Subramanian Ramakrishnan

Modeling full-length video using Markov-modulated gamma-based framework

All traffic models for MPEG-like encoded variable bit rate (VBR) video can be broadly categorized into 1) data-rate models (DRMs) and 2) frame-size models (FSMs). Almost all proposed VBR traffic models are DRMs. DRMs generate only data arrival rate, and are good for estimating average packet-loss and ATM buffer overflowing probabilities, but fail to identify such details as percentage of frames affected. FSMs generate sizes of individual MPEG frames, and are good for studying frame loss rate in addition to data loss rate. Among three previously proposed FSMs: 1) one generates frame sizes for full-length movies without preserving group-of-pictures (GOP) periodicity; 2) one generates VBR video traffic for news videos from scene content description provided to it; and 3) one generates frame sizes for full-length movies without preserving size-based video-segment transitions. In this paper, we propose two FSMs that generate frame sizes for full-length VBR videos preserving both GOP periodicity and size-based video-segment transitions.First, two-pass algorithms for analysis of full-length VBR videos are presented. After two-pass analysis, these algorithms identify size-based classes of video shots into which the GOPs are partitioned. Frames in each class produce three data sets, one each for I-, B-, and P-type frames. Each of these data sets is modeled with an axis-shifted Gamma distribution. Markov renewal processes model (size-based) video segment transitions. We have used QQ plots to show visual similarity of model-generated VBR video data sets with original data set. Leaky-bucket simulation study has been used to show similarity of data and frame loss rates between model-generated VBR videos and original video. Our study of frame-based VBR video revealed that even a low data-loss rate could affect a large fraction of I frames, causing a significant degradation of the quality of transmitted video.

Convergence in the calculation of the handoff arrival rate: a log-time iterative algorithm

Modeling to study the performance of wireless networks in recent years has produced sets of nonlinear equations with interrelated parameters. Because these nonlinear equations have no closed-form solution, the numerical values of the parameters are calculated by iterative algorithms. In a Markov chain model of a wireless cellular network, one commonly used expression for calculating the handoff arrival rate can lead to a sequence of oscillating iterative values that fail to converge. We present an algorithm that generates a monotonic sequence, and we prove that the monotonic sequence always converges. Lastly, we give a further algorithm that converges logarithmically, thereby permitting the handoff arrival rate to be calculated very quickly to any desired degree of accuracy.

Interspecific Variation in Critical Patch Size and Gap‐Crossing Ability as Determinants of Geographic Range Size Distributions

How biological processes such as reproduction and dispersal relate to the size of species’ geographic ranges constitutes a major challenge in spatial ecology and biogeography. Here we develop a spatially explicit theoretical framework that links fundamental population‐level ecological traits (e.g., rates of dispersal and population growth or decay) with landscape heterogeneity to derive estimates of species’ geographic range sizes and, further, distributions of geographic range sizes across species. Although local (patch‐scale) population dynamics in this model are completely deterministic, we consider a fragmented landscape of patches and gaps in which the spatial heterogeneity is itself stochastic. This stochastic spatial structure, which juxtaposes landscape‐level patch and gap characteristics against population‐level critical patch sizes and maximum gap‐crossing abilities, determines how far a novel species can spread from its evolutionary origin. Given reasonable assumptions about landscape structure and about the distribution of critical patch sizes and critical gap lengths among species, we obtain distributions of geographic range sizes that are qualitatively similar to those routinely found in nature (e.g., many species with small geographic ranges). Collectively, our results suggest that both interspecific differences in population‐level traits and the landscapes through which species spread help determine patterns of occupancy and geographic extent.

Study of long-duration MPEG-trace segmentation methods for developing frame-size-based traffic models

Texture and temporal variations in scenes, and peculiarities of MPEG compression algorithms result in very complex frame-size data sets for any long-duration variable bit rate (VBR) video. A major hurdle in capturing the statistical behavior of such a data trace can be removed by segmentation of all frames into an appropriate number of analytically characterizable classes. However, video-trace segmentation techniques, particularly those which also enable preserving periodicity of group of pictures (GOP) in the modeled data, are lacking in the literature.In this paper, we propose and evaluate few techniques for segmenting frame-size data sets in any long-duration video trace. The proposed techniques partition the group of pictures in a video into size-based groups called shot-classes. Frames in each shot-class have three data-sets--one each for intra (I-), bi-directional (B-), and predictive (P-) type frames. We have evaluated the performance of the proposed segmentation techniques by modeling each of I-, B-, and P-type frame in each shot-class by a Gamma distribution. Accuracy and usefulness of the proposed segmentation methods in building frame-size traffic models have been evaluated by QQ plots and the leaky-bucket simulation study. The results reveal that one of the segmentation techniques is very effective in characterizing the frame-size data behavior in a long-duration VBR video.

Features of some discrete-time cyclic queueing networks

A class of discrete-time closed cyclic networks is analyzed, where queues at each node have ample waiting room and have independent geometric service times with possibly unequal means. If each node has a single server or if there are sufficiently many parallel servers at each node to accommodate all jobs, equilibrium vectors of product form are obtained. For some other cases, equilibrium vectors of product form need not exist. For the single-server model, a normalization constant is computed and used to determine the queue-length distribution at a node.

Segmenting full-length VBR video into shots for modeling with Markov-modulated gamma-based framework

All traffic models for MPEG-like encoded variable bit rate (VBR) video can be categorized into (i) data rate models (DRMs), and (ii) frame size models (FSMs). Almost all proposed VBR traffic models are DRMs. Since DRMs generate only data arrival rate, they are good for estimating average packet-loss and ATM buffer over-flowing probabilities, but fail to identify such details as percentage of frames affected. FSMs generate sizes of individual MPEG frames, and are good for studying frame loss rate in addition to data loss rate. Among three previously proposed FSMs: (i) one generates frame sizes for full-length movies without preserving GOP-periodicity; (ii) another generates frame sizes for full-length movies without preserving size-based video-segment transitions; and (iii) the third generates VBR video traffic for news videos from scene content description provided to it presupposing a proper segmentation. In this paper, we propose two segmentation techniques for VBR videos - (a) Equal Number of GOPs in all shot classes (ENG), and (b) Geometrically Increasing Interval Lengths for shot classes (GIIL). Each technique partitions the GOPs in the video into size-based shot classes. Frames in each class produce three data-sets one each for I-, B-, and P-type frames. Each of these data-sets can be modeled with an axis shifted Gamma distribution. Markov renewal processes model interclass transitions. We have used QQ plots to show visual similarity of model-generated VBR video data-sets with original data-set. Leaky-bucket simulation study has been used to show similarity of data and frame loss rates between model-generated videos and original video. Our study of frame-based VBR video revealed GIIL segmentation technique separates the I-, B-, and P- frames in well behaved shot classes whose statistical properties can be captured by Gamma-based models.

Traffic models for MPEG-4 spatial scalable video

MPEG-4 spatial scalable encoding scheme (SSES) provides different resolutions and wide range of VBR, (variate bit rate) video to satisfy requirements of end users with variant screen resolutions and network bandwidth. In a SSES, one base layer traffic and one (or more) enhancement layer(s) traffic are generated. Although many traffic models have been developed for single layer video traffic, none exists for VBR, SSES video traffic. Our extensive studies suggest that MMG (Markov-modulated gamma) model can capture base layer traffic quite well. However, it cannot be used for modeling enhancement layer traffic for two reasons: (1) enhancement layers have no I-frames, (2) enhancement layer traffic and base layer traffic are not independent and have a strong correlation. In this paper, we propose two models for enhancement layer traffic and aggregate traffic. To maintain the correlation between base layer and enhancement layers, we augment the base-layer state transition model. The augmentation uses state transition relation between base layer and enhancement layer traffic or between base layer and aggregate traffic. The models have been validated by QQ plots and leaky-bucket simulations. The model generated traffic streams quite accurately mimic original traffic streams.

Bandwidth estimation for multiplexed videos using MMG-based single video traffic model

A video on demand (VoD) system is expected to transmit many movies over a single channel as demanded by the end users. When several videos are transmitted simultaneously over a link the effective bandwidth required per video is usually much lower than that needed by a single video because of multiplexing gain. Fast and accurate estimation of multiplexing gain is necessary for developing call admission control (CAC) algorithms. Known models which estimate queue size and effective bandwidth of multiplexed video system cannot capture frame size variations in different segments of a video, and are not very useful particularly when the number of videos is not too large. The multinomial model proposed in this paper is built on a Markov-modulated gamma (MMG)-based traffic model of a single video. It takes into consideration average frame size variations in different segments of a video and can predict multiplexing gain for any number of multiplexed videos. The model has been validated using MPEG traces of commercial movies.

Monotonicity and Asymptotic Queue-Length Distribution in Discrete-Time Networks

For closed, cyclic, discrete-time networks with one server per node and with independent, geometric service times, in equilibrium, the joint queue-length distribution can be realized as the joint distribution of independent random variables, conditionally given their sum. This tool helps establish monotonicity properties of performance measures and also helps show that the queue-length random variables are negatively associated. The queue length at a node is asymptotically analyzed through a family of networks with a fixed number of node types, where the number of nodes approaches infinity, the ratio of jobs to nodes has a positive limit, and each node type has a limiting density. The queue-length distribution at any node is shown to converge, in a strong sense, to a distribution that is conditionally geometric. As a by-product, this approach settles open issues regarding occupancy proportion and average queue length at a node type.

Queue length and occupancy in discrete-time cyclic networks with several types of nodes

For a discrete-time, closed, cyclic queueing network, where the nodes have independent, geometric service times, the equilibrium rate of local progress is determined. Faster nodes are shown to have a capacity depending only on the service probabilities. A family of such networks, each with the same number of types of nodes, is analyzed. If the number of nodes approaches infinity, and if the ratio of jobs to nodes has a positive limit and each node type has an asymptotic density, then for a given node type, the limits of the proportion of occupied nodes and the expected queue length are calculated. These values depend on the service parameter and on the asymptotic rate of local progress. The faster nodes can attain their capacity only when the limiting density of nodes of slowest type is zero.