The effect of multiple time scales and subexponentiality in MPEGvideo streams on queueing behavior

Guided by the empirical observation that real-time MPEG video streams exhibit both multiple time scale and subexponential characteristics, we construct a video model that captures both of these characteristics and is amenable to queueing analysis. We investigate two fundamental approaches for extracting the model parameters: using sample path and second-order statistics-based methods. The model exhibits the following two canonical queueing behaviors. When strict stability conditions are satisfied, i.e., the conditional mean of each scene is smaller than the capacity of the server, precise modeling of the interscene dynamics (long-term dependency) is not essential for the accurate prediction of small to moderately large queue sizes. In this case, the queue length distribution is determined using quasistationary (perturbation theory) analysis. When weak stability conditions are satisfied, i.e., the conditional mean of at least one scene type is greater than the capacity of the server, the dominant effect for building a large queue size is the subexponential (long-tailed) scene length distribution. In this case, precise modeling of intrascene statistics is of secondary importance for predicting the large queueing behavior. A fluid model, whose arrival process is obtained from the video data by replacing scene statistics with their means, is shown to asymptotically converge to the exact queue distribution. Using the transition scenario of moving from one stability region to the other by a change in the value of the server capacity, we synthesize recent queueing theoretic advances and ad hoc results in video modeling, and unify a broad range of seemingly contradictory experimental observations found in the literature. As a word of caution for the widespread usage of second-order statistics modeling methods, we construct two processes with the same second-order statistics that produce distinctly different queueing behaviors     

Pricing, provisioning and peering: dynamic markets fordifferentiated Internet services and implications for networkinterconnections

This paper presents a decentralized auction-based approach to pricing of edge-allocated bandwidth in a differentiated services Internet. The players in our network economy model are one raw-capacity seller per network, one broker per service per network, and users, to play the roles of whole-sellers, retailers, and end-buyers, respectively, in a two-tier wholeseller/retailer market, which is best interpreted as a “sender-pay” model. With the progressive second price auction mechanism as the basic building block, we conduct a game theoretic analysis, deriving optimal strategies for buyers and brokers, and show the existence of networkwide market equilibria. In addition to pricing, another key consideration in building differentiated network services is the feasibility of maintaining stable and consistent service level agreements across multiple networks where demand-driven dynamic allocations are made only at the edges. Based on the proposed game-theoretic model, we are able to construct an explicit necessary and sufficient condition for the stability of the game, which determines the sustainability of any set of service level agreement configurations between Internet service providers. These analytical results are validated with simulations of user and broker dynamics, using the distributed progressive second price auction as the spot market mechanism in a scenario with three interconnected networks, and two services based on the proposed standard expedited forwarding and assured forwarding per-hop behavior