3,148 research outputs found
Analysis of Multiserver Retrial Queueing System: A Martingale Approach and an Algorithm of Solution
The paper studies a multiserver retrial queueing system with servers.
Arrival process is a point process with strictly stationary and ergodic
increments. A customer arriving to the system occupies one of the free servers.
If upon arrival all servers are busy, then the customer goes to the secondary
queue, orbit, and after some random time retries more and more to occupy a
server. A service time of each customer is exponentially distributed random
variable with parameter . A time between retrials is exponentially
distributed with parameter for each customer. Using a martingale
approach the paper provides an analysis of this system. The paper establishes
the stability condition and studies a behavior of the limiting queue-length
distributions as increases to infinity. As , the paper
also proves the convergence of appropriate queue-length distributions to those
of the associated `usual' multiserver queueing system without retrials. An
algorithm for numerical solution of the equations, associated with the limiting
queue-length distribution of retrial systems, is provided.Comment: To appear in "Annals of Operations Research" 141 (2006) 19-52.
Replacement corrects a small number of misprint
A Survey on Delay-Aware Resource Control for Wireless Systems --- Large Deviation Theory, Stochastic Lyapunov Drift and Distributed Stochastic Learning
In this tutorial paper, a comprehensive survey is given on several major
systematic approaches in dealing with delay-aware control problems, namely the
equivalent rate constraint approach, the Lyapunov stability drift approach and
the approximate Markov Decision Process (MDP) approach using stochastic
learning. These approaches essentially embrace most of the existing literature
regarding delay-aware resource control in wireless systems. They have their
relative pros and cons in terms of performance, complexity and implementation
issues. For each of the approaches, the problem setup, the general solution and
the design methodology are discussed. Applications of these approaches to
delay-aware resource allocation are illustrated with examples in single-hop
wireless networks. Furthermore, recent results regarding delay-aware multi-hop
routing designs in general multi-hop networks are elaborated. Finally, the
delay performance of the various approaches are compared through simulations
using an example of the uplink OFDMA systems.Comment: 58 pages, 8 figures; IEEE Transactions on Information Theory, 201
A Queueing Characterization of Information Transmission over Block Fading Rayleigh Channels in the Low SNR
Unlike the AWGN (additive white gaussian noise) channel, fading channels
suffer from random channel gains besides the additive Gaussian noise. As a
result, the instantaneous channel capacity varies randomly along time, which
makes it insufficient to characterize the transmission capability of a fading
channel using data rate only. In this paper, the transmission capability of a
buffer-aided block Rayleigh fading channel is examined by a constant rate input
data stream, and reflected by several parameters such as the average queue
length, stationary queue length distribution, packet delay and overflow
probability. Both infinite-buffer model and finite-buffer model are considered.
Taking advantage of the memoryless property of the service provided by the
channel in each block in the the low SNR (signal-to-noise ratio) regime, the
information transmission over the channel is formulated as a \textit{discrete
time discrete state} queueing problem. The obtained results show that
block fading channels are unable to support a data rate close to their ergodic
capacity, no matter how long the buffer is, even seen from the application
layer. For the finite-buffer model, the overflow probability is derived with
explicit expression, and is shown to decrease exponentially when buffer size is
increased, even when the buffer size is very small.Comment: 29 pages, 11 figures. More details on the proof of Theorem 1 and
proposition 1 can be found in "Queueing analysis for block fading Rayleigh
channels in the low SNR regime ", IEEE WCSP 2013.It has been published by
IEEE Trans. on Veh. Technol. in Feb. 201
Stable Throughput and Delay Analysis of a Random Access Network With Queue-Aware Transmission
In this work we consider a two-user and a three-user slotted ALOHA network
with multi-packet reception (MPR) capabilities. The nodes can adapt their
transmission probabilities and their transmission parameters based on the
status of the other nodes. Each user has external bursty arrivals that are
stored in their infinite capacity queues. For the two- and the three-user cases
we obtain the stability region of the system. For the two-user case we provide
the conditions where the stability region is a convex set. We perform a
detailed mathematical analysis in order to study the queueing delay by
formulating two boundary value problems (a Dirichlet and a Riemann-Hilbert
boundary value problem), the solution of which provides the generating function
of the joint stationary probability distribution of the queue size at user
nodes. Furthermore, for the two-user symmetric case with MPR we obtain a lower
and an upper bound for the average delay without explicitly computing the
generating function for the stationary joint queue length distribution. The
bounds as it is seen in the numerical results appear to be tight. Explicit
expressions for the average delay are obtained for the symmetrical model with
capture effect which is a subclass of MPR models. We also provide the optimal
transmission probability in closed form expression that minimizes the average
delay in the symmetric capture case. Finally, we evaluate numerically the
presented theoretical results.Comment: Submitted for journal publicatio
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Analysis of a class of distributed queues with application
Recently we have developed a class of media access control algorithms for different types of Local Area Networks. A common feature of these LAN algorithms is that they represent various strategies by which the processors in the LAN can simulate the availability of a centralized packet transport facility, but whose service incorporates a particular type of change over time known as 'moving sever' overhead. First we describe the operation of moving server systems in general, for both First-Come - First-Served and Head-of-the-Line orders of service, together with an approach for their delay analysis in which we transform the moving server queueing system into a conventional queueing system having proportional waiting times. Then we describe how the various LAN algorithms may be obtained from the ideal moving server system, and how a significant component of their performance characteristics is determined by the performance characteristics of that ideal system. Finally, we evaluate the compatibility of such LAN algorithms with separable queueing network models of distributed systems by computing the interdeparture time distribution for M/M/1 in the presence of moving server overhead. Although it is not exponential, except in the limits of low server utilization or low overhead, the interdeparture time distribution is a weighted sum of exponential terms with a coefficient of variation not much smaller than unity. Thus, we conjecture that a service centre with moving server overhead could be used to represent one of these LAN algorithms in a product form queueing network model of a distributed system without introducing significant approximation errors
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