QoS Stochastic Traffic Engineering for the wireless support of real-time streaming applications

Abstract

In this work, the Stochastic Traffic Engineering (STE) problem arising from the support of QoS-demanding real-time (e.g., delay and delay-jitter sensitive) media-streaming applications over unreliable IP-over-wireless pipes is addressed. Two main contributions are presented. First, we develop an optimal resource-management policy that allows a joint scheduling of the source rate, transmit energy and playout rate. Salient features of the proposed scheduling policy are that: (i) it is self-adaptive; and, (ii) it is able to provide hard (i.e., deterministic) QoS guarantees, in terms of hard limited playout delay, playout rate-jitter and pre-roll delay. Second, by referring to power and bandwidth limited access scenarios, we develop a traffic analysis of the underlying IP-over-wireless pipes that allows us to analyze the effects of both fading-induced errors and congestion-induced packet’s losses on the end-to-end performance of the proposed scheduler.

Introduction

Due to the unreliable randomly time-varying transport quality currently offered by IP-over-wireless connections, providing QoS guarantees to real-time media applications over energy-limited congestion-prone wireless IP domains is a still open challenging task, that requires an optimized (possibly, self-adaptive) management of the floating resources done available by the underlying pipe [2]. By referring to the streaming connection sketched in Fig. 1, in principle, the ultimate goal of a well designed resource’s allocation policy is to perform: (i) the self-adaptive control of the media encoding rate (i.e., the self-adaptive control of the source rate); (ii) the energy-saving control of the transmit rate; and, (iii) the self-adaptive control of the decoding rate (i.e., the self-adaptive control of the playout rate). A suitable means to attain this goal is provided by the optimization framework and self-adaptive controlling mechanisms offered by the Stochastic Traffic Engineering (STE). As it is known [1], [4], [5], STE aims at solving the traffic management problem in a cost-efficient way, when the networking connections are affected by some form of uncertainty, as, for example, the random behavior of the state of IP-over-wireless pipes. Differently from the (more) usual QoS resource’s allocation, the STE approach, not only aims at guaranteing target QoS levels, but also attempts to optimize an overall system-wide performance metric.

Triggered by these considerations, in this work we resort to the STE principles for designing a joint self-adaptive scheduler for the streaming system of Fig. 1. The target of this scheduler is to effectively cope with both the fading and congestion-induced fluctuations of the underlying transport pipe. Its ultimate target is to provide the supported real-time application with Hard QoS guarantees, while minimizing the battery-consumption at the transmit host. Specifically, as sketched in Fig. 1, we model the (possibly mobile) battery-powered source node (i.e., the Source Host (SH)) as a time-slotted fluid G/G/1 queue that embraces a Variable Bit Rate (VBR) media encoder, whose output rate (i.e., the source rate) may be adaptively controlled. Analogously, the receive node (i.e., the Destination Host (DH)) is assumed to be equipped with a G/G/1 queue, whose output rate (i.e., the playout rate) may be also controlled. In principle, both queues may be considered implemented at the Application (APP) layers of the underlying protocol stack, so that the corresponding wireless connection of Fig. 1 models the overall resulting peer-to-peer virtual pipe. The transmit server of Fig. 1 controls the rate of the traffic flow sent over the pipe on a per-slot basis, by modulating the instantaneous energy radiated by the transmit modem equipping the Physical (PHY) layer of the SH. The considered system-wide performance metric to be maximized is the resulting transmit rate averaged over both the fading and congestion-induced statistics of the state of the overall end-to-end wireless pipe.

In this application scenario, the tackled STE problem deals with the closed-form design of the scheduler that jointly performs the optimal self-adaptive management of the source, transmit and playout rates, under seven constraints. The first one is on the available average energy and it may arise from energy limitations typically imposed by the PHY layer of the considered modems. The second and the third constraint upper limit the available capacities (i.e., sizes) of the transmit and playout buffers, while the fourth constraint arises from the APP layer and fixes the maximum instantaneous source rate. The latter constraint is typically dictated by the finest granularity level allowed by the adopted media encoder (such as, for example, the minimum size of the quantization step [2]). The fifth constraint upper bounds the pre-roll delay [2], while the sixth and the seventh constraint introduce hard (i.e., deterministic) upper and lower bounds on the instantaneous values of the playout rate. We anticipate that the combined action of these last three constraints allows to guarantee hard upper bounds on the playout delay, playout rate-jitter and pre-roll delay. Overall, since both the considered performance metric and the energy constraint are expressed in terms of averages over the statistics of the connection’s state, the tackled optimization problem is an instance of STE problem.

In this context, optimized schedulers derived by exploiting the analytical tools of the Nonlinear Optimization are presented, for example, in [3], [4], [5], [6], [7], [8], [9], [10], [11]. Specifically, the paper in [3] models and analyzes the effects of error-impaired feedback signalling on the end-to-end closed-loop congestion-control of TCP/IP-based networks. Although the therein considered application scenario is the wireless one, the model of the end-to-end connection considered in [3] does not account for the presence of playout buffers and does not consider any constraint on energy resources actually available at the wireless terminals. Both contributions in [4], [5] explicitly account for the probabilistic nature of the considered networking scenarios. However, they assume that the probability distribution of the considered system’s state is (fully) known a priori, while our scheduler is capable to work without any a priori probabilistic information about the state of the underlying wireless pipe of Fig. 1, i.e., it is capable to operate in a self-adaptive way. In [6], the authors develop an optimized policy for controlling both transmit power and playout rate of the therein considered streaming system. Their target is to minimize the average power consumption and maximize the rendered average media quality. However, [6] focuses on delay-tolerant streaming applications, while our STE problem embraces the real-time control of the source, transmit and playout rates for delay-sensitive applications. In [7], [11], end-to-end congestion-control and failure-resistant TE problems are considered. Roughly speaking, both contributions develop distributed algorithms for the flow-control that aim at achieving optimized tradeoffs among user’s utility and system-wide performance. However, these contributions focus on wired-type application scenarios and, more importantly, do not account for constraints on the allowed delay and delay-jitter. More recently, some STE aspects related to the wireless access are tackled in [8], [9], [10]. Specifically, in [8] a traffic estimator and a related proactive load-distribution mechanism are developed, so as to balance the aggregate traffic experienced by Municipal access networks that support Voice over Wi-Fi (VoWiFi) applications. Author of [9] presents a STE-based rate-controller that attempts to equalize the coverage ranges attained by multi-rate 3G–4G transmission systems through the introduction of suitable adaptive queue-delays. The contribution in [10] develops a closed-loop control algorithm that exploits traffic-prediction for the optimal scheduling of multiple real-time flows accessing to IEEE 802.11e wireless networks working in the HCCA mode. Specifically, the scheduling problem tackled in [10] is solved by exploiting both the (instantaneous) backlogs of the transmit buffers and their predicted input flows (e.g., the predicted rates of the packet arrivals) as the (instantaneous) state of overall access network. Interestingly, under the operating conditions detailed in [10, Section 2], the access scheduling algorithm developed in [10] is formally proved to be stable, even when each user demands for a minimum access rate at each slot. Although all contributions in [8], [9], [10] deal with queue-based STE problems, they do not consider, indeed, the control of the playout rate, and do not account for (possible) limitations on the available average energy. Furthermore, the effects of the fading phenomena are not explicitly modelled and accounted for.

In the application context of multimedia systems and services, Adaptive Media Playout (AMP) policies that aim at minimizing suitable rate-distortion functions are the focus of several (quite recent) contributions [14], [24], [25], [26], [27]. In [14], the authors provide analytical results about the design and performance evaluation of adaptive playout policies for various streaming applications. However, no control of the source rate and transmit energy is considered in [14]. Authors of [24] propose a content-based adaptive media player that exploits the perceived motion-energy computed by measuring the motion activity of the delivered video sequence. By pursuing a similar approach, in [25] an adaptive algorithm for controlling the playout rate is developed, while the authors of [26] present an AMP controller than utilizes the quality of the connection to acquire a coarse estimate of the playout rate. Finally, [27] proposes a statistical-model-based AMP controller that leverages on suitable real-time measures of the arrival and departure flows to adaptively tune both the playout buffer’s threshold and the playout rate. Overall, all contributions in [14], [24], [25], [26], [27] are not STE-oriented, so that they do not consider the adaptive control of the source rate and/or transmit energy, and, what is more, do not provide hard QoS guarantees.

The rest of this paper is organized as follows. After introducing in Section 2 the considered networking architecture for media streaming, Section 3 develops the STE-based optimal scheduler and points out its basic structural properties. In Section 4, we carry out the traffic analysis of a TCP-friendly IP-based wireless access network, where our optimal scheduler may be actually applied. Section 5 focuses on testing performance of the proposed scheduler, while some conclusive remarks are drawn in the final Section 6. Proofs of the main results are provided in the final Appendix A, where some analytical conditions for the feasibility of the considered STE problem are also developed.

About the adopted notation, underlined letters denote vectors, scalar random variables (r.v.’s) are denoted by bold characters, while their outcomes are indicated by the corresponding no bold symbols. Furthermore, E{·} is the expectation operator, ${\mathbb{R}}_0^{+}$ is the set of nonnegative real numbers, ${\mathbb{R}}^{+}$ is the set of strictly positive real numbers, ≜ means “equal by definition”, [x]⁺ indicates the max{x, 0}, while p_σ(σ) is the probability density function (pdf) of the r.v. σ. Finally, ${\text{E}}_{\sigma }\{\phi (\mathit{\sigma }\text{;}s\text{;}q)\}\triangleq \int \phi (\sigma \text{;}s\text{;}q)p_{\sigma }(\sigma )d\sigma$ denotes the expectation of the function φ(σ; s; q) carried out over the pdf of the r.v. σ, and $[f(x){]}_a^b$ indicates the max{a; min{f(x); b}}.