Metrics, fundamental trade-offs and control policies for delay-sensitive applications in volatile environments

Abstract

With the explosion of consumer demand, media streaming will soon be the dominant type of Internet traffic. Since such applications are intrinsically delay-sensitive, the conventional network control policies and coding algorithms may not be appropriate tools for data dissemination over networks. The major issue with design and analysis of delay-sensitive applications is the notion of delay, which significantly varies across different applications and time scales. We present a framework for studying the problem of media streaming in an unreliable environment. The focus of this work is on end-user experience for such applications. First, we take an analytical approach to study fundamental rate-delay-reliability trade-offs in the context of media streaming for a single receiver system. We consider the probability of interruption in media playback (buffer underflow) as well as the number of initially buffered packets (initial waiting time) as the Quality of user Experience (QoE) metrics. We characterize the optimal trade-off between these metrics as a function of system parameters such as the packet arrival rate and the file size, for different channel models. For a memoryless channel, we model the receiver's queue dynamics as an M/D/1 queue. Then, we show that for arrival rates slightly larger than the play rate, the minimum initial buffering required to achieve certain level of interruption probability remains bounded as the file size grows. For the case where the arrival rate and the play rate match, the minimum initial buffer size should scale as the square root of the file size. We also study media streaming over channels with memory, modeled using Markovian arrival processes. We characterize the optimal trade-off curves for the infinite file size case, in such Markovian environments. Second, we generalize the results to the case of multiple servers or peers streaming to a single receiver. Random linear network coding allows us to simplify the packet selection strategies and alleviate issues such as duplicate packet reception. We show that the multi-server streaming problem over a memoryless channel can be transformed into a single-server streaming problem, for which we have characterized QoE trade-offs. Third, we study the design of media streaming applications in the presence of multiple heterogeneous wireless access methods with different access costs. Our objective is to analytically characterize the trade-off between usage cost and QoE metrics. We model each access network as a server that provides packets to the user according to a Poisson process with a certain rate and cost. User must make a decision on how many packets to buffer before playback, and which networks to access during the playback. We design, analyze and compare several control policies. In particular, we show that a simple Markov policy with a threshold structure performs the best. We formulate the problem of finding the optimal control policy as a Markov Decision Process (MDP) with a probabilistic constraint. We present the Hamilton-Jacobi-Bellman (HJB) equation for this problem by expanding the state space, and exploit it as a verification method for optimality of the proposed control policy. We use the tools and techniques developed for media streaming applications in the context of power supply networks. We study the value of storage in securing reliability of a system with uncertain supply and demand, and supply friction. We assume storage, when available, can be used to compensate, fully or partially, for the surge in demand or loss of supply. We formulate the problem of optimal utilization of storage with the objective of maximizing system reliability as minimization of the expected discounted cost of blackouts over an infinite horizon. We show that when the stage cost is linear in the size of the blackout, the optimal policy is myopic in the sense that all shocks are compensated by storage up to the available level of storage. However, when the stage cost is strictly convex, it may be optimal to curtail some of the demand and allow a small current blackout in the interest of maintaining a higher level of reserve to avoid a large blackout in the future. Finally, we examine the value of storage capacity in improving system's reliability, as well as the effects of the associated optimal policies under different stage costs on the probability distribution of blackouts.