2,906 research outputs found
A Fixed-Point Algorithm for Closed Queueing Networks
In this paper we propose a new efficient iterative scheme for solving closed queueing networks with phase-type service time distributions. The method is especially efficient and accurate in case of large numbers of nodes and large customer populations. We present the method, put it in perspective, and validate it through a large number of test scenarios. In most cases, the method provides accuracies within 5% relative error (in comparison to discrete-event simulation)
Rejoinder on: queueing models for the analysis of communication systems
In this rejoinder, we respond to the comments and questions of three discussants of our paper on queueing models for the analysis of communication systems. Our responses are structured around two main topics: discrete-time modeling and further extensions of the presented queueing analysis
Power series approximations for two-class generalized processor sharing systems
We develop power series approximations for a discrete-time queueing system with two parallel queues and one processor. If both queues are nonempty, a customer of queue 1 is served with probability beta, and a customer of queue 2 is served with probability 1-beta. If one of the queues is empty, a customer of the other queue is served with probability 1. We first describe the generating function U(z (1),z (2)) of the stationary queue lengths in terms of a functional equation, and show how to solve this using the theory of boundary value problems. Then, we propose to use the same functional equation to obtain a power series for U(z (1),z (2)) in beta. The first coefficient of this power series corresponds to the priority case beta=0, which allows for an explicit solution. All higher coefficients are expressed in terms of the priority case. Accurate approximations for the mean stationary queue lengths are obtained from combining truncated power series and Pad, approximation
Stability Region of a Slotted Aloha Network with K-Exponential Backoff
Stability region of random access wireless networks is known for only simple
network scenarios. The main problem in this respect is due to interaction among
queues. When transmission probabilities during successive transmissions change,
e.g., when exponential backoff mechanism is exploited, the interactions in the
network are stimulated. In this paper, we derive the stability region of a
buffered slotted Aloha network with K-exponential backoff mechanism,
approximately, when a finite number of nodes exist. To this end, we propose a
new approach in modeling the interaction among wireless nodes. In this
approach, we model the network with inter-related quasi-birth-death (QBD)
processes such that at each QBD corresponding to each node, a finite number of
phases consider the status of the other nodes. Then, by exploiting the
available theorems on stability of QBDs, we find the stability region. We show
that exponential backoff mechanism is able to increase the area of the
stability region of a simple slotted Aloha network with two nodes, more than
40\%. We also show that a slotted Aloha network with exponential backoff may
perform very near to ideal scheduling. The accuracy of our modeling approach is
verified by simulation in different conditions.Comment: 30 pages, 6 figure
Two-dimensional fluid queues with temporary assistance
We consider a two-dimensional stochastic fluid model with ON-OFF inputs
and temporary assistance, which is an extension of the same model with
in Mahabhashyam et al. (2008). The rates of change of both buffers are
piecewise constant and dependent on the underlying Markovian phase of the
model, and the rates of change for Buffer 2 are also dependent on the specific
level of Buffer 1. This is because both buffers share a fixed output capacity,
the precise proportion of which depends on Buffer 1. The generalization of the
number of ON-OFF inputs necessitates modifications in the original rules of
output-capacity sharing from Mahabhashyam et al. (2008) and considerably
complicates both the theoretical analysis and the numerical computation of
various performance measures
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