978 research outputs found
Rare event analysis of Markov-modulated infinite-server queues: a Poisson limit
This article studies an infinite-server queue in a Markov environment, that is, an infinite-server queue with arrival rates and service times depending on the state of a Markovian background process. Scaling the arrival rates (i) by a factor N and the rates (ij) of the background process by N1+E (for some E>0), the focus is on the tail probabilities of the number of customers in the system, in the asymptotic regime that N tends to . In particular, it is shown that the logarithmic asymptotics correspond to those of a Poisson distribution with an appropriate mean
Asymptotic analysis by the saddle point method of the Anick-Mitra-Sondhi model
We consider a fluid queue where the input process consists of N identical
sources that turn on and off at exponential waiting times. The server works at
the constant rate c and an on source generates fluid at unit rate. This model
was first formulated and analyzed by Anick, Mitra and Sondhi. We obtain an
alternate representation of the joint steady state distribution of the buffer
content and the number of on sources. This is given as a contour integral that
we then analyze for large N. We give detailed asymptotic results for the joint
distribution, as well as the associated marginal and conditional distributions.
In particular, simple conditional limits laws are obtained. These shows how the
buffer content behaves conditioned on the number of active sources and vice
versa. Numerical comparisons show that our asymptotic results are very accurate
even for N=20
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Performance modelling of a multiple threshold RED mechanism for bursty and correlated Internet traffic with MMPP arrival process
Access to the large web content hosted all over the world by users of the Internet engage
many hosts, routers/switches and faster links. They challenge the internet backbone to operate at
its capacity to assure e±cient content access. This may result in congestion and raises concerns over
various Quality of Service (QoS) issues like high delays, high packet loss and low throughput of the
system for various Internet applications. Thus, there is a need to develop effective congestion control
mechanisms in order to meet various Quality of Service (QoS) related performance parameters. In this
paper, our emphasis is on the Active Queue Management (AQM) mechanisms, particularly Random
Early Detection (RED). We propose a threshold based novel analytical model based on standard RED
mechanism. Various numerical examples are presented for Internet traffic scenarios containing both the
burstiness and correlation properties of the network traffic
Rare event analysis of Markov-modulated infinite-service queues: A Poisson limit
This paper studies an infinite-server queue in a Markov environment, that is, an infinite-server
queue with arrival rates and service times depending on the state of a Markovian background
process. Scaling the arrival rates by a factor and the rates of the background process by N^{1+\vareps}
(for some \vareps > 0), the focus is on the tail probabilities of the number of customers in the system, in
the asymptotic regime that tends to . In particular, it is shown that the logarithmic asymptotics
correspond to those of a Poisson distribution with an appropriate mean
Sample path large deviations for queues with many inputs
This paper presents a large deviations principle for the average of real-valued processes indexed by the positive integers, one which is particularly suited to queueing systems with many traffic flows. Examples are given of how it may be applied to standard queues with finite and infinite buffers, to priority queues and to finding most likely paths to overflow
A discrete-time Markov modulated queuing system with batched arrivals
This paper examines a discrete-time queuing system with applications to
telecommunications traffic. The arrival process is a particular Markov
modulated process which belongs to the class of discrete batched Markovian
arrival processes. The server process is a single server deterministic queue. A
closed form exact solution is given for the expected queue length and delay. A
simple system of equations is given for the probability of the queue exceeding
a given length.Comment: to appear Performance Evaluatio
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