3,787 research outputs found
Robust measurement-based buffer overflow probability estimators for QoS provisioning and traffic anomaly prediction applicationm
Suitable estimators for a class of Large Deviation approximations of rare
event probabilities based on sample realizations of random processes have been
proposed in our earlier work. These estimators are expressed as non-linear
multi-dimensional optimization problems of a special structure. In this paper,
we develop an algorithm to solve these optimization problems very efficiently
based on their characteristic structure. After discussing the nature of the
objective function and constraint set and their peculiarities, we provide a
formal proof that the developed algorithm is guaranteed to always converge. The
existence of efficient and provably convergent algorithms for solving these
problems is a prerequisite for using the proposed estimators in real time
problems such as call admission control, adaptive modulation and coding with
QoS constraints, and traffic anomaly detection in high data rate communication
networks
Robust measurement-based buffer overflow probability estimators for QoS provisioning and traffic anomaly prediction applications
Suitable estimators for a class of Large Deviation approximations of rare event probabilities based on sample realizations of random processes have been proposed in our earlier work. These estimators are expressed as non-linear multi-dimensional optimization problems of a special structure. In this paper, we develop an algorithm to solve these optimization problems very efficiently based on their characteristic structure. After discussing the nature of the objective function and constraint set and their peculiarities, we provide a formal proof that the developed algorithm is guaranteed to always converge. The existence of efficient and provably convergent algorithms for solving these problems is a prerequisite for using the proposed estimators in real time problems such as call admission control, adaptive modulation and coding with QoS constraints, and traffic anomaly detection in high data rate communication networks
Modulated Branching Processes, Origins of Power Laws and Queueing Duality
Power law distributions have been repeatedly observed in a wide variety of
socioeconomic, biological and technological areas. In many of the observations,
e.g., city populations and sizes of living organisms, the objects of interest
evolve due to the replication of their many independent components, e.g.,
births-deaths of individuals and replications of cells. Furthermore, the rates
of the replication are often controlled by exogenous parameters causing periods
of expansion and contraction, e.g., baby booms and busts, economic booms and
recessions, etc. In addition, the sizes of these objects often have reflective
lower boundaries, e.g., cities do not fall bellow a certain size, low income
individuals are subsidized by the government, companies are protected by
bankruptcy laws, etc.
Hence, it is natural to propose reflected modulated branching processes as
generic models for many of the preceding observations. Indeed, our main results
show that the proposed mathematical models result in power law distributions
under quite general polynomial Gartner-Ellis conditions, the generality of
which could explain the ubiquitous nature of power law distributions. In
addition, on a logarithmic scale, we establish an asymptotic equivalence
between the reflected branching processes and the corresponding multiplicative
ones. The latter, as recognized by Goldie (1991), is known to be dual to
queueing/additive processes. We emphasize this duality further in the
generality of stationary and ergodic processes.Comment: 36 pages, 2 figures; added references; a new theorem in Subsection
4.
Dynamic Product Assembly and Inventory Control for Maximum Profit
We consider a manufacturing plant that purchases raw materials for product
assembly and then sells the final products to customers. There are M types of
raw materials and K types of products, and each product uses a certain subset
of raw materials for assembly. The plant operates in slotted time, and every
slot it makes decisions about re-stocking materials and pricing the existing
products in reaction to (possibly time-varying) material costs and consumer
demands. We develop a dynamic purchasing and pricing policy that yields time
average profit within epsilon of optimality, for any given epsilon>0, with a
worst case storage buffer requirement that is O(1/epsilon). The policy can be
implemented easily for large M, K, yields fast convergence times, and is robust
to non-ergodic system dynamics.Comment: 32 page
On Coding for Reliable Communication over Packet Networks
We present a capacity-achieving coding scheme for unicast or multicast over
lossy packet networks. In the scheme, intermediate nodes perform additional
coding yet do not decode nor even wait for a block of packets before sending
out coded packets. Rather, whenever they have a transmission opportunity, they
send out coded packets formed from random linear combinations of previously
received packets. All coding and decoding operations have polynomial
complexity.
We show that the scheme is capacity-achieving as long as packets received on
a link arrive according to a process that has an average rate. Thus, packet
losses on a link may exhibit correlation in time or with losses on other links.
In the special case of Poisson traffic with i.i.d. losses, we give error
exponents that quantify the rate of decay of the probability of error with
coding delay. Our analysis of the scheme shows that it is not only
capacity-achieving, but that the propagation of packets carrying "innovative"
information follows the propagation of jobs through a queueing network, and
therefore fluid flow models yield good approximations. We consider networks
with both lossy point-to-point and broadcast links, allowing us to model both
wireline and wireless packet networks.Comment: 33 pages, 6 figures; revised appendi
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
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