial queue. The model represents dynamics of short TCP transfers in the Internet. Analytical results are available only for a specific example with two queues in tandem. We propose approximation procedures involving simple analytic expressions, based on mean value analysis (MVA) and on fixed point approach (FPA). The mean sojourn time of a job in the system and the mean number of visits to the orbit queue are estimated by the MVA which needs as an input the fractions of blocked jobs in the primary queues. The fractions of blocked jobs are estimated by FPA. Using a benchmark example of the system with two primary queues, we conclude that the approximation works well in the light traffic regime. We note that our approach becomes exact if the blocking probabilities are fixed. Finally, we consider two optimization problems regarding minimizing mean total sojourn time of a job in the system: (i) finding the best order of queues and (ii) allocating a given capacity among the primary queues.