Markov Modulated Poisson Process Research Articles

A Study on Performance Modelling and Analysis of Network on Chip under M-Port N-Tree Bursty Traffic

Physical constrains of integrated circuits (commonly called chip) in regards to size and finite number of wires, has made the design of System-on-Chip (SoC) more interesting to study in terms of finding better solutions for the complexity of the chip- interconnections. The SoC has hundreds of Processing Elements (PEs), and a single shared bus can no longer be acceptable due to poor scalability with the system size. Networks on Chip (NoC) have been proposed as a solution to mitigate complex on-chip communication problems for complex SoCs. They consist of computational resources in the form of PE cores and switching nodes which allow PEs to communicate with each other. Performance modelling and analysis has great theoretical and practical importance. This research is devoted to developing efficient and cost effective analytical tools for the performance analysis and enhancement of NoCs with m-port n- tree topology under bursty traffic. Therefore a new analytical model is developed to investigate the performance of NoCs with the m- port n-tree topology under bursty traffic. Even though it is broadly proved in practice that fat-tree topology and its varieties result in lower latency, higher throughput and bandwidth, still most studies on NoCs adopt Mesh, Torus and Spidergon topologies. The analytical results and those obtained from extensive simulation experiments have shown a good degree of accuracy for predicting the network performance under different design alternatives and various traffic conditions. Recent measurement studies have strongly verified that the traffic generated by many real-world applications in communication networks exhibits bursty and self-similar properties in nature and the message destinations are uniformly distributed. NoC's performance is generally affected by different traffic patterns generated by the processing elements. As the first step in the research, a new analytical model is developed to capture the burstiness and self-similarity characteristics of the traffic within NoCs through the use of Markov Modulated Poisson Process. The performance results of the developed model highlight the importance of accurate traffic modelling in the study and performance evaluation of NoCs. Having developed an efficient analytical tool to capture the traffic behaviour with a higher accuracy, in the next step, the research focuses on the effect of topology on the performance of NoCs. Many important challenges still remain as vulnerabilities within the design of NoCs with topology being the most important. Therefore a new analytical model is developed to investigate the performance of NoCs with the m-port n-tree topology under bursty traffic. Even though it is broadly proved in practice that fat-tree topology and its varieties result in lower latency, higher throughput and bandwidth, still most studies on NoCs adopt Mesh, Torus and Spidergon topologies. The results iii gained from the developed model and advanced simulation experiments significantly show the effect of fat-tree topology in reducing latency and increasing the throughput of NoCs. In order to obtain deeper understanding of NoCs performance attributes and for further improvement, in the final stage of the research, the developed analytical model was extended to consider the use of virtual channels within the architecture of NoCs. Extensive simulation experiments were carried out which show satisfactory improvements in the throughput of NoCs with fat-tree topology and VCs under bursty traffic. The analytical results and those obtained from extensive simulation experiments have shown a good degree of accuracy for predicting the network performance under different design alternatives and various traffic conditions.

Loss behavior of internet router with priority based self-similar synchronous traffic-multi server queueing system with Markovian input

In this paper, queueing behavior of the Internet router employing priority based partial buffer sharing mechanism under synchronous self-similar traffic input is investigated. Input traffic is modelled by Markov modulated Poisson process (MMPP). In view of wavelength division multiplexing technology, output port of the router is modelled as multi-server (MMPP/D/c/K) queueing system. Service times (packet lengths) are assumed to be deterministic as the traffic under consideration is slotted synchronous. Performance measures, namely, high priority and low priority packet loss probabilities, and mean length of non-critical and critical periods against the system parameters and traffic parameters are computed by means of matrix-geometric methods and approximate Markovian model. These results are useful in dimensioning the router to provide differentiated services and quality of service guarantee.

Modelling and dimensioning of a high-radix datacentre optical packet switch with recirculating optical buffers

Recently, high port-count optical packet switches, based on the Arrayed Waveguide Grating (AWG) device, have been proposed for providing the very high bandwidth and connectivity degree that will be required in future datacentre interconnection networks. A practical, cost-effective realisation of such a switch requires that over-subscription of the AWG cross-connect output ports be allowed, with the resulting packet contention being resolved using a packet buffering facility in the switch. In this paper, we propose an efficient AWG switch architecture of this type that uses a recirculating optical packet buffering scheme and we develop analytic modelling methods to estimate the switch packet blocking probability and packet buffering delay. The analytic model resolves internal traffic flows in the switch as Markov-modulated Poisson Processes (MMPP) and also allows modelling of offered load to the switch as a MMPP process. Taking this model of the switch, we first show its accuracy compared to discrete event simulations and then use it to develop a heuristic optimisation algorithm to dimension the switch hardware components, with the objective of minimising the operating cost by optimally dimensioning the main power consuming components, subject to constraints on the maximum contention probability and average and maximum propagation delays. The resulting optimised switch design demonstrates the proposed architecture to be a promising candidate for future high-port count datacentre switches.

Performance Modelling and Analysis of Software-Defined Networking under Bursty Multimedia Traffic

Software-Defined Networking (SDN) is an emerging architecture for the next-generation Internet, providing unprecedented network programmability to handle the explosive growth of big data driven by the popularisation of smart mobile devices and the pervasiveness of content-rich multimedia applications. In order to quantitatively investigate the performance characteristics of SDN networks, several research efforts from both simulation experiments and analytical modelling have been reported in the current literature. Among those studies, analytical modelling has demonstrated its superiority in terms of cost-effectiveness in the evaluation of large-scale networks. However, for analytical tractability and simplification, existing analytical models are derived based on the unrealistic assumptions that the network traffic follows the Poisson process, which is suitable to model nonbursty text data, and the data plane of SDN is modelled by one simplified Single-Server Single-Queue (SSSQ) system. Recent measurement studies have shown that, due to the features of heavy volume and high velocity, the multimedia big data generated by real-world multimedia applications reveals the bursty and correlated nature in the network transmission. With the aim of capturing such features of realistic traffic patterns and obtaining a comprehensive and deeper understanding of the performance behaviour of SDN networks, this article presents a new analytical model to investigate the performance of SDN in the presence of the bursty and correlated arrivals modelled by the Markov Modulated Poisson Process (MMPP). The Quality-of-Service performance metrics in terms of the average latency and average network throughput of the SDN networks are derived based on the developed analytical model. To consider a realistic multiqueue system of forwarding elements, a Priority-Queue (PQ) system is adopted to model the SDN data plane. To address the challenging problem of obtaining the key performance metrics, for example, queue-length distribution of a PQ system with a given service capacity, a versatile methodology extending the Empty Buffer Approximation (EBA) method is proposed to facilitate the decomposition of such a PQ system to two SSSQ systems. The validity of the proposed model is demonstrated through extensive simulation experiments. To illustrate its application, the developed model is then utilised to study the strategy of the network configuration and resource allocation in SDN networks.

Production control policies to maintain service levels in different seasons

We analyze a manufacturing system that produces a single type of product to serve multiple classes of customers with seasonal demands. The manufacturer has the flexibility to vary production rates to adapt to seasonal demands. We model the seasonal demand using a Markov modulated Poisson process, and analyze the underlying Markov decision problem to derive optimal production and inventory control policies for the manufacturer. We show that the optimal policy is characterized by a season dependent inventory threshold vector for adjusting production rates and rationing inventory. Further, we impose service level constraints according to the customer classes in each season, and analyze the impact of the service level constraints on the optimal policy and cost under different seasonal demand conditions.

Countrywide arrhythmia: emergency event detection using mobile phone data

Large scale social events that involve violence may have dramatic political, economic and social consequences. These events may result in higher crime rates, spreading of infectious diseases, economic crises, and even in migration phenomena (e.g., refugees across borders or internally displaced people). Hence, researchers have started using mobile phone data for developing tools to identify such emergency events in real time. In our paper, we apply a stochastic model, namely a Markov modulated Poisson process, for spatio-temporal detection of hourly and daily behavioral anomalies. We use the call volumes collected from an entire geographic region. Our work is based on the assumption that people tend to make calls when extraordinary events take place. We validate our methodology using a dataset of mobile phone records and events (emergency and non-emergency) from the Republic of Cote d’Ivoire. Our results show that we can successfully capture anomalous calling patterns associated with violent events, riots, as well as social non-emergency events such as holidays, sports events. Moreover, call volume changes also show significant temporal and spatial differences depending on the type of an event. Our results provide insights for the long-term goal of developing a real-time event detection system based on mobile phone data.

Compact Markov-modulated models for multiclass trace fitting

Markov-modulated Poisson processes (MMPPs) are stochastic models for fitting empirical traces for simulation, workload characterization and queueing analysis purposes. In this paper, we develop the first counting process fitting algorithm for the marked MMPP (M3PP), a generalization of the MMPP for modeling traces with events of multiple types. We initially explain how to fit two-state M3PPs to empirical traces of counts. We then propose a novel form of composition, called interposition, which enables the approximate superposition of several two-state M3PPs without incurring into state space explosion. Compared to exact superposition, where the state space grows exponentially in the number of composed processes, in interposition the state space grows linearly in the number of composed M3PPs. Experimental results indicate that the proposed interposition methodology provides accurate results against artificial and real-world traces, with a significantly smaller state space than superposed processes.

A multi-item approach to repairable stocking and expediting in a fluctuating demand environment

We consider a single inventory location where multiple types of repairable spare parts are kept for service and maintenance of several different fleets of assets. Demand for each part is a Markov modulated Poisson process (MMPP). Each fleet has a target for the maximum expected number of assets down for lack of a spare part. The inventory manager can meet this target by stocking repairables and by expediting the repair of parts. Expedited repairs have a shorter lead time. There are multiple repair shops (or departments) that handle the repair of parts and the load imposed on repair shops by expedited repairs is constrained. A dual-index policy makes stocking and expediting decisions that depend on demand fluctuations for each spare part type. We formulate the above problem as a non-linear non-convex integer programing problem and provide an algorithm based on column generation to compute feasible near optimal solutions and tight lower bounds. We show how to use the MMPP to model demand fluctuations in maintenance and other settings, including a moment fitting algorithm. We quantify the value of lead time flexibility and show that effective use of this flexibility can yield cost reductions of around 25 percent.

Unsupervised visit detection in smart homes

Assistive technologies for elderly often use ambient sensor systems to infer activities of daily living (ADL). In general such systems assume that only a single person (the resident) is present in the home. However, in real world environments, it is common to have visits and it is crucial to know when the resident is alone or not. We deal with this challenge by presenting a novel method that models regular activity patterns and detects visits. Our method is based on the Markov modulated Poisson process (MMPP), but is extended to allow the incorporation of multiple feature streams. The results from the experiments on nine months of sensor data collected in two apartments show that our model significantly outperforms the standard MMPP. We validate the generalisation of the model using two new data sets collected from an other sensor network.

A Queueing Model for Tiered Inspection Lines in Airports

This paper proposes a tiered inspection system for airport security, wherein passengers are divided into three classes based on historical security records. A two-dimensional Markov process and a Markov modulated Poisson process (MMPP) queue were used in the formu- lation of the security inspection system. Simulated annealing was then used to obtain near- optimum solution for the model. The efficacy of the proposed model was evaluated using the arrival data of passengers at Taoyuan International Airport and other two international airports. A comparison with two conventional queueing models with regard to the average waiting time demonstrated the effectiveness of the proposed security inspection system in enhancing service efficiency and boosting the level of security.

An Aggregated Process-Based Traffic Generator for Network Performance Evaluation

Nowadays, it is desirable to generate traffic which can reflect realistic network traffic environment for performance evaluation of network equipments. Existing traffic generation solutions mainly include special test equipments, software traffic generators and field programmable gate array (FPGA)-based traffic generators. However, special test equipments are generally too expensive, software traffic generators could not achieve high data rates and FPGA-based traffic generators mostly lack flexibility. This paper presents a novel traffic generation solution according to an aggregated process-based model to overcome the weakness of above methods. The traffic generator can generate real-time Poisson, two-state Markov-modulated Poisson process (MMPP-2) and self-similar traffic by hardware. The main structure of the traffic generator is presented and statistical properties of the generated traffic have been evaluated. Experiment results indicate that the proposed traffic generation solution can achieve better performance of the generated traffic compared with existing FPGA-based traffic generators while the required date rates can be up to Gbps line rate.

Performance Analysis of Wavelength Division Multiplexing Asynchronous Internet Router Employing Space Priority Mechanism under Self-Similar Traffic Input—Multi-Server Queueing System with Markovian Input and Erlang-k Services

In this paper, we analyze the queueing behaviour of wavelength division multiplexing (WDM) Internet router employing partial buffer sharing (PBS) mechanism with self-similar traffic input. In view of WDM technology in networking, each output port of the router is modelled as multi-server queueing system. To guarantee the quality of service (QoS) in Broadband integrated services digital network (B-ISDN), PBS mechanism is a promising one. As Markov modulated Poisson process (MMPP) emulates self-similar Internet traffic, we can use MMPP as input process of queueing system to investigate queueing behaviour of the router. In general, as network traffic is asynchronous (unslotted) and of variable packet lengths, service times (packet lengths) are assumed to follow Erlang-k distribution. Since, the said distribution is relatively general compared to deterministic and exponential. Hence, specific output port of the router is modelled as MMPP/Ek/s/C queueing system. The long-term performance measures namely high priority and low priority packet loss probabilities and the short-term performance measures namely mean lengths of critical and non-critical periods against the system parameters and traffic parameters are computed by means of matrix-geometric methods and approximate Markovian model. This kind of analysis is useful in dimensioning the router under self-similar traffic input employing PBS mechanism to provide differentiated services (DiffServ) and QoS guarantee.

Efficient simulation of non-Poisson non-stationary point processes to study queueing approximations

A nonstationary point process can be efficiently simulated by exploiting a representation as the composition of a rate-one process and the cumulative arrival rate function, provided that an efficient algorithm is available for generating the rate-one process, as is the case for stationary renewal processes, Markov modulated Poisson processes and many other processes. Overall efficiency can be achieved by constructing a table of the inverse cumulative arrival rate function when it is not explicitly available.

Internet router modeling using Circulant Markov modulated Poisson process- impact of fractal onset time (FOT)

Fractal point process (FPP) emulates self-similar traffic and its important characteristic is fractal onset time (FOT). However, this process being asymptotic in nature has less effective in queueing based performance analysis. In this paper, we propose a model of variance based Markovian fitting. The proposed method is to match the variance of FPP and that of superposed Circulant Markov modulated Poisson Process (CMMPP). Superposition consists of several 2-state CMMPPs and Poisson process. We present how well resultant CMMPP could approximate FPP which emulates self-similar traffic. We investigate queueing behavior of resultant queueing system in terms of packet loss probability. We demonstrate how FOT affects the fitting model and queueing behavior. Analytical results are compared with the simulation results without FOT for the validation. We conclude from the numerical example that network nodes with a self-similar input traffic can be well represented by a queueing system with CMMPP input.

Anomaly Detection Using an MMPP-based GLRT

Detection of anomalous network traffic is accomplished using a generalized likelihood ratio test (GLRT) applied to traffic arrival times. The network traffic arrival times are modelled using a Markov modulated Poisson process (MMPP). The GLRT is implemented using an estimate of the MMPP parameter obtained from training data that is not anomalous. MMPP parameter estimation is accomplished using Ryden's expectation-maximization (EM) approach. Using data from the 1999DARPA intrusion detection evaluation, the performance of a GLRT using an MMPP, a Poisson process, and a mixture of exponentials is compared. The MMPP-based GLRT has the best performance and the largest computational requirements.

Adapting Hidden Markov Models for Online Learning

In modern computer systems, the intermittent behaviour of infrequent, additional loads affects performance. Often, representative traces of storage disks or remote servers can be scarce and obtaining real data is sometimes expensive. Therefore, stochastic models, through simulation and profiling, provide cheaper, effective solutions, where input model parameters are obtained. A typical example is the Markov-modulated Poisson process (MMPP), which can have its time index discretised to form a hidden Markov model (HMM). These models have been successful in capturing bursty behaviour and cyclic patterns of I/O operations and Internet traffic, using underlying properties of the discrete (or continuous) Markov chain. However, learning on such models can be cumbersome in terms of complexity through re-training on data sets. Thus, we provide an online learning HMM (OnlineHMM), which is composed of two existing variations of HMMs: first, a sliding HMM using a moving average technique to update its parameters “on-the-fly” and, secondly, a multi-input HMM capable of training on multiple discrete traces simultaneously. The OnlineHMM reduces data processing times significantly and thence synthetic workloads become computationally more cost effective. We measure the accuracy of reproducing representative traces through comparisons of moments and autocorrelation on original data points and HMM-generated synthetic traces. We present, analytically, the training steps saved through the OnlineHMM's adapted Baum-Welch algorithm and obtain, through simulation, mean waiting times of a queueing model. Finally, we conclude our work and offer model extensions for the future.

Delay-Aware Energy-Efficient Communications Over Nakagami- <inline-formula> <tex-math notation="LaTeX">$m$</tex-math></inline-formula> Fading Channel With MMPP Traffic

In this paper, we propose a cross-layer design framework for transmitting Markov modulated Poisson process (MMPP) traffic over Nakagami- m fading channel with delay demands. The adaptive modulation and coding (AMC) technique is used at the physical layer. The energy efficiency is described as the average throughput over the average transmission power, where both of throughput and transmit power have full consideration of the queuing system. We first derive the closed-form expressions of the delay and the energy efficiency with the stationary distribution of the system. We then derive the energy efficient thresholds to choose the AMC transmission modes. At last, we derive the transmission policy to maximize the energy efficiency with delay constraints. Numerical results are provided to support the theoretical development.

When Random-Order-of-Service outperforms First-Come-First-Served

This letter focuses on the waiting time of customers in a single-server queueing system, served according to one of two well-known scheduling disciplines, Random-Order-of-Service (ROS) and First-Come-First-Served (FCFS). Arrivals are modeled with a Markov-Modulated Poisson Process (MMPP); service times are exponential. For two basic settings, ROS outperforms FCFS by several percent in terms of mean waiting time. This finding is supported by Monte Carlo simulation, as well as an intuitive argument, motivating the usefulness of ROS as alternative to FCFS.

Double-observer line transect surveys with Markov-modulated Poisson process models for animal availability.

We develop maximum likelihood methods for line transect surveys in which animals go undetected at distance zero, either because they are stochastically unavailable while within view or because they are missed when they are available. These incorporate a Markov-modulated Poisson process model for animal availability, allowing more clustered availability events than is possible with Poisson availability models. They include a mark-recapture component arising from the independent-observer survey, leading to more accurate estimation of detection probability given availability. We develop models for situations in which (a) multiple detections of the same individual are possible and (b) some or all of the availability process parameters are estimated from the line transect survey itself, rather than from independent data. We investigate estimator performance by simulation, and compare the multiple-detection estimators with estimators that use only initial detections of individuals, and with a single-observer estimator. Simultaneous estimation of detection function parameters and availability model parameters is shown to be feasible from the line transect survey alone with multiple detections and double-observer data but not with single-observer data. Recording multiple detections of individuals improves estimator precision substantially when estimating the availability model parameters from survey data, and we recommend that these data be gathered. We apply the methods to estimate detection probability from a double-observer survey of North Atlantic minke whales, and find that double-observer data greatly improve estimator precision here too.

Computational analysis of a Markovian queueing system with geometric mean-reverting arrival process

In the queueing literature, an arrival process with random arrival rate is usually modeled by a Markov-modulated Poisson process (MMPP). Such a process has discrete states in its intensity and is able to capture the abrupt changes among different regimes of the traffic source. However, it may not be suitable for modeling traffic sources with smoothly (or continuously) changing intensity. Moreover, it is less parsimonious in that many parameters are involved but some are lack of interpretation. To cope with these issues, this paper proposes to model traffic intensity by a geometric mean-reverting (GMR) diffusion process and provides an analysis for the Markovian queueing system fed by this source. In our treatment, the discrete counterpart of the GMR arrival process is used as an approximation such that the matrix geometric method is applicable. A conjecture on the error of this approximation is developed out of a recent theoretical result, and is subsequently validated in our numerical analysis. This enables us to calculate the performance measures with high efficiency and precision. With these numerical techniques, the effects from the GMR parameters on the queueing performance are studied and shown to have significant influences.