213,441 research outputs found
The Mx/G/1 queue with queue length dependent service times
We deal with the MX/G/1 queue where service times depend on the queue length at the service initiation. By using Markov renewal theory, we derive the queue length distribution at departure epochs. We also obtain the transient queue length distribution at time t and its limiting distribution and the virtual waiting time distribution. The numerical results for transient mean queue length and queue length distributions are given.Bong Dae Choi, Yeong Cheol Kim, Yang Woo Shin, and Charles E. M. Pearc
On a generic class of two-node queueing systems
This paper analyzes a generic class of two-node queueing systems. A first queue is fed by an onāoff Markov fluid source; the input of a second queue is a function of the state of the Markov fluid source as well, but now also of the first queue being empty or not. This model covers the classical two-node tandem queue and the two-class priority queue as special cases. Relying predominantly on probabilistic argumentation, the steady-state buffer content of both queues is determined (in terms of its Laplace transform). Interpreting the buffer content of the second queue in terms of busy periods of the first queue, the (exact) tail asymptotics of the distribution of the second queue are found. Two regimes can be distinguished: a first in which the state of the first queue (that is, being empty or not) hardly plays a role, and a second in which it explicitly does. This dichotomy can be understood by using large-deviations heuristics
Heavy-traffic analysis of k-limited polling systems
In this paper we study a two-queue polling model with zero switch-over times
and -limited service (serve at most customers during one visit period
to queue , ) in each queue. The arrival processes at the two queues
are Poisson, and the service times are exponentially distributed. By increasing
the arrival intensities until one of the queues becomes critically loaded, we
derive exact heavy-traffic limits for the joint queue-length distribution using
a singular-perturbation technique. It turns out that the number of customers in
the stable queue has the same distribution as the number of customers in a
vacation system with Erlang- distributed vacations. The queue-length
distribution of the critically loaded queue, after applying an appropriate
scaling, is exponentially distributed. Finally, we show that the two
queue-length processes are independent in heavy traffic
Simple and efficient importance sampling scheme for a tandem queue with server slow-down
This paper considers importance sampling as a tool for rare-event simulation. The system at hand is a so-called tandem queue with slow-down, which essentially means that the server of the first queue (or: upstreanm queue) switches to a lower speed when the second queue (downstream queue) exceeds some threshold. The goal is to assess to what extent such a policy succeeds in protecting the first queue, and therefore we focus on estimating the probability of overflow in the downstream queue.\ud
It is known that in this setting importance sampling with traditional state-independent distributions performs poorly. More sophisticated state-dependent schemes can be shown to be asymptotically efficient, but their implementation may be problematic, as for each state the new measure has to be computed. This paper presents an algorithm that is considerably simpler than the fully state-dependent scheme; it requires low computational effort, but still has high efficiency
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