Queueing networks with a single shared server: light and heavy traffic

@article{Boon2011QueueingNW,
  title={Queueing networks with a single shared server: light and heavy traffic},
  author={Marko A. A. Boon and Robert D. van der Mei and Erik M. M. Winands},
  journal={SIGMETRICS Perform. Evaluation Rev.},
  year={2011},
  volume={39},
  pages={44-46}
}
  • M. BoonR. MeiE. Winands
  • Published 15 September 2011
  • Computer Science, Mathematics
  • SIGMETRICS Perform. Evaluation Rev.
We study a queueing network with a single shared server, that serves the queues in a cyclic order according to the gated service discipline. External customers arrive at the queues according to independent Poisson processes. After completing service, a customer either leaves the system or is routed to another queue. This model is very generic and finds many applications in computer systems, communication networks, manufacturing systems and robotics. Special cases of the introduced network… 

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References

SHOWING 1-8 OF 8 REFERENCES

A queueing network with a single cyclically roving server

This paper derives the generating function and the expected number of customers present in the network queues at arbitrary epochs, and compute the expected values of the delays observed by the customers, and introduces pseudo-conservation laws for this network of queues.

A cyclic service tandem queueing model with parallel queues in the first stage

This paper presents an analysis for the steady state of a two-stage tandem queueing model served by a single server, in which the first stage has two queues in parallel. Generating functions are

An M/G/1 queue with multiple types of feedback and gated vacations

This paper considers a single-server queue with Poisson arrivals and multiple customer feedbacks. If the first service attempt of a newly arriving customer is not successful, he returns to the end of

A single server tandem queue

  • S. S. Nair
  • Mathematics
    Journal of Applied Probability
  • 1971
Avi-Itzhak, Maxwell and Miller (1965) studied a queueing model with a single server serving two service units with alternating priority. Their model explored the possibility of having the alternating

Polling Systems in Heavy Traffic: A Bessel Process Limit

The analysis here extends earlier work of the authors to the general case of nonzero switch overtimes, and shows that, under the standard heavy-traffic scaling, the total unfinished work in the system tends to a Bessel-type diffusion in the heavy-Traffic limit.

Polling systems and multitype branching processes

  • J. Resing
  • Mathematics
    Queueing Syst. Theory Appl.
  • 1993
If the service discipline in each queue satisfies a certain property it is shown that the joint queue length process at polling instants of a fixed queue is a multitype branching process (MTBP) with immigration.

Towards a unifying theory on branching-type polling systems in heavy traffic

  • R. Mei
  • Mathematics
    Queueing Syst. Theory Appl.
  • 2007
It is shown that for this class of polling models the vector that describes the state of the system at these polling instants, say X, satisfies the following heavy-traffic behavior, leading to exact—and in many cases even closed-form—expressions for the Laplace-Stieltjes Transform of the complete asymptotic queue-length and waiting-time distributions.

Customer Routing on Polling Systems