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73
Effective Bandwidths for Stationary Sources
, 1995
"... At a buffered switch in an ATM (asynchronous transfer mode) network it is important to know what combinations of different types of traffic can be carried simultaneously without risking more than a very small probability of overflowing the buffer. We show that a simple and serviceable measure of eff ..."
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Cited by 37 (7 self)
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At a buffered switch in an ATM (asynchronous transfer mode) network it is important to know what combinations of different types of traffic can be carried simultaneously without risking more than a very small probability of overflowing the buffer. We show that a simple and serviceable measure of effective bandwidths may be computed for stationary traffic sources. For large buffers the effective bandwidth of a source is a function only of its mean rate, index of dispersion and the size of the buffer. Keywords: communications, effective bandwidths, large deviations, stationary processes 1 Effective bandwidths The traffic in an ATM network is packaged in cells and carried over links between switches in the network. Traffic sources are bursty and so for periods of time cells may arrive at a switch faster than they can be switched to output links. For this reason, switches are buffered and the problem is to know how much total total traffic can be carried while keeping the probability of b...
Large Deviations and the Generalized Processor Sharing Scheduling: Upper and Lower Bounds  Part I: TwoQueue Systems
 Queueing Systems
, 1995
"... We prove asymptotic upper and lower bounds on the asymptotic decay rate of persession queue length tail distributions for a single constant service rate server queue shared by multiple sessions with the generalized processor sharing (GPS) scheduling discipline. The simpler case of a GPS system with ..."
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Cited by 36 (0 self)
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We prove asymptotic upper and lower bounds on the asymptotic decay rate of persession queue length tail distributions for a single constant service rate server queue shared by multiple sessions with the generalized processor sharing (GPS) scheduling discipline. The simpler case of a GPS system with only two queues needs special attention, as under this case, it is shown that the upper bounds and lower bounds match, thus yielding exact bounds. This result is established in this part (Part I) of the paper. The general case is much more complicated, and is treated separately in Part II of the paper [42], where tight upper and lower bound results are proved by examining the dynamics of bandwidth sharing nature of GPS scheduling. The proofs use samplepath large deviation principle and are based on some recent large deviation results for a single queue with a constant service rate server. These results have implications in call admission control for highspeed communication networks. 1 Int...
Stochastic Modeling Of Traffic Processes
 Frontiers in Queueing: Models, Methods and Problems
, 1996
"... Modern telecommunications networks are being designed to accomodate a heterogenous mix of traffic classes ranging from traditional telephone calls to video and data services. Thus, traffic models are of crucial importance to the engineering and performance analysis of telecommunications system, nota ..."
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Cited by 34 (0 self)
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Modern telecommunications networks are being designed to accomodate a heterogenous mix of traffic classes ranging from traditional telephone calls to video and data services. Thus, traffic models are of crucial importance to the engineering and performance analysis of telecommunications system, notably congestion and overload controls and capacity estimation. This chapter surveys teletraffic models, addressing both theoretical and computational aspects. It first surveys the main classes of teletraffic models commonly used in teletraffic modeling, and then proceeds to survey traffic methods for computing statistics relevant to the engineering a teletraffic network. 1 INTRODUCTION Traffic is the driving force of telecommunications systems, representing customers making phone calls, transferring data files and other electronic information, or more recently, transmitting compressed video frames to a display device. The most common modeling context is queueing; traffic is offered to a qu...
Application of the Many Sources Asymptotic and Effective Bandwidths to Traffic Engineering
, 1999
"... ..."
Modeling Heterogeneous Network Traffic in Wavelet Domain: Part II  NonGaussian Traffic
 IEEE/ACM Transactions on Networking
, 1999
"... Following our work described in Part I of this paper that modeled various correlation structures of Gaussian traffic in wavelet domain, we extend our previous models to heterogeneous network traffic with either a nonGaussian distribution or a periodic structure. To include a nonGaussian distributi ..."
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Cited by 25 (1 self)
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Following our work described in Part I of this paper that modeled various correlation structures of Gaussian traffic in wavelet domain, we extend our previous models to heterogeneous network traffic with either a nonGaussian distribution or a periodic structure. To include a nonGaussian distribution, we first investigate what higherorder statistics are pertinent by exploring a relationship between timescale analysis of wavelets and cumulative traffic. We then develop a novel algorithm in the wavelet domain to capture the important statistics. By utilizing local properties of wavelet basis in both space and time, we further extend such wavelet models to periodic MPEG traffic. As wavelets provide a natural fit to higherorder statistics as well as localized spatial and temporal dependence of periodic traffic at different time scales, the resulting wavelet models for both nonGaussian and periodic traffic are simple and accurate with the lowest computational complexity attainable. 1 I...
Effective Bandwidth in High Speed Digital Networks
 IEEE Journal on Selected Areas in Communications
, 1999
"... The theory of large deviations provides a simple unified basis for statistical mechanics, information theory and queueing theory. The objective of this paper is to use large deviation theory and the Laplace method of integration to provide an simple intuitive overview of the recently developed theor ..."
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Cited by 24 (5 self)
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The theory of large deviations provides a simple unified basis for statistical mechanics, information theory and queueing theory. The objective of this paper is to use large deviation theory and the Laplace method of integration to provide an simple intuitive overview of the recently developed theory of effective bandwidth for high speed digital networks, especially ATM networks. This includes (i) identification of the appropriate energy function, entropy function and effective bandwidth function of a source, (ii) the calculus of the effective bandwidth functions, (iii) bandwidth allocation and buffer management, (iv) traffic descriptors, and (v) envelope processes and conjugate processes for fast simulations and bounds.
Modelling communication networks, present and future
 THE CLIFFORD PATTERSON LECTURE
, 1995
"... Modern communication networks are able to respond to randomly uctuating demands and failures by allowing bu ers to ll, by rerouting tra c and by reallocating resources. They are able to do this so well that, in many respects, largescale networks appear as coherent, almost intelligent, organisms. The ..."
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Cited by 22 (0 self)
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Modern communication networks are able to respond to randomly uctuating demands and failures by allowing bu ers to ll, by rerouting tra c and by reallocating resources. They are able to do this so well that, in many respects, largescale networks appear as coherent, almost intelligent, organisms. The design and control of such networks present challenges of a mathematical, engineering and economic nature. In this lecture I describe some of the models that have proved useful in the analysis of stability, statistical sharing and pricing, in systems ranging from the telephone networks of today to the information superhighways of tomorrow.
Veciana, “On flatrate and usagebased pricing for tiered commodity Internet services
 Proc. CISS
, 2008
"... In this note, we discuss issues pertaining to endtoend qualityofservice management of commodity Internet applications and associated pricing incentive mechanisms. The issue of service differentiation is first studied using a simple twoclass model including delay and throughput sensitive traffic. ..."
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Cited by 19 (4 self)
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In this note, we discuss issues pertaining to endtoend qualityofservice management of commodity Internet applications and associated pricing incentive mechanisms. The issue of service differentiation is first studied using a simple twoclass model including delay and throughput sensitive traffic. We show that by introducing service differentiation one can make more efficient use of resources, however this depends on the differences in required QoS as well as the typical capacities of the systems involved. As such, service differentiation may be more beneficial in lower capacity access networks than in high capacity core networks. We then focus on delaysensitive and study flatrate versus usagebased pricing under overload conditions. Our results suggest that in overload scenarios usagebased pricing is advantageous both from the system perspective, i.e., reduces degree of overload, and individual users ’ perspective, increases their perceived utilization. 1.
Veciana, “Spatial energy balancing through proactive multipath routing in multihop wireless networks
 Tech. Rep., Wireless Networking and Communications Group (WNCG), University of Texas at Austin, TX. [Online] Available: http://www.ece.utexas.edu/∼gustavo
, 2004
"... Abstract—In this paper, we investigate the use of proactive multipath routing to achieve energyefficient operation of ad hoc wireless networks. The focus is on optimizing tradeoffs between the energy cost of spreading traffic and the improved spatial balance of energy burdens. We propose a simple s ..."
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Cited by 18 (2 self)
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Abstract—In this paper, we investigate the use of proactive multipath routing to achieve energyefficient operation of ad hoc wireless networks. The focus is on optimizing tradeoffs between the energy cost of spreading traffic and the improved spatial balance of energy burdens. We propose a simple scheme for multipath routing based on spatial relationships among nodes. Then, combining stochastic geometric and queueing models, we develop a continuum model for such networks, permitting an evaluation of different types of scenarios, i.e., with and without energy replenishing and storage capabilities. We propose a parameterized family of energy balancing strategies and study the spatial distributions of energy burdens based on their associated secondorder statistics. Our analysis and simulations show the fundamental importance of the tradeoff explored in this paper, and how its optimization depends on the relative values of the energy reserves/storage, replenishing rates, and network load characteristics. For example, one of our results shows that the degree of spreading should roughly scale as the square root of the bits meters load offered by a session. Simulation results confirm that proactive multipath routing decreases the probability of energy depletion by orders of magnitude versus that of a shortest path routing scheme when the initial energy reserve is high. Index Terms—Gaussian random field, I queue, sensor networks, shotnoise process, stochastic geometry. I.
Manysources Delay Asymptotics with Applications to Priority Queues
"... In this paper, we study discretetime priority queueing systems fed by a large number of arrival streams. We first provide bounds on the actual delay asymptote in terms of the virtual delay asymptote. Then, under suitable assumptions on the arrival process to the queue, we show that these asymptote ..."
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Cited by 18 (5 self)
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In this paper, we study discretetime priority queueing systems fed by a large number of arrival streams. We first provide bounds on the actual delay asymptote in terms of the virtual delay asymptote. Then, under suitable assumptions on the arrival process to the queue, we show that these asymptotes are the same. As an application of this result, we then consider a priority queueing system with two queues. Using the earlier result, we derive an upper bound on the tail probability of the delay. Under certain assumptions on the rate function of the arrival process, we show that the upper bound is tight. We then consider a system with Markovian arrivals and numerically evaluate the delay tail probability and validate these results with simulations.