Buffer Behavior for Mixed Arrivals and Single Server with Random Interruptions

A queueing model with finite buffer size, mixed input traffic (Poisson and burst Poisson arrivals), synchronous transmission and server interruptions through a Bernoulli sequence of independent random variables is studied. Using average burst length, traffic intensity and input traffic mixture ratio as parameters, the relationships among buffer size, overflow probability and expected message queueing delay are obtained. An integrated digital voice-data system with synchronous time division multiplexing (STDM) for a large number of voice sources and mixed arrival process for data messages is considered as an application for this model. The results of this study are portrayed on graphs and may be used as guidelines in buffer design problems in digital voice-data systems. The queueing model developed is quite general in a sense that it covers pure Poisson and burst Poisson arrival processes and the mixture of the two as well.     

Effective bandwidth approach to connection admission control formultimedia traffic in ATM networks

The authors propose an effective bandwidth approach to connection admission control in ATM networks. The aggregate arrival traffic is accurately modelled by a two-state Markov modulated Poisson process (MMPP) via the matching of four important statistics. If the buffer is large, admission control can be achieved by computing the effective bandwidth of the two-state MMPP. Simulation tests show that approach is simple and results in higher utilisation compared with conventional methods     

Optimal load control of spc switches: Waiting time minimization

We address the problem of load control of a switching node with a centralized processor architecture. The problem of finding regulators that minimize the mean dialtone delay is formulated and solved using a semi-Markov decision process model. The results show that for Poisson arrivals one may reduce this delay by up to 60%, depending on the arrival intensity, the service time distribution, and the dialling time distribution, by using an optimal regulator instead of a very simple, but natural, one. We also study the transient properties of the optimal regulators, their behaviour for an MMPP arrival process, and discuss their robustness with respect to various model assumptions.This work was performed while the author was with the Department of Communication Systems, Lund Institute of Technology.     

Modeling multiple IP traffic streams with rate limits

We start with the premise, and provide evidence that it is valid, that a Markov-modulated Poisson process (MMPP) is a good model for Internet traffic at the packet/byte level. We present an algorithm to estimate the parameters and size of a discrete MMPP (D-MMPP) from a data trace. This algorithm requires only two passes through the data. In tandem-network queueing models, the input to a downstream queue is the output from an upstream queue, so the arrival rate is limited by the rate of the upstream queue. We show how to modify the MMPP describing the arrivals to the upstream queue to approximate this effect. To extend this idea to networks that are not tandem, we show how to approximate the superposition of MMPPs without encountering the state-space explosion that occurs in exact computations. Numerical examples that demonstrate the accuracy of these methods are given. We also present a method to convert our estimated D-MMPP to a continuous-time MMPP, which is used as the arrival process in a matrix-analytic queueing model.     

Optimal buffer sharing

We address the problem of designing optimal buffer management policies in shared memory switches when packets already accepted in the switch can be dropped (pushed-out). Our goal is to maximize the overall throughput, or equivalently to minimize the overall loss probability in the system. For a system with two output ports, we prove that the optimal policy is of push-out with threshold type (POT). The same result holds if the optimality criterion is the weighted sum of the port loss probabilities. For this system, we also give an approximate method for the calculation of the optimal threshold, which we conjecture to be asymptotically correct. For the N-ported system, the optimal policy is not known in general, but we show that for a symmetric system (equal traffic on all ports) it consists of always accepting arrivals when the buffer is not full, and dropping one from the longest queue to accommodate the new arrival when the buffer is full. Numerical results are provided which reveal an interesting and somewhat unexpected phenomenon. While the overall improvement in loss probability of the optimal POT policy over the optimal coordinate-convex policy is not very significant, the loss probability of an individual output port remains approximately constant as the load on the other port varies and the optimal POT policy is applied, a property not shared by the optimal coordinate-convex policy     

Buffer losses vs. deadline violations for ABR traffic in an ATM switch: A computational approach

The B‐ISDN will carry a variety of traffic types: the Variable Bit Rate traffic (VBR), of which compressed video is an example, Continuous Bit Rate traffic (CBR), of which telemetry is an example, Data traffic, and Available Bit Rate traffic (ABR) that represents aggregate data traffic with very limited guarantees on quality. Of these, VBR and CBR have timing constraints and need synchronous bandwidth; data traffic is relatively delay insensitive. In this paper, we consider the VBR, Data and ABR traffic types and obtain the cumulative distribution function (cdf) of the queueing delay experienced by a burst of ABR traffic in the output buffer of an ATM switch. The cdf is used to trade off buffer loss probabilities against deadline violation probabilities through adjusting the buffer size and (delay) deadline values. Large buffers result in low losses but queueing delays can become excessive and cause a high level of deadline violations. Both losses and violations are detrimental and an operating point must be chosen to achieve a balance. In this paper we study the nature of the trade off. We develop a stochastic Petri net model assuming periodic burst arrivals for VBR and Poisson arrival processes for the Data and ABR traffic types at the burst level, and solve the model analytically (numerically) using a decomposition approach. This decomposition, along with the inherent decomposability of the tagged customer approach for obtaining the cdf opens up a possibility of carrying out fast computations using a parallel machine for selecting the operating point each time that a call is admitted. This revised version was published online in June 2006 with corrections to the Cover Date.     

An application of Markovian arrival process (MAP) to modelingsuperposed ATM cell streams

First, we propose a new modeling method for superposed ATM traffic by the MMPP(2), which is a special case of the MAP(2). In this new method, we measure the mean and autocorrelation of cell interarrival times, and the histogram of the number of arrivals during measurement windows of fixed size. The MMPP(2) has interarrival times with a second-order hyper-exponential distribution with coefficient of variation c_ν > 1. However, superposed traffic is often observed to have c_ν < 1. To cover this situation, we extend the MMPP(2) to a MAP(3) by adding a new state with inter-state transition accompanied by an arrival. For the MAP(3) model, we take into account the second moment of the interarrival times. From numerical examples, we observe that both the proposed MMPP(2) and MAP(3) yields very good estimation of the cell loss ratio (CLR) for usual superpositions of voice and/or VBR video sources. However, when we have superpositions from CBR video sources together with other VBR sources, c _ν. is much less than 1, and the MAP(3) outperform the MMPP(2), as expected. The proposed MAP(3) well characterizes the cell scale component as well as the burst scale component of superposed traffic streams     

Buffer sizing for synchronous self-routeing broadband packet switches with bursty traffic

Previous studies on the performance of synchronous self-routeing packet switches have assumed that the input traffic is random, i.e. there is no correlation between adjacent packet arrivals. This assumption is generally not valid in the data communication environment (e.g. host-to-host communication) where a file transfer usually generates a string of correlated packets. The consequence is that the random traffic assumption greatly underestimates the buffer requirement of the switch. In this paper, we model each input traffic stream as a binary source as a first step to understand the performance of a packet switch in a bursty traffic environment. We found that, given a fixed traffic load (or switch utilization), the required buffer size increases linearly as the burstiness index (the average burst length) of the traffic increases. In addition, the required buffer size is more sensitive to the burstiness of the traffic, when the average traffic load is higher and when the packet loss requirement is more stringent. Initial applications of broadband packet switches are likely to be the interconnections of LANs and hosts. The results of the study indicate that the high burstiness in certain broadband traffic significantly reduces the allowable switch utilization, given a fixed amount of buffers. To increase the switch utilization, an appropriate congestion control mechanism needs to be implemented.     

Performance analysis of a dynamic handoff scheme in wireless networks with heterogeneous call arrival processes

The Guard Channel Scheme (GCS) and Handoff Queueing Scheme (HQS) are the popular and practical strategies to prioritize handoff calls in wireless cellular networks. A key issue of giving handoff calls the higher priority is how to achieve a tradeoff among the handoff call blocking probability, new call blocking probability and handoff delay. This paper extends GCS and HQS and presents an efficient handoff scheme that dynamically manages the channels reserved for handoff calls depending on the current status of the handoff queue. A three-dimensional Markov model is developed to analyze the performance of this scheme and investigate the desirable performance tradeoff. The Poisson process and Markov-Modulated-Poisson-Process (MMPP) are used to model the arrival processes of new and handoff calls, respectively. The accuracy of this model is evaluated through the extensive comparison of the analytical results to those obtained from discrete-event simulation experiments. Performance measures in terms of the mean number of calls in the system, aggregate response time, aggregate call blocking probability, handoff call blocking probability, new call blocking probability and handoff delay are evaluated. The analytical model is used to investigate the effects of the number of channels originally reserved for handoff calls, the number of dynamic channels, and the ratio of the rate of handover calls to the aggregate arrival rate on the system performance.     

Optimal buffer management policies for shared-buffer ATM switches

Shared-buffer ATM switches can have severe cell loss under asymmetrical or heavy loading conditions, which makes buffer management essential. In this paper, we study the shared-buffer system under the class of all work-conserving pushout policies and derive the properties of the optimal policy, which gives the least-average expected total cell loss probability. In a 2×2 system with independent identically distributed Bernoulli arrivals, we show that the optimal policy can be characterized by a single threshold. In the case of correlated arrivals, modeled by a discrete batch Markovian arrival process, the optimal policy has multiple thresholds, one for each phase of the arrival process. For the N×N shared buffer ATM switch, we are unable to prove optimality of any policy, but we study the system via simulations. We provide a dynamic buffer management policy and compare its performance with that of static threshold-type policies     

ATM modelling: parameterisation of 4-phase MMPP model for admissioncontrol of superposed traffic sources

A new approach is adopted to parameterise the 4-phase Markov modulated Poisson process (MMPP) to find the 4-phase arrival and transition rate parameters. This parameterisation is a major step in applying the 4-phase MMPP model to asynchronous transfer mode (ATM) modelling in the connection admission control (CAC) and in the bandwidth allocation of traffic     

Packet Trains--Measurements and a New Model for Computer Network Traffic

Traffic measurements on a ring local area computer network at the Massachusetts Institute of Technology are presented. The analysis of the arrival pattern shows that the arrival processes are neither Poisson nor compound Poisson. An alternative model called "packet train" is proposed. In the train model, the traffic on the network consists of a number of packet streams between various pairs of nodes on the network. Each node-pair stream (or node-pair process, as we call them) consists of a number of trains. Each train consists of a number of packets (or cars) going in either direction (from node A to B or from node B to A). The intercar gap is large (compared to packet transmission time) and random. The intertrain time is even larger. The Poisson and the compound Poisson arrivals are shown to be special cases of the train arrival model. Another important observation is that the packet arrivals exhibit a "source locality." If a packet is seen on the network going from A to B, the probability of the next packet going from A to B or from B to A is very high. Implications of the train arrivals and of source locality on the design of bridges, gateways, and reservation protocols are discussed. A numbet of open problems requiring development of analysis techniques for systems with train arrival processes are also described.     

Buffer Behavior for Mixed Input Traffic and Single Constant Output Rate

A queueing model with limited waiting room (buffer), mixed input traffic (Poisson and compound Poisson arrivals), and constant service rate is studied. Using average burst length, traffic intensity, and input-traffic mixture rate as parameters, we obtain relationships among buffer size, overflow probabilities, and expected message-queueing delay due to buffering. These relationships are portrayed on graphs that can be used as a guide in buffer design. Although this study arose in the design of statistical multiplexors, the queueing model developed is quite general and may be useful for other industrial applications.     

光突发交换网络基于优先级与突发包分割的光缓存方法

为了保证光突发交换(OBS)网络中不同优先级业务的服务质量(Qos)和有效地降低突发包的丢失率,提出了一种基于优先级与突发包分割的光缓存方法.该方法通过在输出数据信道上设置光纤延迟线组来缓存被分割的冲突突发包.当冲突发生时,基于突发包的优先级进行"竞争突发包头部分割或者原突发包尾部分割,,处理;无冲突部分进行交换或者直...     

Improved loss calculations at an ATM multiplexer

In this paper we develop a simple and accurate analytical technique to determine the loss probability at an access node to an asynchronous transfer mode (ATM) network. This is an important problem from the point of view of admission control and network design. The arrival processes we analyze are the Markov-modulated Poisson process (MMPP) and the Markov-modulated fluid (MMF) process. These arrival processes have been shown to model various traffic types, such as voice, video, and still images, that are expected to be transmitted by ATM networks. Our hybrid analytical technique combines results from large buffer theories and quasi-stationary approaches to analyze the loss probability of a finite-buffer queue being fed by Markov-modulated sources such as the MMPP and MMF. Our technique is shown to be valid for both heterogeneous and homogeneous sources. We also show that capacity allocation based on the popular effective-bandwidth scheme can lead to considerable under-utilization of the network and that allocating bandwidth based on our model can improve the utilization significantly. We provide numerical results for different types of traffic and validate our model via simulations     

基于标值更新通信量模型的ATM缓冲区信元丢失率分析方法

提出了一种不同于传统分析方法（如ＭＭＰＰ／Ｄ／１）的直接基于输入通信量带宽分布和自相关特性的信元丢失率分析方法,应用标值更新模型近似实际输入通信量的低阶统计特性,给出了一个基于马尔柯夫链极限概率的信元丢失率估计公式。该方法可以估计突发级的信元丢失率,而且具有算法简单,计算量小,数值稳定性好等特点。     

On the Handoff Arrival Process in Cellular Communications

Handoffs in cellular communication systems cause interactions among cells that can be modeled using multi-dimensional birth–death process approaches and the concept of system state. However, exact numerical calculation of traffic performance characteristics is hindered by unmanageably large system state spaces even for systems of modest size. Previous analytical models get around the difficulty by isolating a cell of interestand invoking a Poisson process assumption for handoff arrivals to the cell. Interactions among cells are characterized by relating the mean handoff and departure rates from cells. The current paper seeks to explore the interactions in more detail. Two additional approximate analytical models are developed for this purpose. Each of these is more complicated than the simple Poisson process model, but is analytically tractable – at least for small system sizes. One model isolates a cluster of cells (rather than just the cell of interest) from the system and invokes a Poisson process assumption for cells on the cluster periphery. Performance is calculated for the central cell. The second model also isolates a cluster of cells surrounding the cell of interest, but uses an equivalent two-state Markov Modulated Poisson Process (MMPP) to characterize handoff arrival processes to the cell of interest from each of the neighboring cells. Poisson handoff arrivals to cells on the cluster periphery are assumed. This approach has fewer states than the cluster approach. Finally we present the exact solution for a regional coverage area consisting of a single seven-cell cluster. Teletraffic performance characteristics are computed for each modeling technique and are compared. It was found that all are in close agreement with the original single isolated cell, Poisson handoff arrival model, which requires the least states.     

Delay Analysis of a Time Division Multiple Access (TDMA) Channel

The delay performance of a Time Division Multiple Access (TDMA) channel for transmitting data messages is considered. The channel is assumed to be fixed assigned to a station with unlimited buffer capacity and Poisson message arrivals. Each message gives rise to one or more packets for transmission into fixed-length time slots. The steady-state probability generating function of the queue size is derived. A formula for the expected message delay is given. The analysis is then generalized to a nonpreemptive priority queue discipline; expected message delay formulas are given for the priority classes.     

Markovian Arrival Process Parameter Estimation With Group Data

This paper addresses a parameter estimation problem of Markovian arrival process (MAP). In network traffic measurement experiments, one often encounters the group data where arrival times for a group are collected as one bin. Although the group data are observed in many situations, nearly all existing estimation methods for MAP are based on nongroup data. This paper proposes a numerical procedure for fitting a MAP and a Markov-modulated Poisson process (MMPP) to group data. The proposed algorithm is based on the expectation-maximization (EM) approach and is a natural but significant extension of the existing EM algorithms to estimate parameters of the MAP and MMPP. Specifically for the MMPP estimation, we provide an efficient approximation based on the proposed EM algorithm. We examine the performance of proposed algorithms via numerical experiments and present an example of traffic analysis with real traffic data.