Zoomable video streaming refers to a new class of interactive video applications, where users can zoom into a video stream to view a selected region of interest in higher resolutions and pan around to move the region of interest. The zoom and pan effects are typically achieved by breaking the source video into a grid of independently decodable tiles. Streaming the tiles to a set of heterogeneous users using broadcast is challenging, as users have different link rates and different regions of interest at different resolution levels. In this paper, we consider the following problem: given the subset of tiles that each user requested, the link rate of each user, and the available time slots, at which resolution should each tile be sent, to maximize the overall video quality received by all users. We design an efficient algorithm to solve the problem above, and evaluate the solution on a testbed using 10 mobile devices. Our method is able to achieve up to 12dB improvements over other heuristic methods.
To further improve streaming performance, the last category of research jointly adapts video data rate and multicast link rate. This category is the most related to our work. @cite_13 investigate the utility optimization problem of scalable video multicast and prove that this problem is NP-Hard. A greedy algorithm is then proposed to schedule the transmissions of layers and determine the corresponding modulation and coding scheme (MCS) assigned for each transmission. @cite_24 suggest a pseudo-polynomial algorithm with dynamic programming to solve the optimization problem. Most recently, MuVi @cite_23 has been designed to investigate the optimal multicast scheduling problem for videos encoded with I, P, and B frames. As the computational complexity of the suggested algorithm @cite_24 grows quadratically with the number of available time slots, it fails to efficiently solve the optimization problem with multiple multicast sessions. To reduce the computational complexity especially for the case of multiple sessions, a fully polynomial time approximation algorithm is presented @cite_0 . The approximation factor, however, linearly decreases with the number of multicast sessions.
@cite_24 @cite_0 @cite_13 @cite_23
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Scalable video coding (SVC), together with adaptive modulation and coding (AMC), can improve wireless multicast streaming video by jointly performing radio resource allocation and modulation and coding scheme (MCS) selection. However, the existing schemes in the literature allocate radio resources for different video layers separately, which leads to a waste of radio resources. In this work, we introduce the notion of joint layer resource allocation which allows to jointly allocate resources to multiple video layers that are assigned the same MCS. We formulate this problem and prove it to be NP-hard. Then we develop a pseudo-polynomial algorithm that finds the optimal total system utility. Our algorithm assumes a very generic utility function and flexible video layer rates. To reduce the complexity of the algorithm, we also propose Fully Polynomial Time Approximation Schemes (FPTAS) for the same problem. Simulation results show that our optimal algorithm offers significant improvement on system utility over a previous optimal algorithm and a greedy algorithm both of which do not support joint layer resource allocation. The proposed approximation algorithm provides controllable tradeoff between performance and computational complexity and, with appropriately chosen parameters, it outperforms the greedy algorithm with 40 less running time. Future 4G cellular networks are featured with high data rate and improved coverage, which will enable realtime video multicast and broadcast services. Scalable video coding is very appropriate for wireless multicast service because it allows to choose different modulation and coding schemes (MCSs) for different video layers and can provide good video quality to users in good channel conditions while still maintaining reasonable video quality for other users. In order to apply scalable video coding to wireless multicast streaming, it is important to choose appropriate MCS for each video layer and to determine the right resource allocation among multiple video sessions. In this paper we propose a two-step dynamic programming algorithm that finds the optimal total system utility of all users where the system utility can be a generic non-negative, non-decreasing function of received rate. Our algorithm supports variable layer size and thus allows flexibility during the video encoding process. Simulation results show that our algorithm offers significant improvement on the video quality over a naive algorithm and an adapted greedy algorithm, especially in the scenarios with multiple real video sequences and limited radio resources. An important issue of supporting multi-user video streaming over wireless networks is how to optimize the systematic scheduling by intelligently utilizing the available network resources while, at the same time, to meet each video's Quality of Service (QoS) requirement. In this work, we study the problem of video streaming over multi-channel multi-radio multihop wireless networks, and develop fully distributed scheduling schemes with the goals of minimizing the video distortion and achieving certain fairness. We first construct a general distortion model according to the network?s transmission mechanism, as well as the rate distortion characteristics of the video. Then, we formulate the scheduling as a convex optimization problem, and propose a distributed solution by jointly considering channel assignment, rate allocation, and routing. Specifically, each stream strikes a balance between the selfish motivation of minimizing video distortion and the global performance of minimizing network congestions. Furthermore, we extend the proposed scheduling scheme by addressing the fairness problem. Unlike prior works that target at users' bandwidth or demand fairness, we propose a media-aware distortion-fairness strategy which is aware of the characteristics of video frames and ensures max-min distortion-fairness sharing among multiple video streams. We provide extensive simulation results which demonstrate the effectiveness of our proposed schemes. This paper presents a rate-distortion (RD) optimized interactive streaming method for multiview video pre-compressed by H.264 Joint Multiview Video Model (JMVM). In the proposed method, multiple encodings are first used to facilitate the flexible server-client interaction. Second, a RD-optimized scheduling strategy is provided to guarantee the optimal view-dependent delivery of multiview video. In the RD-optimized scheduling strategy, a distortion model is proposed to estimate the expected end-to-end distortion by accounting for both coding and packet-loss-induced distortions, as well as rendering-induced distortion. With the end-to-end distortion model, the server can select the optimal encoding combination for transmission. Experimental results demonstrate that the proposed method can achieve a significant end-to-end RD performance improvement over the selective streaming methods with simulcast coding or scalable multiview coding. In addition, it has better error-resilience performance to combat with packet-losses over the Internet protocol (IP) networks. We consider the content delivery problem in a fading multi-input single-output channel with cache-aided users. We are interested in the scalability of the equivalent content delivery rate when the number of users, @math , is large. Analytical results show that, using coded caching and wireless multicasting, without channel state information at the transmitter, linear scaling of the content delivery rate with respect to @math can be achieved in some different ways. First, if the multicast transmission spans over @math independent sub-channels, e.g., in quasi-static fading if @math , and in block fading or multi-carrier systems if @math , linear scaling can be obtained, when the product of the number of transmit antennas and the number of sub-channels scales logarithmically with @math . Second, even with a fixed number of antennas, we can achieve the linear scaling with a threshold-based user selection requiring only one-bit feedbacks from the users. When CSIT is available, we propose a mixed strategy that combines spatial multiplexing and multicasting. Numerical results show that, by optimizing the power split between spatial multiplexing and multicasting, we can achieve a significant gain of the content delivery rate with moderate cache size. One central issue in practically deploying network coding is the adaptive and economic allocation of network resource. We cast this as an optimization, where the net-utility-the difference between a utility derived from the attainable multicast throughput and the total cost of resource provisioning-is maximized. By employing the MAX of flows characterization of the admissible rate region for multicasting, this paper gives a novel reformulation of the optimization problem, which has a separable structure. The Lagrangian relaxation method is applied to decompose the problem into subproblems involving one destination each. Our specific formulation of the primal problem results in two key properties. First, the resulting subproblem after decomposition amounts to the problem of finding a shortest path from the source to each destination. Second, assuming the net-utility function is strictly concave, our proposed method enables a near-optimal primal variable to be uniquely recovered from a near-optimal dual variable. A numerical robustness analysis of the primal recovery method is also conducted. For ill-conditioned problems that arise, for instance, when the cost functions are linear, we propose to use the proximal method, which solves a sequence of well-conditioned problems obtained from the original problem by adding quadratic regularization terms. Furthermore, the simulation results confirm the numerical robustness of the proposed algorithms. Finally, the proximal method and the dual subgradient method can be naturally extended to provide an effective solution for applications with multiple multicast sessions Managing the Quality-of-Experience (QoE) of video streaming for wireless clients is becoming increasingly important due to the rapid growth of video traffic on wireless networks. The inherent variability of the wireless channel as well as the Variable Bit Rate (VBR) of the compressed video streams make QoE management a challenging problem. Prior work has studied this problem in the context of transmitting a single video stream. In this paper, we investigate multiplexing schemes to transmit multiple video streams from a base station to mobile clients that use number of playout stalls as a performance metric. In this context, we present an epoch-by-epoch framework to fairly allocate wireless transmission slots to streaming videos. In each epoch our scheme essentially reduces the vulnerability to stalling by allocating slots to videos in a way that maximizes the minimum ‘playout lead’ across all videos. Next, we show that the problem of allocating slots fairly is NP-complete even for a constant number of videos. We then present a fast lead-aware greedy algorithm for the problem. Our choice of greedy algorithm is motivated by the fact that this algorithm is optimal when the channel quality of a user remains unchanged within an epoch (but different users may experience different channel quality). Moreover, our experimental results based on public MPEG-4 video traces and wireless channel traces that we collected from a WiMAX test-bed show that the lead-aware greedy approach performs a fair distribution of stalls across the clients when compared to other algorithms, while still maintaining similar or lower average number of stalls per client. We consider the design of a scheduling policy for video streaming in a wireless network formed by several users and helpers (e.g., base stations). In such networks, any user is typically in the range of multiple helpers. Hence, an efficient policy should allow the users to dynamically select the helper nodes to download from and determine adaptively the quality level of the requested video segment. In order to obtain a tractable formulation, we follow a “divide and conquer” approach. First, we formulate a network utility maximization (NUM) problem where the network utility function is a concave and component-wise nondecreasing function of the time-averaged users' requested video quality index, and maximization is subject to the stability of all queues in the system. Second, we solve the NUM problem by using a Lyapunov drift plus penalty approach, obtaining a dynamic adaptive scheme that decomposes into two building blocks: 1) adaptive video quality and helper selection (run at the user nodes); and 2) dynamic allocation of the helper-to-user transmission rates (run at the help nodes). Our solution provably achieves NUM optimality in a strong per-sample path sense (i.e., without assumptions of stationarity and ergodicity). Third, we observe that, since all queues in the system are stable, all requested video chunks shall be eventually delivered. Fourth, in order to translate the requested video quality into the effective video quality at the user playback, it is necessary that the chunks are delivered within their playback deadline. This requires that the largest delay among all queues at the helpers serving any given user is less than the pre-buffering time of that user at its streaming session startup phase. In order to achieve this condition with high probability, we propose an effective and decentralized (albeit heuristic) scheme to adaptively calculate the pre-buffering and re-buffering time at each user. In this way, the system is forced to work in the “smooth streaming regime,” i.e., in the regime of very small playback buffer underrun rate. Through simulations, we evaluate the performance of the proposed algorithm under realistic assumptions of a network with densely deployed helper and user nodes, including user mobility, variable bit-rate video coding, and users joining or leaving the system at arbitrary times. The objective of this paper is to study the performance of a multicell vector perturbation (MVP) precoding technique under practical situations in a network multiple-input multiple-output (MIMO) scheme employing joint transmission. The conventional perturbation strategy that minimizes the total power is considered, and the power at each base station (BS) is properly scaled to enforce per-BS power constraints. In our scenario, we consider multiple-antenna users and use block diagonalization (BD) as the linear front-end precoder for VP. The sum rate for the MVP in the case of uniformly distributed input and an asymptotic upper bound on the sum rate at high signal-to-noise ratios (SNRs) are derived. In addition, using the asymptotic upper bound on the individual user rates, we propose a proportionally fair (PF) user scheduling algorithm of lower complexity and better performance compared with the benchmark fair semiorthogonal user selection (SUS) algorithm. As opposed to the PF-SUS, the proposed PF scheduling algorithm requires no predefined correlation threshold. Furthermore, we study the impact of backhaul delay on the performance of both VP and BD by deriving bounds on the sum rate. The numerical results show that MVP in the case of perfect channel state information (CSI) outperforms multicell BD. In the presence of a backhaul delay, the performance of MVP significantly degrades, but the upper bound on the sum rate for MVP is still higher than for multicell BD. Wired and wireless data networks have witnessed a rapid proliferation of multimedia applications such as Internet video streaming, video conferencing, etc. A desirable key feature for multimedia transmission over multiuser environments is the ability of adapting rate and quality of video stream to different QoS conditions. The most efficient approach to address the scalability of multimedia applications is to encode video streams in compliance with the scalable video coding (SVC) standard, which is proposed as an extension to H.264 AVC standard. This paper addresses the rate control and bandwidth sharing for multimedia applications that are relying on SVC-encoded video streams. In previous studies, idealistic utility functions, mainly in the form of a staircase function, were used to cast the rate allocation for SVC-encoded streams as an optimization problem. These utility functions make the optimization problem non-convex and even non-differentiable, for which achieving optimality through dual-based approaches proves quite challenging. Towards this goal, we introduce an accurate analytical model of the utility function for SVC-encoded video streams. Using the abovementioned utility model and adopting the utility-proportional optimization approach, we come up with a convex formulation and propose a dual-based distributed algorithm for rate allocation of SVC-encoded streams. To the best of our knowledge, this is the first work that focuses on an accurate utility function modeling for SVC-encoded streams. Simulation experiments show that the proposed algorithm is quite efficient in achieving the convergence towards the global optimality. Many topology-dependent transmission scheduling algorithms have been proposed to minimize the time-division multiple-access frame length in multihop packet radio networks (MPRNs), in which changes of the topology inevitably require recomputation of the schedules. The need for constant adaptation of schedules-to-mobile topology entails significant problems, especially in highly dynamic mobile environments. Hence, topology-transparent scheduling algorithms have been proposed, which utilize Galois field theory and Latin squares theory. We discuss the topology-transparent broadcast scheduling design for MPRNs. For single-channel networks, we propose the modified Galois field design (MGD) and the Latin square design (LSD) for topology-transparent broadcast scheduling. The MGD obtains much smaller minimum frame length (MFL) than the existing scheme while the LSD can even achieve possible performance gain when compared with the MGD, under certain conditions. Moreover, the inner relationship between scheduling designs based on different theories is revealed and proved, which provides valuable insight. For topology-transparent broadcast scheduling in multichannel networks, in which little research has been done, the proposed multichannel Galois field design (MCGD) can reduce the MFL approximately M times, as compared with the MGD when M channels are available. Numerical results show that the proposed algorithms outperform existing algorithms in achieving a smaller MFL. In this paper, we concentrate on opportunistic scheduling for multicast information. We pose the problem as a multicast throughput optimization problem. As a solution we present how one can jointly utilize fixed-rate and rateless erasure coding along with simple rate adaptation techniques in order to achieve the optimal multicast throughput per user. We first investigate the performance of the proposed system under i.i.d. channel conditions. Our analysis shows a linear gain for the multicast capacity over i.i.d. Rayleigh fading channels with respect to the number of users. Since the established results require coding over large number of blocks and hence induce large decoding delays, we extend our analysis to the cases where we code over shorter block lengths and thus quantify the delay-capacity tradeoffs under a simple setting. We further look into non-i.i.d. channel conditions and show achievable gains by modifying a scheduling heuristic whose fairness is well- established for opportunistic scheduling of unicast flows. Our overall evaluations demonstrate that under both i.i.d. and non-i.i.d. channel conditions, opportunistic multicasting with erasure coding can significantly improve the performance over the traditional techniques used in today's communication systems. The goal of this paper is to determine the data routes, subchannel schedules, and power allocations that maximize a weighted-sum rate of the data communicated over a generic OFDMA wireless network in which the nodes are capable of simultaneously transmitting, receiving and relaying data. Two instances are considered. In the first instance, subchannels are allowed to be time-shared by multiple links, whereas in the second instance, each subchannel is exclusively used by one of the links. Using a change of variables, the first problem is transformed into a convex form. In contrast, the second problem is not amenable to such a transformation and results in a complex mixed integer optimization problem. To develop insight into this problem, we utilize the first instance to obtain efficiently computable lower and upper bounds on the weighted-sum rate that can be achieved in the absence of time-sharing. Another lower bound is obtained by enforcing the scheduling constraints through additional power constraints and a monomial approximation technique to formulate the design problem as a geometric program. Numerical investigations show that the obtained rates are higher when time-sharing is allowed, and that the lower bounds on rates in the absence of time-sharing are relatively tight. This paper considers jointly optimal design of crosslayer congestion control, routing and scheduling for ad hoc wireless networks. We first formulate the rate constraint and scheduling constraint using multicommodity flow variables, and formulate resource allocation in networks with fixed wireless channels (or single-rate wireless devices that can mask channel variations) as a utility maximization problem with these constraints. By dual decomposition, the resource allocation problem naturally decomposes into three subproblems: congestion control, routing and scheduling that interact through congestion price. The global convergence property of this algorithm is proved. We next extend the dual algorithm to handle networks with timevarying channels and adaptive multi-rate devices. The stability of the resulting system is established, and its performance is characterized with respect to an ideal reference system which has the best feasible rate region at link layer. We then generalize the aforementioned results to a general model of queueing network served by a set of interdependent parallel servers with time-varying service capabilities, which models many design problems in communication networks. We show that for a general convex optimization problem where a subset of variables lie in a polytope and the rest in a convex set, the dual-based algorithm remains stable and optimal when the constraint set is modulated by an irreducible finite-state Markov chain. This paper thus presents a step toward a systematic way to carry out cross-layer design in the framework of “layering as optimization decomposition” for time-varying channel models. In this paper, we propose a joint subchannel and power allocation algorithm for the downlink of an orthogonal frequency-division multiple access (OFDMA) mixed femtocell macrocell network deployment. Specifically, the total throughput of all femtocell user equipments (FUEs) is maximized while the network capacity of an existing macrocell is always protected. Towards this end, we employ an iterative approach in which OFDM subchannels and transmit powers of base stations (BS) are alternatively assigned and optimized at every step. For a fixed power allocation, we prove that the optimal policy in each cell is to give each subchannel to the user with the highest signal-to-interference-plus-noise ratio (SINR) on that subchannel. For a given subchannel assignment, we adopt the successive convex approximation (SCA) approach and transform the highly nonconvex power allocation problem into a sequence of convex subproblems. In the arithmetic-geometric mean (AGM) approximation, we apply geometric programming to find optimal solutions after condensing a posynomial into a monomial. On the other hand, logarithmic and d ifference-of-two- c oncave-functions (D.C.) approximations lead us to solving a series of convex relaxation programs. With the three proposed SCA-based power optimization solutions, we show that the overall joint subchannel and power allocation algorithm converges to some local maximum of the original design problem. While a central processing unit is required to implement the AGM approximation-based solution, each BS locally computes the optimal subchannel and power allocation for its own servicing cell in the logarithmic and D.C. approximation-based solutions. Numerical examples confirm the merits of the proposed algorithm. In this paper, we systematically formulate the problem of multi-user wireless video transmission as a multi-user Markov decision process (MUMDP) by explicitly considering the users' heterogeneous video traffic characteristics, time-varying network conditions as well as, importantly, the dynamic coupling among the users' resource allocations across time, which are often ignored in existing multi-user video transmission solutions. To comply with the decentralized wireless networks' architecture, we propose to decompose the MUMDP into multiple local MDPs using Lagrangian relaxation. Unlike in conventional multi-user video transmission solutions stemming from the network utility maximization framework, the proposed decomposition enables each wireless user to individually solve its own local MDP (i.e. dynamic single-user cross-layer optimization) and the network coordinator to update the Lagrangian multipliers (i.e. resource prices) based on not only current, but also the future resource needs of all users, such that the long-term video quality of all users is maximized. This MUMDP solution provides us the necessary foundations and structures for solving multiuser video communication problems. However, to implement this framework in practice requires statistical knowledge of the experienced environment dynamics, which is often unavailable before transmission time. To overcome this obstacle, we propose a novel online learning algorithm, which allows the wireless users to simultaneously update their policies at multiple states during each time slot. This is different from conventional learning solutions, which often update the current visited state per time slot. The proposed learning algorithm can significantly improve the learning performance, thereby dramatically improving the video quality experienced by the wireless users over time. Our simulation results demonstrate the efficiency of the proposed MUMDP framework as compared to conventional multi-user video transmission solutions. We address the problem of prioritized video streaming over lossy overlay networks. We propose to exploit network path diversity via a novel randomized network coding (RNC) approach that provides unequal error protection (UEP) to the packets conveying the video content. We design a distributed receiver-driven streaming solution, where a client requests packets from the different priority classes from its neighbors in the overlay. Based on the received requests, a node in turn forwards combinations of the selected packets to the requesting peers. Choosing a network coding strategy at every node can be cast as an optimization problem that determines the rate allocation between the different packet classes such that the average distortion at the requesting peer is minimized. As the optimization problem has log-concavity properties, it can be solved with low complexity by an iterative algorithm. Our simulation results demonstrate that the proposed scheme respects the relative priorities of the different packet classes and achieves a graceful quality adaptation to network resource constraints. Therefore, our scheme substantially outperforms reference schemes such as baseline network coding techniques as well as solutions that employ rateless codes with built-in UEP properties. The performance evaluation provides additional evidence of the substantial robustness of the proposed scheme in a variety of transmission scenarios. With the advent of next-generation, bandwidth-intensive multimedia applications such as HDTV, interactive distance learning, and movie broadcasts from studios, it is becoming imperative to exploit the enormous bandwidth promised by the rapidly growing wavelength-division-multiplexing (WDM) technology. These applications require multicasting of information from a source to several destination nodes which should be performed judiciously to conserve expensive network resources. In this study, we investigate two switch architectures to support multicasting in a WDM network: one using an opaque (optical-electronic-optical approach and the other using a transparent (all-optical) approach. For both these switch architectures, we present mathematical formulations for routing and wavelength assignment of several light-tree-based multicast sessions on a given network topology at a globally optimal cost. We expand our work to also accommodate: 1) fractional-capacity sessions (where a session's capacity is a fraction of a wavelength channel's bandwidth, thereby leading to "traffic-groomed" multicast sessions) and 2) sparse splitting constraints, i.e., limited fanout of optical splitters and limited number of such splitters at each node. We illustrate the solutions obtained on different networks by solving these optimization problems, which turn out to be mixed integer linear programs (MILPs). Because the MILP is computationally intensive and does not scale well for large problem sizes, we also propose fast heuristics for establishing a set of multicast sessions in a network with or without wavelength converters and with fractional-capacity sessions. We find that, for all scenarios, the heuristics which arrange the sessions in ascending order with respect to destination set size and or cost perform better in terms of network resource usage than the heuristics which arrange the sessions in descending order. The enormous success of advanced wireless devices is pushing the demand for higher wireless data rates. Denser spectrum reuse through the deployment of more access points (APs) per square mile has the potential to successfully meet such demand. In principle, distributed multiuser multiple-input-multiple-output (MU-MIMO) provides the best approach to infrastructure density increase since several access points are connected to a central server and operate as a large distributed multiantenna access point. This ensures that all transmitted signal power serves the purpose of data transmission, rather than creating interference. In practice, however, a number of implementation difficulties must be addressed, the most significant of which is aligning the phases of all jointly coordinated APs. In this paper, we propose AirSync, a novel scheme that provides timing and phase synchronization accurate enough to enable distributed MU-MIMO. AirSync detects the slot boundary such that all APs are time-synchronous within a cyclic prefix (CP) of the orthogonal frequency-division multiplexing (OFDM) modulation and predicts the instantaneous carrier phase correction along the transmit slot such that all transmitters maintain their coherence, which is necessary for multiuser beamforming. We have implemented AirSync as a digital circuit in the field programmable gate array (FPGA) of the WARP radio platform. Our experimental testbed, comprising four APs and four clients, shows that AirSync is able to achieve timing synchronization within the OFDM CP and carrier phase coherence within a few degrees. For the purpose of demonstration, we have implemented two MU-MIMO precoding schemes, Zero-Forcing Beamforming (ZFBF) and Tomlinson-Harashima Precoding (THP). In both cases, our system approaches the theoretical optimal multiplexing gains. We also discuss aspects related to the MAC and multiuser scheduling design, in relation to the distributed MU-MIMO architecture. To the best of our knowledge, AirSync offers the first realization of the full distributed MU-MIMO multiplexing gain, namely the ability to increase the number of active wireless clients per time-frequency slot linearly with the number of jointly coordinated APs, without reducing the per client rate. In much of the theoretical literature on wireless algorithms, issues of message dissemination are considered together with issues of contention management. This combination leads to complicated algorithms and analysis, and makes it difficult to extend the work to harder communication problems. In this paper, we present results of a current project aimed at simplifying such algorithms and analysis by decomposing the treatment into two levels, using abstract "MAC layer" specifications to encapsulate the contention management. We use two different abstract MAC layers: the basic one of [14, 15] and a new probabilistic layer. We first present a typical randomized contention-manageent algorithm for a standard graph-based radio network model We show that it implements both abstract MAC layers. We combine this algorithm with greedy algorithms for single-message and multi-message global broadcast and analyze the combination, using both abstract MAC layers as intermediate layers. Using the basic MAC layer, we prove a bound of O(D log(n ∈) log Δ) for the time to deliver a single message everywhere with probability 1 -- ∈, where D is the network diameter, n is the number of nodes, and Δ is the maximum node degree. Using the probabilistic layer, we prove a bound of O((D + log(n ∈)) log Δ), which matches the best previously-known bound for single-message broadcast over the physical network model. For multi-message broadcast, we obtain bounds of O((D + kΔ) log(n ∈) log Δ) using the basic layer and O((D + kΔ log(n ∈)) log Δ) using the probabilistic layer, for the time to deliver a message everywhere in the presence of at most k concurrent messages.