Buffer Occupancy Distribution Research Articles

Steady-State Analysis of Buffer Occupancy for Different Forwarding Strategies in Mobile Opportunistic Network

We perform a study on the buffer occupancy 1 1 The term buffer occupancy refers to the amount (or number) of data (or packets) present in the buffer. We shall be using the terms buffer occupancy and system size interchangeably as deemed fit. and its steady-state properties in a mobile opportunistic network (MON) for different forwarding strategies. Nodes in MON adhere to replication based strategy in order to ensure reliable delivery. Such replications occur in bulks during intermittent and very short contact events, which often lead to buffer congestion in the relay nodes, thereby affecting the network performance. The state-of-the-art on buffer management in MON relies on local information exchange to measure buffer occupancy, which leads to overhead. Therefore, to find the average buffer occupancy, we first study the aggregated bulk transfer size using real-life contact traces and find that it follows a log-normal distribution. Since the contact rate has been observed to follow a Poisson distribution, we model the packet arrival process in each node as a compound Poisson process. Furthermore, the departure process is modeled as packets dropped due to time-to-live expiry, which is shown to have an exponential distribution. Using the above model, we derive the steady-state probability distribution of buffer occupancy of an arbitrary node for three different classes of replication scheme, viz., epidemic routing, probabilistic routing, and time-varying probabilistic routing. The results of this paper help in assessing how fast a node buffer gets depleted under different routing algorithms, which will help in designing better buffer management techniques and routing algorithms.

Transient solution of fluid queue modulated by two independent birth-death processes

The objective of this paper is to study the transient distribution of the buffer content in any intermediate node of a wireless network based on IEEE 802.11 standards. The steady state solution of the discussed model has already been given in Arunachalam et al. (2010). The methodology used, maps the underlying model to a fluid queue model driven by two independent finite state birth-death processes with the aim to simplify the solution which is obtained in closed form with numerical illustration. Along with the buffer occupancy distribution, other performance measures: throughput, server utilisation and expected buffer content are also obtained numerically.

An Analysis Framework for Buffer-Aided Relaying Under Time-Correlated Fading Channels

In this paper, we propose a framework to analyze the performance of buffer-aided (BA) relaying under time-correlated fading channels in terms of the queueing behavior of packets at the relay's buffer. Unlike independent and identically distributed (i.i.d.) fading, correlated fading brings challenges in performance analysis since the state transition probabilities of buffer occupancy become time variant. To overcome this issue, we first establish an aggregate quasi-birth-death (QBD) Markov chain integrating both the buffer occupancy process and the channel fading process, then analyze the stationary distribution of the aggregate chain, and finally extract the stationary distribution of buffer occupancy from it. Using the stationary distribution of buffer occupancy, system throughput, end-to-end delay, and outage probability are derived. Numerical results verify our analyses and show that the throughput of BA relaying under correlated fading channels can approach the one under i.i.d. fading only for loose delay constraints or high fading margins. For stringent delay constraints and low fading margins, correlated fading causes great degradation of throughput. In particular, a throughput loss of about 16% under an infinite buffer (28% under a finite buffer) is observed for the requirement of an average delay of 20 slots and a fading margin of 5 dB. This means that the designs based on i.i.d. fading are not always feasible for correlated fading. According to these observations, some insights on performance degradation and guidelines on redesigning improved policies under correlated fading are provided.

Effective Bandwidth for Delay Tolerant Secondary User Traffic in Multi-PU, Multi-SU Dynamic Spectrum Access Networks

In this paper, we study two important quality of service (QoS) parameters of dynamic spectrum access (DSA) networks with multiple primary and secondary users. We assume that the secondary users (SUs) are delay tolerant and model the primary user (PU) and SU activity as Markov chains with ON and OFF states. We derive a closed form expression for the probability distribution of buffer occupancy for secondary networks under steady state conditions and formulate an expression for the effective bandwidth under buffer overflow constraints. Extensive simulations are used to validate our analysis.

Analysis and experimental evaluation of rate adaptation with transmit buffer information

In hardware, packet loss may happen due to overflow at a finite-depth transmit buffer in addition to the packet corruption in the channel. To reduce such losses and further improve spectral efficiency via rate selection, we exploit either statistical or instantaneous knowledge of transmit buffer occupancy and source packet distribution in IEEE 802.11-based systems, which have highly variable frame durations. We consider a traditional method of rate adaptation based on channel quality information and evaluate the throughput gain in hardware when the buffer occupancy and source packet distribution information are known. Our optimization objective is to maximize the throughput with constant transmit power since most wireless standards (e.g., 802.11, Bluetooth, ZigBee) operate in this manner. We study both cases with and without probe packets during the transmission. By evaluating the effect of diverse buffer sizes with different packet arrival distributions, both our theoretical analysis and our experimental results show that the throughput can be improved as much as 35% when the source packet distribution and buffer status information are exploited.

A Node Operating Point Approach for Stochastic Analysis with Network Calculus

The operating point of a node is an interesting concept from large deviations theory which defines the asymptotic buffer occupancy distribution at the node. The effective band-width function evolved out of large deviations theory, establishes the crucial connection between the node operating point and the theory of statistical network calculus. This paper uses the concepts of effective bandwidth and effective capacity to describe independent stochastic arrival and service processes, respectively, and to identify node operating point to perform stochastic analysis with network calculus. The two main advantages of the approach used in this paper are: (i) the use of operating point to perform stochastic analysis provides insight into the queue dynamics, and (ii) the use of effective bandwidth and effective capacity functions within the framework of statistical network calculus allows efficient evaluation of performance bounds.

A fluid queue modulated by two independent birth–death processes

We present a fluid queue model driven by two independent finite state birth–death processes with the objective to study the buffer occupancy distribution in any intermediate node in a communication network. In a communication network, at any node, the arrival and service of the packets are with variable rates. To model this scenario we develop a fluid queue with an infinite capacity buffer which receives fluid at variable rate and also releases fluid at variable rates. Because of variable inflow and outflow rates of the fluid, the proposed fluid queue is driven by the current states of two independent finite state birth–death processes evolving in the background which on merging give rise to a continuous time Markov chain which is not a birth–death process. Using the fluid queue model, we obtain the steady-state distribution of the buffer occupancy at any intermediate node during packet transmission in a communication network. As a special case, we consider a wireless network based on the IEEE 802.11 standard. We present the buffer occupancy distribution at any intermediate node in closed form with a numerical illustration. Along with buffer occupancy distribution, we also obtain various performance measures such as expected buffer content, average throughput, server utilization and mean delay which are relevant to packet transmission in such a communication network. Finally, we present numerical results to illustrate the feasibility of the proposed model. The results are in accordance with the expected behavior of these performance measures.

A resequencing model for high-speed packet-switching networks

In this paper, we propose a framework to study the resequencing mechanism in high-speed networks. This framework allows us to estimate the packet resequencing delay and the resequencing buffer occupancy distributions when data traffic is dispersed on multiple disjoint paths. In contrast to most existing work, the end-to-end path delay distribution is decoupled from the resequencing model. Thus, once the end-to-end path delay distribution is obtained, such as from historical data, our model may be used. In this paper, we illustrate our proposed model with Gaussian distributed path delays. Our results show that the packet resequencing delay and the resequencing buffer occupancy drop when the traffic is spread over a larger number of homogeneous paths, although the network performance improvement quickly saturates when the number of paths increases. We find that the number of paths used in multipath routing should be small, say, up to three.

Network queue and loss analysis using histogram-based traffic models

This paper proposes a new performance analysis for obtaining the queue length distribution in a finite size buffer system. This analysis uses a simple traffic model based on histograms that captures the arrival rate distribution on a network model. In order to reflect the second-order statistics (long-range dependence and self-similarity) of network traffic this basic model has been extended using the Hurst parameter. The buffer occupancy distribution is obtained using these traffic models and defining a new stochastic process that works directly with histograms. The loss probability and network delay distribution can be obtained using this distribution. The estimation of the expected traffic loss probability is a key issue in provisioning Quality of Service in telecommunications networks. This paper shows that the proposed buffer occupancy distribution and loss probability calculations techniques are very precise.

Long range dependence in network traffic and the closed loop behaviour of buffers under adaptive window control

We consider an Internet link carrying http-like traffic, i.e., transfers of finite volume files arriving at random time instants. These file transfers are controlled by an adaptive window protocol (AWP); an example of such a protocol is TCP. We provide analysis for the auto-covariance function of the AWP-controlled traffic into the link’s buffer; this traffic, in general, cannot be represented by an on–off process. The analysis establishes that, for TCP-controlled transfer of Pareto-distributed file sizes with infinite second moment, the traffic into the link buffer is long range-dependent (LRD). We also develop an analysis for obtaining the stationary distribution of the link buffer occupancy under an AWP-controlled transfer of files sampled from some distribution. For any AWP, the analysis provides us with the Laplace–Stieltjes transform (LST) of the distribution of the link buffer occupancy process in terms of the functions defining the AWP and the file size distribution. The analysis also provides a necessary and a sufficient condition for the finiteness of the mean link buffer content; these conditions again have explicit dependence on the AWP used and the file size distribution. This establishes the sensitivity of the buffer occupancy process to the file size distribution. Combining the results from the above analyses, we provide various examples in which the closed loop control of an AWP results in finite mean link buffer occupancy even though the file sizes are Pareto-distributed (with infinite second moment), and the traffic into the link buffer is long range-dependent (with Hurst parameters which would suggest an infinite mean queue occupancy under open loop analysis). We also study the effect of window reductions due to active queue management and find that window reductions lead to further lightening of the tail of buffer occupancy distribution. The significance of this work is three-fold: (i) by looking at the window evolution as a function of the amount of data served and not as a function of time, this work provides a new framework for analysing various processes related to the link buffer under AWP-controlled transfer of files with a general file size distribution; (ii) it indicates that the buffer behaviour in the Internet may not be as poor as predicted from an open loop analysis of a queue fed with LRD traffic; and (iii) it shows that the buffer behaviour (and hence the throughput performance for finite buffers) is sensitive to the distribution of file sizes.

Large Buffer Asymptotics for Fluid Queues with Heterogeneous M/G/ Weibullian Inputs

In this paper we consider a generalization of the so called M/G/∞ model where M types of sessions enter a buffer. The instantaneous rates of the sessions are functions of the occupancy of an M/G/∞ system with Weibullian G distributions. In particular we assume that a session of type i transmits ri cells per unit time and lasts for a random time τ with a Weibull distribution given by Pr (τ>x)∼e−γixαi, where 0 0. We show that the complementary buffer occupancy distribution for large buffer size is Weibullian whose parameters can be determined as the solution of a deterministic nonlinear knapsack problem. For αi<0.5, upper and lower bound factors are determined. When specialized to the homogeneous case, i.e., when all the sessions are identical, the result coincides with a lower bound reported in the literature.

The lightening effect of adaptive window control

We consider adaptive window (e.g., TCP) controlled transfer of http-like traffic (i.e., finite volume file transfers starting at random time instants) over a link, and develop an analysis for obtaining the stationary distribution of the link buffer occupancy. The significance of this work is that it provides a framework for analyzing the "closed-loop" behavior of the link buffer under adaptive window controlled transfer of files with a general file size distribution. We find that the tail of the stationary distribution of the buffer occupancy is lighter than may be expected from an open loop analysis. We also find that the tail of the buffer distribution is sensitive to the distribution of the file sizes, which provides insight into the sensitivity of TCP performance to file size distribution.

Tail Asymptotics for HOL Priority Queues Handling a Large Number of Independent Stationary Sources

In this paper we study the asymptotics of the tail of the buffer occupancy distribution in buffers accessed by a large number of stationary independent sources and which are served according to a s...

Analysis of large ATM switches using a platform-independent simulation environment

This paper presents a general simulation approach applied to the problem of performance evaluation of large switching fabrics. Experimental results in the form of cell queuing delay and buffer occupancy distributions for switches with up to 2048 inputs and outputs operating under a wide variety of loads are presented. The traditional dilemma between simulation model validity and its run-time where a more general purpose model inevitably results in longer execution times, is eliminated by the introduction of a new parameter: the architecture of the simulation platform. With model validity as an invariant, the simulation platform can range from a sequential computer via shared memory and distributed memory general purpose parallel processors up to a dedicated emulator, on the condition that the software engineering problem has been solved, i.e. that there is a software tool available that automates that task of generating simulation code for various platforms from a single model, taking the characteristics of the platforms (granularity) into account. An analytical model of the class of applications under study gives insight into the influence of machine and problem parameters on simulator run-time performance. Examples of its use for the choice of an optimal parallel architecture for a given problem and of its use for the estimation of application behavior on a given parallel machine architecture are presented.

An access protocol for speech/data/video integration in TDMA-based advanced mobile systems

One key requirement in the radio access design of advanced, third-generation mobile systems is the ability to accommodate a variety of service types via flexible and efficient multiple-access protocols. This paper introduces a multiple-access protocol, SIR++ (service integration for radio access), which has the potential for meeting the service requirements of speech, video, and bursty data traffic in an efficient way. SLR++ is evolved from and generalizes a former protocol, SIR, which only considered the requirements of speech and data. The paper also evaluates the buffer occupancy distribution associated with an (H.263) video connection by solving a worst case model of the system.

Analysis of communication systems with timed token protocols using the power-series algorithm

The IEEE 802.4 and FDDI (Fibre Distributed Data Interface) standards are high speed MAC (Medium Access Control) protocols for LAN/MANs employing a timer-controlled token passing mechanism, the so-called Timed Token Protocol, to control station access to the shared media. MAC protocols belonging to the class of timed token protocols support synchronous and real-time (i.e., time-critical) applications, and provide priority among asynchronous (i.e., non time-critical) applications. During the last few years, a lot of research has focused on the study of timed token protocols to obtain performance measures such as throughputs or mean waiting times. The recent development of the Power-Series Algorithm (PSA) has opened new perspectives in the analysis of this class of protocols. This paper shows the versatility of the PSA technique to evaluate the station buffer occupancy and delay distributions of a very general model which can be used to represent the behavior of several LAN/MANs MAC protocols, among which the timed token MAC protocols. Specifically, the focus of the paper is on the solution of an almost exact model of the IEEE 802.4 MAC protocol. Since the model we propose and solve numerically by exploiting the PSA technique is an approximate model of the FDDI MAC protocol, the paper also reports on a comparison between performance measures obtained for this model and simulation results for the corresponding (exact) model of FDDI.

Analysis of communication systems with timed token protocols using the power-series algorithm

Abstract The IEEE 802.4 and FDDI (Fibre Distributed Data Interface) standards are high speed MAC (Medium Access Control) protocols for LAN/MANs employing a timer-controlled token passing mechanism, the so-called Timed Token Protocol, to control station access to the shared media. MAC protocols belonging to the class of timed token protocols support synchronous and real-time (i.e., time-critical) applications, and provide priority among asynchronous (i.e., non time-critical) applications. During the last few years, a lot of research has focused on the study of timed token protocols to obtain performance measures such as throughputs or mean waiting times. The recent development of the Power-Series Algorithm (PSA) has opened new perspectives in the analysis of this class of protocols. This paper shows the versatility of the PSA technique to evaluate the station buffer occupancy and delay distributions of a very general model which can be used to represent the behavior of several LAN/MANs MAC protocols, among which the timed token MAC protocols. Specifically, the focus of the paper is on the solution of an almost exact model of the IEEE 802.4 MAC protocol. Since the model we propose and solve numerically by exploiting the PSA technique is an approximate model of the FDDI MAC protocol, the paper also reports on a comparison between performance measures obtained for this model and simulation results for the corresponding (exact) model of FDDI.

On the use of fractional Brownian motion in the theory of connectionless networks

An abstract model for aggregated connectionless traffic, based on the fractional Brownian motion, is presented. Insight into the parameters is obtained by relating the model to an equivalent burst model. Results on a corresponding storage process are presented. The buffer occupancy distribution is approximated by a Weibull distribution. The model is compared with publicly available samples of real Ethernet traffic. The degree of the short-term predictability of the traffic model is studied through an exact formula for the conditional variance of a future value given the past. The applicability and interpretation of the self-similar model are discussed extensively, and the notion of ideal free traffic is introduced.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Efficient window flow control for high speed data networks with small buffers

As the transmission speeds of emerging data networks scale up, the effects of propagation delays, which do not scale, become quite consequential for the design of sliding windows which are needed for congestion control. It was previously shown that optimal window lengths grow linearly with transmission speed λ, thus making the cost of memory for buffers a major factor. However, it was also shown that the moments of the number of packets in the buffers are onlyO(\(\sqrt {{\mathbf{ }}\lambda }\)), the remaining packets are in the course of being propagated. This fact underlies the proposal made here which requires smallO(\(\sqrt {{\mathbf{ }}\lambda {\mathbf{ }}ln{\mathbf{ }}\lambda }\)) buffers and yet guarantees that the ratio of the realized throughput to the ideal throughput approaches unity with increasing λ. That is, buffers when properly sized overflow so rarely that even with a rudimentary (conversely, easily implemented) protocol like go-back-n, the loss in throughput due to retransmissions is negligible. This result is arrived at by obtaining an explicit characterization for large λ of thetail of the distribution of buffer occupancy in the closed network with window sized buffers; in the case of a single-hop virtual circuit the characterization is by a Gaussian conditioned to be nonnegative. Numerical and simulation results are presented to corroborate the performance predictions of the theory for the case of 45 Mbits/sec transmission speed.

Discrete time queues with phase dependent arrivals

The queueing behavior of many communication systems is well modeled by a queueing system in which time is slotted, and the number of entities that arrive during a slot is dependent upon the state of a discrete time, discrete state Markov chain. Techniques for analyzing such systems have appeared in the literature from time to time, but distributions have been presented in only rare instances In the paper, the authors present the probability generating function (PGF) for joint and marginal buffer occupancy distributions of statistical time division multiplexing systems in this class. They discuss inversion of the PGF using discrete Fourier transforms, and also discuss a simple technique for obtaining moments of the queue length distribution. Numerical results, including queue length distributions for some special cases, are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>