Markov Modulated Poisson Process Research Articles

Statistical Multiplexing of Homogeneous Streams results in Linear Bandwidth Gains

Statistical multiplexing of traffic streams results in reduced network bandwidth requirement. The resulting gain increases with the increase in the number of streams being multiplexed together. However, the exact shape of the gain curve, as more and more streams are multiplexed together, is not known. In this paper, we first present the generalized result that the statistical gain of combining homogeneous traffic streams, of any traffic type, is a linear function of the number of streams being multiplexed. That is, given a fixed Quality of Service (QoS) constraint, like percentile delay, D, the bandwidth requirement of n streams to satisfy the delay constraint D is n x R x c where R is the bandwidth requirement of a single stream that satisfies the constraint D and c e (0,1]. We present the linear bandwidth gain result, using an extensive simulation study for video traces, specifically, streaming video (IPTV traces) and interactive video (CISCO Telepresence traces). The linear bandwidth gain result is then verified using analytical tools from two different domains. First, we validate the linearity using Queueing Theory Analysis, specifically using Interrupted Poisson Process (IPP) and Markov Modulated Poisson Process (MMPP) modeling. Second, we formally prove the linear behavior using the Asymptotic Analysis of Algorithms, specifically, the Big-O analysis.

Study about effects of self-similar IP network traffic on queuing and network performance

The paper examines self-similar properties of real communication network traffic data over a wide range of time scales. These self-similar properties are very different from the properties of traditional models based on Poisson and Markov-modulated Poisson processes. Advanced self-similar models of sequentional generators and fixed-length sequence generators, and efficient algorithms that are used to simulate self-similar behaviour of IP network traffic processes are developed and applied. Simulations and numerical results are shown and analysed. Furthermore, simulations with stochastic and long range dependent traffic source models are conducted; and efficient algorithms for buffer overflow simulation in finite buffer single server model under self-similar traffic load are developed and applied. Simulations and numerical results are shown and analysed.

Performance Modelling and Analysis of the TXOP Scheme in Wireless Multimedia Networks with Heterogeneous Stations

The explosive growth in advanced multimedia applications poses great challenges for design and deployment of wireless communication networks. Transmission Opportunity (TXOP) is a promising MAC protocol extension for provisioning of differentiated Quality-of-Service (QoS) in multimedia WLANs. However, for analytical tractability and simplicity, most existing performance models of TXOP have been restricted to unrealistic working scenarios where the traffic is saturated or follows a Poisson process, which is unable to capture the heterogeneous characteristics of multimedia traffic. To fill this gap, this paper proposes an original analytical model for TXOP in WLANs with heterogeneous stations in the presence of multimedia applications. Specifically, the traffic generated by heterogeneous stations with background, voice and video applications is modelled by the non-bursty Poisson, bursty Markov-Modulated Poisson Process, and fractal self-similar process, respectively. QoS measures including throughput, end-to-end delay, and frame loss probability are derived. The extensive comparison between the analytical results and those obtained from simulation experiments subject to the traffic parameters of real-world voice and video sources validates the accuracy of the developed model for WLANs with practical multimedia applications. The performance results reveal the importance of taking into account the heterogeneous stations for the accurate evaluation of TXOP in wireless multimedia networks.

Adaptive cognitive media delivery over composite wireless networks

Over-the-top (OTT) content-on-demand (CoD) media delivery should ideally adapt to the available resources in an opportunistic manner. The dynamic nature of the Internet traffic and wireless local area networking technologies, which are typical within the home, must be considered in order to efficiently use resources without the need and limitations associated with centralised or fixed allocation of resources. It is also undesirable for devices to continuously monitor the available channels, especially if they are battery powered. Therefore, cooperation between devices and modelling of the dynamic adaptive traffic and terminal behaviour is necessary in order that the most suitable resource sharing strategies are employed. This article examines the exploitation of cognitive resource management for delivery of OTT CoD within unmanaged wireless environments. Channel and traffic models are derived based on the Markov modulated Poisson process and this knowledge is used to derive optimal resource sharing policies. Results from simulation and experimental implementation are presented.

Characterizing pairwise contact patterns in human contact networks

We use a counting process representation of the pairwise contact process to analyze pairwise contact patterns. Studying two real-world traces, we find that the pairwise contact patterns have three characteristics. First, human contact patterns are influenced by daily and weekly cycles of activity. Second short time intervals with intensive contact event (bursts) are separated by long periods with few contact events. Third, the pairwise contact process exhibits long range dependence. We introduce a Markov modulated Poisson process (MMPP) as a flexible model for pairwise contact process exhibiting both regular structure and irregular bursts of activity. Using standard statistical techniques, we demonstrate that the proposed model is consistent with the empirical data. Our work has significant implication for mobility modeling and performance analysis in human contact networks.

Threshold dividend strategies for a Markov-additive risk model

We consider the following risk reserve model. The premium income is a level dependent Markov-modulated Brownian motion. Claim sizes are iid with a phase-type distribution. The claim arrival process is a Markov-modulated Poisson process. For this model the payment of dividends under a threshold dividend strategy and the time until ruin will be analysed.

Context-Capture Multi-Valued Decision Fusion With Fault Tolerant Capability For Wireless Sensor Networks

Wireless sensor networks (WSNs) are usually utilized to perform decision fusion of event detection. Current decision fusion schemes are based on binary valued decision and do not consider bursty contextcapture. However, bursty context and multi-valued data are important characteristics of WSNs. One on hand, the local decisions from sensors usually have bursty and contextual characteristics. Fusion center must capture the bursty context information from the sensors. On the other hand, in practice, many applications need to process multi-valued data, such as temperature and reflection level used for lightening prediction. To address these challenges, the Markov modulated Poisson process (MMPP) and multi-valued logic are introduced into WSNs to perform context-capture multi-valued decision fusion. The overall decision fusion is decomposed into two parts. The first part is the context-capture model for WSNs using superposition MMPP. Through this procedure, the fusion center has a higher probability to get useful local decisions from sensors. The second one is focused on multi-valued decision fusion. Fault detection can also be performed based on MVL. Once the fusion center detects the faulty nodes, all their local decisions are removed from the computation of the likelihood ratios. Finally, we evaluate the capability of context-capture and fault tolerant. The result supports the usefulness of our scheme.

A shock and wear system with memory of the phase of failure

We study a system subject to shocks arriving following a Markovian arrival process. These shocks can be repairable or fatal. The non-fatal shocks cause damage to the system. The lifetimes between shocks and the repair times are governed by phase-type distributions. Repair is not as good as new, a geometric process is introduced for modeling the successive operational times. After a prefixed number of shocks, the system is replaced by a new and identical one. When the system is repaired, it returns to the operational phase in which the shock arrived, this is a model with memory of the phase of failure. This system is studied in a transient and stationary regime, the availability and the rates of occurrence of the different types of failures are calculated. This system extends others previously published in the literature. Numerical applications illustrate the calculations of the paper using the Poisson process, the PH-renewal process, and the Markov-modulated Poisson process as special cases of the arrival of shocks. These applications are performed presenting the results in an algorithmic form to be computationally implemented.

Bandwidth allocation under end-to-end percentile delay bounds

We describe an efficient and accurate approximation method for calculating the bandwidth that should be allocated on each link along the path of a point-to-point Multiprotocol Label Switching connection, so that the end-to-end delay D is less than or equal to a given value T with a probability γ, that is, P(D ≤ T) = γ. We model a connection by a tandem queuing network of infinite capacity queues. The arrival process of packets to the connection is assumed to be bursty and correlated and it is depicted by a two-stage Markov-Modulated Poisson Process. The service times are exponentially distributed. The proposed method uses only the first queue of the tandem queuing network to construct an upper and lower bound of the required bandwidth so that P(D ≤ T) = γ. Subsequently, we estimate the required bandwidth using a simple interpolation function between the two bounds. Extensive comparisons with simulation showed that the results obtained have an average relative error of 1.25%. Copyright © 2011 John Wiley & Sons, Ltd.

Performance modeling of QoS in a multicode multicarrier CDMA wireless network with fading

AbstractFor emerging wireless mesh networks, multicode multicarrier CDMA(MC‐CDMA) based technology is one of the most viable candidates. We perform stochastic modelling of the queues at the mobile station for uplink communication with multicode multicarrier CDMA system with two types of traffic, namely real‐time and non‐real‐time. Each traffic is assigned its own codes. However, the non‐real‐time traffic is allowed to use codes assigned to real‐time traffic, when real‐time traffic is not using its codes. Based on the probability of bit error for a multicode MC‐CDMA system, we first compute the probability of packet error. The packet in error will be inserted into the queue until it successfully gets through to the receiver. The packet arrival process at the input queue is modelled as Markov modulated Poisson processes (MMPP). The QoS performance in terms of packet loss for real‐time traffic and the occupancy distribution for non‐real‐time traffic is evaluated using matrix geometric techniques. We present numerical results for low and high load of real‐time traffic with varying loads of non‐real‐time traffic. We observe the binomial tweaking feature of occupancy distribution at higher loads due to batch departures. Copyright © 2009 John Wiley & Sons, Ltd.

Pricing collateralized debt obligations with Markov-modulated Poisson processes

For the valuation of a CDO (collateralized debt obligation), a standard approach in practice is to employ the Gaussian copula model of (Li, 7) [J. Fixed Income, 2000, 9, 43–54]. However, this model is limited in that its framework is completely static, failing to capture the dynamic evolution of the CDO. In general, portfolio credit derivatives are subject to two kinds of risk, a default event risk, when any underlying firm involved in the CDO fails to fulfill its obligations, and credit spread risk, due to the change of the default intensity over time. In dealing with either type of risk, it is absolutely necessary to develop a dynamic model incorporating the stochastic behavior of the macro-economic conditions and their influence on the default intensity. In this paper, a dynamic stochastic model is developed where the macro-economic conditions are assumed to follow a birth–death process, which would affect loss distributions characterized by a Markov-modulated Poisson process (MMPP). By exploiting the stochastic structure of the MMPP, efficient computational procedures are established for evaluating time-dependent loss distributions and prices of the CDO. Numerical results are presented, demonstrating the potential usefulness of the model by estimating the underlying parameters based on real market data.

Modeling Cross Correlation in Three-Moment Four-Parameter Decomposition Approximation of Queueing Networks

In two-moment decomposition approximations of queueing networks, the arrival process is modeled as a renewal process, and each station is approximated as a GI/G/1 queue whose mean waiting time is approximated based on the first two moments of the interarrival times and the service times. The departure process is also approximated as a renewal process even though the autocorrelation of this process may significantly affect the performance of the subsequent queue depending on the traffic intensity. When the departure process is split into substreams by Markovian random routing, the split processes typically are modeled as independent renewal processes even though they are correlated with each other. This cross correlation might also have a serious impact on the queueing performance. In this paper, we propose an approach for modeling both the cross correlation and the autocorrelation by a three-moment four-parameter decomposition approximation of queueing networks. The arrival process is modeled as a nonrenewal process by a two-state Markov-modulated Poisson process, viz., MMPP(2). The cross correlation between randomly split streams is accounted for in the second and third moments of the merged process by the innovations method. The main contribution of the present research is that both the cross correlation and the autocorrelation can be modeled in parametric decomposition approximations of queueing networks by integrating the MMPP(2) approximation of the arrival/departure process and the innovations method. We also present numerical results that strongly support our refinements.

Design of Active Queue Management for Robust Control on Access Router for Heterogeneous Networks

The Internet architecture is a packet switching technology that allows dynamic sharing of bandwidth among different flows with in an IP network. Packets are stored and forwarded from one node to the next until reaching their destination. Major issues in this integration are congestion control and how to meet different quality of service requirements associated with various services. In other words streaming media quality degrades with increased packet delay and jitter caused by network congestion. To mitigate the impact of network congestion, various techniques have been used to improve multimedia quality and one of those techniques is Active Queue Management (AQM). Access routers require a buffer to hold packets during times of congestion. A large buffer can absorb the bursty arrivals, and this tends to increase the link utilizations but results in higher queuing delays. Traffic burstiness has a considerable negative impact on network performance. AQM is now considered an effective congestion control mechanism for enhancing transport protocol performance over wireless links. In order to have good link utilization, it is necessary for queues to adapt to varying traffic loads. This paper considers a particular scheme which is called Adaptive AQM (AAQM) and studies its performance in the presence of feedback delays and its ability to maintain a small queue length as well as its robustness in the presence of traffic burstiness. The paper also presents a method based on the well-known Markov Modulated Poisson Process (MPP) to capture traffic burstiness and buffer occupancy. To demonstrate the generality of the presented method, an analytic model is described and verified by extensive simulations of different adaptive AQM algorithms. The analysis and simulations show that AAQM outperforms the other AQMs with respect to responsiveness and robustness.

Maximum likelihood-based analysis of single-molecule photon arrival trajectories

In this work we explore the statistical properties of the maximum likelihood-based analysis of one-color photon arrival trajectories. This approach does not involve binning and, therefore, all of the information contained in an observed photon strajectory is used. We study the accuracy and precision of parameter estimates and the efficiency of the Akaike information criterion and the Bayesian information criterion (BIC) in selecting the true kinetic model. We focus on the low excitation regime where photon trajectories can be modeled as realizations of Markov modulated Poisson processes. The number of observed photons is the key parameter in determining model selection and parameter estimation. For example, the BIC can select the true three-state model from competing two-, three-, and four-state kinetic models even for relatively short trajectories made up of 2 × 10(3) photons. When the intensity levels are well-separated and 10(4) photons are observed, the two-state model parameters can be estimated with about 10% precision and those for a three-state model with about 20% precision.

Traffic Modeling in PLC Networks using a Markov Fluid Model with Autocorrelation Function Fitting

In this paper, we present an analysis of VoIP (Voice over IP) traffic and data transfer using PLC (PowerLine Communications) network. We propose a model based on MMFM (Markov Modulated Fluid Models) for data and VoIP traffic in PLC networks. Simulations and comparisons were carried out to verify the efficiency of the proposed traffic model over the Poisson and MMPP (Markov Modulated Poisson Process) models.

Species Occupancy Modeling for Detection Data Collected Along a Transect

The proportion of sampling sites occupied by a species is a concept of interest in ecology and biodiversity conservation. Occupancy surveys based on collecting detection data along transects have become increasingly popular to monitor some species. To date, the analysis of such data has been carried out by discretizing the data, dividing the transects into discrete segments. Here we propose alternative occupancy models which describe the detection process as a continuous point process. These models provide a more natural description of the data and eliminate the need to divide transects into segments, which can be arbitrary and may lead to increased bias in the estimator of occupancy or increased chances of obtaining estimates on the boundary of the parameter space. We present a model that assumes independence between detections and an alternative model that describes the detection process as a Markov modulated Poisson process to account for potential clustering in the detections. The utility of these models is illustrated with the analysis of data from a recent survey of the Sumatran tiger Panthera tigris sumatrae. The models can also be applied to surveys that collect continuous data in time, such as those based on the use of camera-trap devices. Supplementary materials for this article are available online.

MMPP+M/D/1 Traffic Model in Video-Data Integrated Service under ATM System

With the advent of 3G mobile communication system, the traffic of wired and wireless networks become voice/video - data integrated service. For real time operation of voice and video signals, circuit switch traffic or Markovian traffic is the best fitted but for data traffic where small amount of delay is tolerable, the non-Markovian traffic like service time of general distribution with finite buffer is preferable. In this paper, Markov modulated Poisson process (MMPP) traffic, which is in concise form of Markovian chain, is used for multimedia traffic and M/D/1 traffic of fixed length packet is considered for asynchronous transfer mode (ATM) cell. The combined model becomes MMPP + M/D/1 traffic, which is used to get the probability density function and mean delay of a voice/video-integrated network.

Optimal design and analysis of a two-hop relay network under Rayleigh fading for packet delay minimization

In this paper, we consider a wireless network consisting of a source node, a destination node and multiple relay nodes under Rayleigh fading. Cooperative diversity in the network is achieved by selecting an opportunistic relay node with the best channel condition to the destination node. We focus on the packet level performance in this paper and analyze the average packet delay of the network for various modulation and coding schemes. We assume that the arrival process of packets follows a Markov modulated Poisson process (MMPP). To derive the average packet delay, we first derive the distribution of the number of packets that are successfully transmitted from the source node to the destination node via a relay node. Using the distribution obtained above, a queueing process of the M/G/1 type is developed to model the queue at the source node. The average packet delay is then obtained from the stationary distribution of the queueing process of the source node by applying Little's Lemma. Based on our results on the average packet delay, the optimal modulation and coding scheme for given network parameters is determined to minimize the average packet delay.We validate our analytic model through simulation. The detailed relations between the average packet delay and network parameters such as average signal to noise ratios (SNRs) between nodes, the number of relay nodes and packet arrival rate, are investigated through numerical studies based on our analytic model as well as simulation studies. From our numerical results, we conclude that the optimal modulation and coding scheme that minimizes the average packet delay depends not only on SNRs of channels between nodes but also on the arrival rate of packets at the data link layer.

Recursions for the MMPP Score Vector and Observed Information Matrix

Exact forward recursions for the score vector and observed information matrix of the Markov-modulated Poisson process (MMPP) are developed. The recursions are motivated by similar recursions developed for hidden Markov models by Lystig and Hughes who extended earlier work by LeGland and Mèvel. Explicit expressions for the first derivative and Hessian of the MMPP transition density matrix are developed and coupled with the recursions. The recursions are implemented and applied to confidence interval estimation in a simulation study.

Advanced Models and Algorithms for Self-Similar IP Network Traffic Simulation and Performance Analysis

Advanced Models and Algorithms for Self-Similar IP Network Traffic Simulation and Performance Analysis The paper examines self-similar (or fractal) properties of real communication network traffic data over a wide range of time scales. These self-similar properties are very different from the properties of traditional models based on Poisson and Markov-modulated Poisson processes. Advanced fractal models of sequentional generators and fixed-length sequence generators, and efficient algorithms that are used to simulate self-similar behavior of IP network traffic data are developed and applied. Numerical examples are provided; and simulation results are obtained and analyzed.