Decomposition of general tandem queueing networks with MMPP input

For tandem queueing networks with generally distributed service times, decomposition often is the only feasible solution method besides simulation. The network is partitioned into individual nodes which are analyzed in isolation. In most existing decomposition algorithms for continuous-time networks, the output of a queue is usually approximated as a renewal process, which becomes the arrival process to the next queue. In this paper, the internal traffic processes are described as semi-Markov processes (SMPs) and Markov modulated Poisson processes (MMPPs). Thus, correlations in the traffic streams, which are known to have a considerable impact on performance, are taken into account to some extent. A two-state MMPP, which arises frequently in communications modeling, serves as input to the first queue of the tandem network. Furthermore, the single nodes may have infinite or finite buffers. Customers who arrive at a full buffer will get lost.

In principle, the analysis of an individual queue as an MMPP/G/1(/K) system delivers a wide range of performance measures. For different examples of tandem networks, stationary mean queue lengths at arbitrary time are compared to simulation data. The relative errors of the results, which are computed promptly by the decomposition component of the tool TimeNET, remain within a reasonable range.     

LRD and SRD traffic: review of results and open issues for the batch renewal process

The batch renewal process is the least-biased choice of process given only the measures of count correlation and interval correlation at all lags.

This paper reviews the batch renewal process, both for LRD (long-range-dependent) traffic and for SRD (short-range-dependent) traffic in the discrete space–discrete time domain, and in the wider context of general traffic in that domain. It shows some applications of the batch renewal process in simple queues and in queueing network models. The paper concludes with open research problems and issues arising from the discussion.     

Communication Delay in Wormhole-Switched Tori Networks under Bursty Workloads

Workloads generated by the real-world parallel applications that are executed on a multicomputer have a strong effect on the performance of its interconnection network—the hardware fabric supporting communication among individual processors. Existing multicomputer networks have been primarily designed and analysed under the assumption that the workload follows the non-bursty Poisson arrival process. As a step towards obtaining a clear understanding of network performance under various workloads, this paper presents a new analytical model for computing message latency in wormhole switched torus networks in the presence of bursty traffic, based on the well-known Markov-Modulated Poisson Process (MMPP). In order to derive the model, the approach for accurately capturing the properties of the composite MMPPs is applied to characterize traffic on network channels. Moreover, a general method has been proposed for calculating the probability of virtual channel occupancy when the traffic on network channels follows a multi-state MMPP process. Simulation experiments reveal that the model exhibits a good degree of accuracy.     

Path-wise performance in a tree-type network: Per-stream loss probability,delay, and delay variance analyses

This paper deals with path-wise performance analysis rather than a nodal one to enrich results previously obtained in the literature under simple but unsatisfactory assumptions, e.g., Poisson processes. First deriving the per-stream loss probability, delay, and delay variance of an isolated queue with multi-class input streams modeled by heterogeneous two-state Markov-modulated Poisson processes (MMPPs), we then propose simple and novel decomposition schemes working together with an input parameter modification scheme to (approximately) extract the per-stream output process for a lossy queue receiving MMPPs under a general service time distribution. The novelty of the decompositions is that they can be easily implemented based on a lossless queueing model. Through numerical experiments, we show that the accuracy in estimating the per-stream output process using such schemes is good. These decomposition schemes together with the input parameter modification scheme and a moment-based fitting algorithm used to fit the per-stream output as a two-state MMPP make analysis of path-wise performance viable by virtually treating each node in isolation along a path to get performance measures sequentially from the source node en route to the destination node.     

MRE hierarchical decomposition of general queueing network models

Summary The principle of Minimum Relative Entropy (MRE), given fully decomposable subset and aggregate mean queue length, utilisation and flow-balance constraints, is used in conjunction with asymptotic connections to infinite capacity queues, to derive new analytic approximations for the conditional and marginal state probabilities of single class general closed queueing network models (QNMs) in the context of a multilevel variable aggregation scheme. The concept of subparallelism is applied to preserve the flow conservation and a universal MRE hierarchical decomposition algorithm is proposed for the approximate analysis of arbitrary closed queueing networks with single server queues and general service-times. Heuristic criteria towards an optimal coupling of network's units at each level of aggregation are suggested. As an illustration, the MRE algorithm is implemented iteratively by using the Generalised Exponential (GE) distributional model to approximate the service and asymptotic flow processes in the network. This algorithm captures the exact solution of separable queueing networks, while for general queueing networks it compares favourably against exact solutions and known approximations.This work is sponsored by the Science and Engineering Research Council (SERC), UK, under grant GR/F29271     

A network oriented information structure: Networks, semantics and structures

This paper describes a network-type information structure applied to store models, necessary for the analysis and design of networks of a general nature—such as electrical networks, queueing networks, critical path networks, etc.—within a computer memory.

The paper presents a view on some general structural quantitative and qualitative properties of networks and illustrates how that view was transported to the organisation of the information structure.     

Traffic modeling, prediction, and congestion control for high-speednetworks: a fuzzy AR approach

In this study, a fuzzy autoregressive (fuzzy-AR) model is proposed to describe the traffic characteristics of high-speed networks. The fuzzy-AR model approximates a nonlinear time-variant process with a combination of several linear local AR processes using a fuzzy clustering method. We propose that the use of this fuzzy-AR model has greater potential for congestion control of packet network traffic. The parameter estimation problem in fuzzy-AR modeling is treated by a clustering algorithm developed from actual traffic data in high-speed networks. Based on the adaptive AR-prediction model and queueing theory, a simple congestion control scheme is proposed to provide an efficient traffic management for high-speed networks. Finally, using the actual Ethernet-LAN packet traffic data, several examples are given to demonstrate the validity of this proposed method for high-speed network traffic control     

Departure process of a single server queueing system with Markov renewal input and general service time distribution

The independence of processes in queueing systems is generally assumed when developing queueing models. However, real systems often involve several process dependencies, and failure to take these into consideration can lead to serious underestimation of the performance measures. We consider herein a single server queueing system with a Markov renewal process (MRP) for its arrival process and a general service time distribution, and derive the distribution function and correlation coefficient of the departure process. Since the departure process also often corresponds to an arrival process in downstream queues, the results obtained here can be used to derive a better approximation of the performance measures of a non-product form general queueing network.     

A general framework for deterministic service guarantees intelecommunication networks with variable length packets

By extending the recently developed filtering theory under the min-plus algebra to the max-plus algebra, we develop a general framework for providing deterministic quality-of-service guarantees in telecommunication networks with variable length packets. The traffic in such networks is modeled by marked point processes that consist of two sequences of variables: the arrival times and the packet lengths. By modifying Cruz's characterization for a counting process, we propose a traffic characterization, called g-regularity, to characterize a marked point process. Based on the traffic characterization, we introduce two basic network elements: traffic regulators that generate g-regular marked point processes; and g-servers that provides quality-of-service for marked point processes. As in the filtering theory under the min-plus algebra, network elements can be joined by concatenation, “filter bank summation”, and feedback to form a composite network element. We illustrate the use of the framework by various examples that include G/G/1 queues, VirtualClock, guaranteed rate servers in tandem, segmentation and reassembly, jitter control, dampers, and window flow control     

基于IP网络规划与设计的抖动模型的研究

提出了一个典型的模型,该模型考虑到包延时的相关性和串联队列的相关性,这对端到端的抖动有重要影响。针对一个单队列的Poisson流量分布的抖动,给出了一个非常易于计算的公式,然后推广到基于串联队列的标记流的端到端抖动。通过模拟实验可以发现,模型的分析值和模拟值基本吻合,在大流量背景下更为精确,更重要的是对于抖动而言该值是可信的,这样就可以用于网络设计过程中。     

Machine allocation algorithms for job shop manufacturing

In this paper we present algorithms for the solution of two server (machine) allocation problems that occur in manufacturing networks. The manufacturing network is modelled as an open network of queues with general interarrival time and service time distributions. The queueing network is analyzed by using the parametric decomposition method: a two-moment approximation scheme. The server allocation problems are solved by means of a marginal analysis scheme. Numerical results on two manufacturing networks are presented.     

Performance analysis of finite-buffered asynchronous multistageinterconnection networks

We present a queueing model for performance analysis of finite-buffered multistage interconnection networks. The proposed model captures network behaviour in an asynchronous communication mode and is based on realistic assumptions. A uniform traffic model is developed first and then extended to capture nonuniform traffic in the presence of a hot-spot. Throughput and delay are computed using the proposed model and the results are validated via simulation. The analysis is extended to predict performance of MIN-based multiprocessors. The effects of buffer length, switch size, and the maximum allowable outstanding requests on the system performance are discussed. Various design decisions using this model are drawn with respect to delay, throughput, and system power     

Extensions and generalizations of smoothed perturbation analysis ina generalized semi-Markov process framework

Under a very general framework, both in terms of finite-time performance measures and system structure, the authors derive smoothed perturbation analysis (SPA) estimators and prove their unbiasedness. The commuting condition, which has been key in previous work, is not required a priori, and thus the framework includes such systems as the GI/G/1/K queue and multiclass queueing networks, which do not satisfy the commuting condition. The generality achieved is traded off against the fact that the estimator is not always easily implementable on a single sample path. The use of the commuting condition in a local sense is proposed to help simplify the estimators derived: queueing and multiclass queueing networks are used as illustrative examples. For a simple multiclass closed queueing network, some simulation results are provided. When the commuting condition is satisfied globally, the framework allows the recovery of previous results on IPA and SPA estimators as corollaries of the main theorems     

A joint maximum likelihood algorithm for simultaneous track correlation and sensorbias estimation

In this study a joint maximum likelihood （JML） algorithm was developed to solve problems re- garding interdependent and contradictory relationships between track correlation and sensor bias estimation in multi-sensor information fusion systems. First, the relationships between track correlation and sensor bias estimation of a multi-sensor system were analyzed. Then, based on these relationships, a JML function of the track correlation and sensor bias estimation was developed, while an iterative two-step optimization procedure was adopted to solve the JML function. In addition, transformation of sensor bias from Cartesian coordinates to polar coordinates and a complete design of track quality and ambiguity processing were provided. Finally, several Monte Carlo simulations were built to test the effect of target density and different sensor bias in the JML algorithm. Simulation results showed that the JML algorithm presented in this paper had a higher correct correlation rate and more accurate sensor bias estimation than traditional methods, demonstrating that the JML algorithm had good performance.     

A new self-routing multicast network

In this paper, we propose a design for a new self-routing multicast network which can realize arbitrary multicast assignments between its inputs and outputs without any blocking. The network design uses a recursive decomposition approach and is based on the binary radix sorting concept. All functional components of the network are reverse banyan networks. Specifically, the new multicast network is recursively constructed by cascading a binary splitting network and two half-size multicast networks. The binary splitting network, in turn, consists of two recursively constructed reverse banyan networks. The first reverse banyan network serves as a scatter network and the second reverse banyan network serves as a quasisorting network. The advantage of this approach is to provide a way to self-route multicast assignments through the network and a possibility to reuse part of network to reduce the network cost. The new multicast network we design is compared favorably with the previously proposed multicast networks. It uses O(n log² n) logic gates, and has O(log² n) depth and O(log² n) routing time where the unit of time is a gate delay. By reusing part of the network, the feedback implementation of the network can further reduce the network cost to O(n log n)     

A queueing analysis for the denial of service (DoS) attacks in computer networks

In most network security analysis, researchers mainly focus on qualitative studies on security schemes and possible attacks, and there are few papers on quantitative analysis in the current literature. In this paper, we propose one queueing model for the evaluation of the denial of service (DoS) attacks in computer networks. The network under DoS attacks is characterized by a two-dimensional embedded Markov chain model. With this model, we can develop a memory-efficient algorithm for finding the stationary probability distribution which can be used to find other interesting performance metrics such as the connection loss probability and buffer occupancy percentages of half-open connections for regular traffic and attack traffic. Different from previous works in the literature, this paper gives a more general analytical approach to the study of security measures of a computer network under DoS attacks. We hope that our approach opens a new avenue to the quantitative evaluation of more complicated security schemes in computer networks.     

The impact of overload conditions on computer network reliability

Performance in terms of reliability of computer networks motivates this paper. A limit theorem on the extreme queue length in open queueing networks in heavy traffic is derived and then applied to a reliability model for computer networks where we relate the time of failure of a computer network to the system parameters.     

Measuring consistency in TTL-based caches

We propose a general modeling framework to evaluate the performance of cache consistency algorithms. In addition to the usual hit rate, we introduce the hit^* rate as a consistency measure, which captures the fraction of non-stale downloads from the cache. We apply these ideas to the analysis of the fixed TTL consistency algorithm in the presence of network delays. The hit and hit^* rates are evaluated when requests and updates are modeled by renewal processes. Classical results on the renewal function lead to various bounds.