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Ben Liang

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Published work

24 published item(s)

preprint2026arXiv

3DTMDet: A Dual-Path Synergy Network of Transformer and SSM for 3D Object Detection in Point Clouds

A fundamental challenge in point cloud object detection lies in the conflict between the extreme sparsity of distant points and the need for remote context understanding. The existing methods typically use 1D serialization to expand the receptive field, which inevitably discards already scarce local geometric details and reduces detection of distant and small objects. To address this issue, we propose 3DTMDet, a novel detection network that synergistically combines state space models (Mamba) with Transformers. The core idea is to utilize SSM's linear complexity and advantages in long sequence modeling to effectively capture global interactions between sparse and distant points, while using Transformer modules with local attention to encode fine-grained geometric structures in local point sets, preserving accurate shape information. We propose the 3D Hybrid Mamba Transformer (3DHMT) block, which uses an SSM-Attention-SSM pipeline to balance global context understanding and local detail preservation, effectively alleviating the tension between receptive field enlargement and geometric preservation in remote detection. In addition, we introduced a voxel generation block inspired by LiDAR physics, which diffuses features along the sensor observation direction to reconstruct the complete object structure of occlusion and distant areas. Extensive experiments conducted on the KITTI and ONCE datasets have shown that 3DTMDet outperforms state-of-the-art detectors. The code is available at https://github.com/QiuBingwen/3DTMDet.

preprint2026arXiv

Coupled Data and Measurement Space Dynamics for Enhanced Diffusion Posterior Sampling

Inverse problems, where the goal is to recover an unknown signal from noisy or incomplete measurements, are central to applications in medical imaging, remote sensing, and computational biology. Diffusion models have recently emerged as powerful priors for solving such problems. However, existing methods either rely on projection-based techniques that enforce measurement consistency through heuristic updates, or they approximate the likelihood $p(\boldsymbol{y} \mid \boldsymbol{x})$, often resulting in artifacts and instability under complex or high-noise conditions. To address these limitations, we propose a novel framework called \emph{coupled data and measurement space diffusion posterior sampling} (C-DPS), which eliminates the need for constraint tuning or likelihood approximation. C-DPS introduces a forward stochastic process in the measurement space $\{\boldsymbol{y}_t\}$, evolving in parallel with the data-space diffusion $\{\boldsymbol{x}_t\}$, which enables the derivation of a closed-form posterior $p(\boldsymbol{x}_{t-1} \mid \boldsymbol{x}_t, \boldsymbol{y}_{t-1})$. This coupling allows for accurate and recursive sampling based on a well-defined posterior distribution. Empirical results demonstrate that C-DPS consistently outperforms existing baselines, both qualitatively and quantitatively, across multiple inverse problem benchmarks.

preprint2022arXiv

Dynamic Regret of Online Mirror Descent for Relatively Smooth Convex Cost Functions

The performance of online convex optimization algorithms in a dynamic environment is often expressed in terms of the dynamic regret, which measures the decision maker's performance against a sequence of time-varying comparators. In the analysis of the dynamic regret, prior works often assume Lipschitz continuity or uniform smoothness of the cost functions. However, there are many important cost functions in practice that do not satisfy these conditions. In such cases, prior analyses are not applicable and fail to guarantee the optimization performance. In this letter, we show that it is possible to bound the dynamic regret, even when neither Lipschitz continuity nor uniform smoothness is present. We adopt the notion of relative smoothness with respect to some user-defined regularization function, which is a much milder requirement on the cost functions. We first show that under relative smoothness, the dynamic regret has an upper bound based on the path length and functional variation. We then show that with an additional condition of relatively strong convexity, the dynamic regret can be bounded by the path length and gradient variation. These regret bounds provide performance guarantees to a wide variety of online optimization problems that arise in different application domains. Finally, we present numerical experiments that demonstrate the advantage of adopting a regularization function under which the cost functions are relatively smooth.

preprint2022arXiv

Random Caching Design for Multi-User Multi-Antenna HetNets with Interference Nulling

The strong interference suffered by users can be a severe problem in cache-enabled networks (CENs) due to the content-centric user association mechanism. To tackle this issue, multi-antenna technology may be employed for interference management. In this paper, we consider a user-centric interference nulling (IN) scheme in two-tier multi-user multi-antenna CEN, with a hybrid most-popular and random caching policy at macro base stations (MBSs) and small base stations (SBSs) to provide file diversity. All the interfering SBSs within the IN range of a user are requested to suppress the interference at this user using zero-forcing beamforming. Using stochastic geometry analysis techniques, we derive a tractable expression for the area spectral efficiency (ASE). A lower bound on the ASE is also obtained, with which we then consider ASE maximization, by optimizing the caching policy and IN coefficient. To solve the resultant mixed integer programming problem, we design an alternating optimization algorithm to minimize the lower bound of the ASE. Our numerical results demonstrate that the proposed caching policy yields performance that is close to the optimum, and it outperforms several existing baselines.

preprint2021arXiv

Distributed coordinated precoding for MIMO cellular network virtualization

This paper presents a new virtualization method for the downlink of a multi-cell multiple-input multiple-output (MIMO) network, to achieve service isolation among multiple Service Providers (SPs) that share the base station resources of an Infrastructure Provider (InP). Each SP designs a virtual precoder for its users in each cell, as its service demand to the InP, without the need to be aware of the existence of the other SPs or to know the channel state information (CSI) outside the cell. The InP performs network virtualization to meet the SPs' service demands while managing both the inter-SP and inter-cell interference. We consider coordinated multi-cell precoding at the InP and formulate an optimization problem to minimize a weighted sum of signal leakage and precoding deviation, with per-cell transmit power constraints. We propose a fully distributed semi-closed-form solution at each cell, without any CSI exchange across cells. We further propose a low-complexity scheme to allocate the virtual transmit power, for the InP to regulate between interference elimination and virtual demand maximization. Simulation results demonstrate that our precoding solution for network virtualization substantially outperforms the traditional spectrum isolation alternative. It can approach the performance of fully cooperative precoding when the number of antennas is large.

preprint2021arXiv

Task Offloading and Resource Allocation with Multiple CAPs and Selfish Users

In this work, we consider a multi-user mobile edge computing system with multiple computing access points (CAPs). Each mobile user has multiple dependent tasks that must be processed in a round-by-round schedule. In every round, a user may process their individual task locally, or choose to offload their task to one of the $M$ CAPs or the remote cloud server, in order to possibly reduce their processing cost. We aim to jointly optimize the offloading decisions of the users and the resource allocation decisions for each CAP over a global objective function, defined as a weighted sum of total energy consumption and the round time. We first present a centralized heuristic solution, termed MCAP, where the original problem is relaxed to a semi-definite program (SDP) to probabilistically generate the offloading decision. Then, recognizing that the users often exhibit selfish behavior to reduce their individual cost, we propose a game-theoretical approach, termed MCAP-NE, which allows us to compute a Nash Equilibrium (NE) through a finite improvement method starting from the previous SDP solution. This approach leads to a solution from which the users have no incentive to deviate, with substantially reduced NE computation time. In simulation, we compare the system cost of the NE solution with those of MCAP, MCAP-NE, a random mapping, and the optimal solution, showing that our NE solution attains near optimal performance under a wide set of parameter settings, as well as demonstrating the advantages of using MCAP to produce the initial point for MCAP-NE.

preprint2020arXiv

Novel Molecular Signaling Method and System for Molecular Communication in Human Body

Recently, Molecular Communication (MC) has been recognized as an enabling technology for nanonetworks where MC is envisioned to enable nanorobots to achieve sophisticated and complex tasks in the human body for promising medical applications. Many MC methods that can be applied in the human body have been proposed and modeled in the literature. However, none of them can be used to convey information between distant points that are separated by body fluids, tissues, or placed in different organs. In this paper, we propose a new method and system for Molecular Communication in the Body, denoted MoSiMe and MoCoBo, respectively. The method takes advantage of how the absorption, distribution, metabolization, and elimination (ADME) bodily processes affects drugs, referred to as Pharmacokinetics (PK) in pharmacology, to enable MC between any points of the human body regardless of their distance even if they are in different parts of the body and separated by tissues and fluids. The architecture, design and components of the MoCoBo system and MoSiMe method are described and different transmitter designs, including a novel passive transmitter design for the first time in telecommunications, are introduced. An analytical model for the body channel is derived and validated with respect to existing human and animal tests. The model captures the ADME bodily processes that affect the kinetics of substances administered to the body. Additionally, an experimental MoCoBo proof of concept platform, capable of reliably sending and receiving a stream of bits between a transmitter and a receiver, is built and validated against clinical trials, animal tests and analytical models. The introduced platform can also be utilized to test modulation techniques and designs for new MoCoBo transmitters and receivers.

preprint2020arXiv

Online Resource Procurement and Allocation in a Hybrid Edge-Cloud Computing System

By acquiring cloud-like capacities at the edge of a network, edge computing is expected to significantly improve user experience. In this paper, we formulate a hybrid edge-cloud computing system where an edge device with limited local resources can rent more from a cloud node and perform resource allocation to serve its users. The resource procurement and allocation decisions depend not only on the cloud's multiple rental options but also on the edge's local processing cost and capacity. We first propose an offline algorithm whose decisions are made with full information of future demand. Then, an online algorithm is proposed where the edge node makes irrevocable decisions in each timeslot without future information of demand. We show that both algorithms have constant performance bounds from the offline optimum. Numerical results acquired with Google cluster-usage traces indicate that the cost of the edge node can be substantially reduced by using the proposed algorithms, up to $80\%$ in comparison with baseline algorithms. We also observe how the cloud's pricing structure and edge's local cost influence the procurement decisions.

preprint2016arXiv

Distributed Real-Time Power Balancing in Renewable-Integrated Power Grids with Storage and Flexible Loads

The large-scale integration of renewable generation directly affects the reliability of power grids. We investigate the problem of power balancing in a general renewable-integrated power grid with storage and flexible loads. We consider a power grid that is supplied by one conventional generator (CG) and multiple renewable generators (RGs) each co-located with storage,and is connected with external markets. An aggregator operates the power grid to maintain power balance between supply and demand. Aiming at minimizing the long-term system cost, we first propose a real-time centralized power balancing solution, taking into account the uncertainty of the renewable generation, loads, and energy prices. We then provide a distributed implementation algorithm, significantly reducing both computational burden and communication overhead. We demonstrate that our proposed algorithm is asymptotically optimal as the storage capacity increases and the CG ramping constraint loosens. Moreover, the distributed implementation enjoys a fast convergence rate, and enables each RG and the aggregator to make their own decisions. Simulation shows that our proposed algorithm outperforms alternatives and can achieve near-optimal performance for a wide range of storage capacity.

preprint2015arXiv

Jointly Optimal Channel Pairing and Power Allocation for Multichannel Multihop Relaying

We study the problem of channel pairing and power allocation in a multichannel multihop relay network to enhance the end-to-end data rate. Both amplify-and-forward (AF) and decode-and-forward (DF) relaying strategies are considered. Given fixed power allocation to the channels, we show that channel pairing over multiple hops can be decomposed into independent pairing problems at each relay, and a sorted-SNR channel pairing strategy is sum-rate optimal, where each relay pairs its incoming and outgoing channels by their SNR order. For the joint optimization of channel pairing and power allocation under both total and individual power constraints, we show that the problem can be decoupled into two subproblems solved separately. This separation principle is established by observing the equivalence between sorting SNRs and sorting channel gains in the jointly optimal solution. It significantly reduces the computational complexity in finding the jointly optimal solution. It follows that the channel pairing problem in joint optimization can be again decomposed into independent pairing problems at each relay based on sorted channel gains. The solution for optimizing power allocation for DF relaying is also provided, as well as an asymptotically optimal solution for AF relaying. Numerical results are provided to demonstrate substantial performance gain of the jointly optimal solution over some suboptimal alternatives. It is also observed that more gain is obtained from optimal channel pairing than optimal power allocation through judiciously exploiting the variation among multiple channels. Impact of the variation of channel gain, the number of channels, and the number of hops on the performance gain is also studied through numerical examples.

preprint2015arXiv

Phase Balancing Using Energy Storage in Power Grids under Uncertainty

Phase balancing is essential to safe power system operation. We consider a substation connected to multiple phases, each with single-phase loads, generation, and energy storage. A representative of the substation operates the system and aims to minimize the cost of all phases and to balance loads among phases. We first consider ideal energy storage with lossless charging and discharging, and propose both centralized and distributed real-time algorithms taking into account system uncertainty. The proposed algorithm does not require any system statistics and asymptotically achieves the minimum system cost with large energy storage. We then extend the algorithm to accommodate more realistic non-ideal energy storage that has imperfect charging and discharging. The performance of the proposed algorithm is evaluated through extensive simulation and compared with that of a benchmark greedy algorithm. Simulation shows that our algorithm leads to strong performance over a wide range of storage characteristics.

preprint2014arXiv

Correlations of Interference and Link Successes in Heterogeneous Cellular Networks

In heterogeneous cellular networks (HCNs), the interference received at a user is correlated over time slots since it comes from the same set of randomly located BSs. This results in the correlations of link successes, thus affecting network performance. Under the assumptions of a K-tier Poisson network, strongest-candidate based BS association, and independent Rayleigh fading, we first quantify the correlation coefficients of interference. We observe that the interference correlation is independent of the number of tiers, BS density, SIR threshold, and transmit power. Then, we study the correlations of link successes in terms of the joint success probability over multiple time slots. We show that the joint success probability is decided by the success probability in a single time slot and a diversity polynomial, which represents the temporal interference correlation. Moreover, the parameters of HCNs have an important influence on the joint success probability by affecting the success probability in a single time slot. Particularly, we obtain the condition under which the joint success probability increases with the BS density and transmit power. We further show that the conditional success probability given prior successes only depends on the path loss exponent and the number of time slots.

preprint2014arXiv

Optimizing User Association and Spectrum Allocation in HetNets: A Utility Perspective

The joint user association and spectrum allocation problem is studied for multi-tier heterogeneous networks (HetNets) in both downlink and uplink in the interference-limited regime. Users are associated with base-stations (BSs) based on the biased downlink received power. Spectrum is either shared or orthogonally partitioned among the tiers. This paper models the placement of BSs in different tiers as spatial point processes and adopts stochastic geometry to derive the theoretical mean proportionally fair utility of the network based on the coverage rate. By formulating and solving the network utility maximization problem, the optimal user association bias factors and spectrum partition ratios are analytically obtained for the multi-tier network. The resulting analysis reveals that the downlink and uplink user associations do not have to be symmetric. For uplink under spectrum sharing, if all tiers have the same target signal-to-interference ratio (SIR), distance-based user association is shown to be optimal under a variety of path loss and power control settings. For both downlink and uplink, under orthogonal spectrum partition, it is shown that the optimal proportion of spectrum allocated to each tier should match the proportion of users associated with that tier. Simulations validate the analytical results. Under typical system parameters, simulation results suggest that spectrum partition performs better for downlink in terms of utility, while spectrum sharing performs better for uplink with power control.

preprint2014arXiv

Real-Time Welfare-Maximizing Regulation Allocation in Dynamic Aggregator-EVs System

The concept of vehicle-to-grid (V2G) has gained recent interest as more and more electric vehicles (EVs) are put to use. In this paper, we consider a dynamic aggregator-EVs system, where an aggregator centrally coordinates a large number of dynamic EVs to perform regulation service. We propose a Welfare-Maximizing Regulation Allocation (WMRA) algorithm for the aggregator to fairly allocate the regulation amount among its EVs. Compared to previous works, WMRA accommodates a wide spectrum of vital system characteristics, including dynamics of EV, limited EV battery size, EV battery degradation cost, and the cost of using external energy sources for the aggregator. The algorithm operates in real time and does not require any prior knowledge of the statistical information of the system. Theoretically, we demonstrate that WMRA is away from the optimum by O(1/V), where V is a controlling parameter depending on EV's battery size. In addition, our simulation results indicate that WMRA can substantially outperform a suboptimal greedy algorithm.

preprint2014arXiv

Uplink Interference Analysis for Two-tier Cellular Networks with Diverse Users under Random Spatial Patterns

Multi-tier architecture improves the spatial reuse of radio spectrum in cellular networks, but it introduces complicated heterogeneity in the spatial distribution of transmitters, which brings new challenges in interference analysis. In this work, we present a stochastic geometric model to evaluate the uplink interference in a two-tier network considering multi-type users and base stations. Each type of tier-1 users and tier-2 base stations are modeled as independent homogeneous Poisson point processes, and tier-2 users are modeled as locally non-homogeneous clustered Poisson point processes centered at tier-2 base stations. By applying a superposition-aggregation-superposition approach, we quantify the interference at both tiers. Our model is also able to capture the impact of two types of exclusion regions, where either tier-2 base stations or tier-2 users are restricted in order to avoid cross-tier interference. As an important application of this analytical model, an intensity planning scenario is investigated, in which we aim to maximize the total income of the network operator with respect to the intensities of tier-2 cells, under constraints on the outage probabilities of tier-1 and tier-2 users. The result of our interference analysis suggests that this maximization can be converted to a standard convex optimization problem. Finally, numerical studies further demonstrate the correctness of our analysis.

preprint2013arXiv

Dominant Resource Fairness in Cloud Computing Systems with Heterogeneous Servers

We study the multi-resource allocation problem in cloud computing systems where the resource pool is constructed from a large number of heterogeneous servers, representing different points in the configuration space of resources such as processing, memory, and storage. We design a multi-resource allocation mechanism, called DRFH, that generalizes the notion of Dominant Resource Fairness (DRF) from a single server to multiple heterogeneous servers. DRFH provides a number of highly desirable properties. With DRFH, no user prefers the allocation of another user; no one can improve its allocation without decreasing that of the others; and more importantly, no user has an incentive to lie about its resource demand. As a direct application, we design a simple heuristic that implements DRFH in real-world systems. Large-scale simulations driven by Google cluster traces show that DRFH significantly outperforms the traditional slot-based scheduler, leading to much higher resource utilization with substantially shorter job completion times.

preprint2013arXiv

Insensitivity of User Distribution in Multicell Networks under General Mobility and Session Patterns

The location of active users is an important factor in the performance analysis of mobile multicell networks, but it is difficult to quantify due to the wide variety of user mobility and session patterns. In particular, the channel holding times in each cell may be arbitrarily distributed and dependent on those in other cells. In this work, we study the stationary distribution of users by modeling the system as a multi-route queueing network with Poisson inputs. We consider arbitrary routing and arbitrary joint probability distributions for the channel holding times in each route. Using a decomposition-composition approach, we show that the user distribution (1) is insensitive to the user movement patterns, (2) is insensitive to general and dependently distributed channel holding times, (3) depends only on the average arrival rate and average channel holding time at each cell, and (4) is completely characterized by an open network with M/M/infinity queues. This result is validated by experiments with the Dartmouth user mobility traces.

preprint2013arXiv

Structured Spectrum Allocation and User Association in Heterogeneous Cellular Networks

We study joint spectrum allocation and user association in heterogeneous cellular networks with multiple tiers of base stations. A stochastic geometric approach is applied as the basis to derive the average downlink user data rate in a closed-form expression. Then, the expression is employed as the objective function in jointly optimizing spectrum allocation and user association, which is of non-convex programming in nature. A computationally efficient Structured Spectrum Allocation and User Association (SSAUA) approach is proposed, solving the optimization problem optimally when the density of users is low, and near-optimally with a guaranteed performance bound when the density of users is high. A Surcharge Pricing Scheme (SPS) is also presented, such that the designed association bias values can be achieved in Nash equilibrium. Simulations and numerical studies are conducted to validate the accuracy and efficiency of the proposed SSAUA approach and SPS.

preprint2013arXiv

To Reserve or Not to Reserve: Optimal Online Multi-Instance Acquisition in IaaS Clouds

Infrastructure-as-a-Service (IaaS) clouds offer diverse instance purchasing options. A user can either run instances on demand and pay only for what it uses, or it can prepay to reserve instances for a long period, during which a usage discount is entitled. An important problem facing a user is how these two instance options can be dynamically combined to serve time-varying demands at minimum cost. Existing strategies in the literature, however, require either exact knowledge or the distribution of demands in the long-term future, which significantly limits their use in practice. Unlike existing works, we propose two practical online algorithms, one deterministic and another randomized, that dynamically combine the two instance options online without any knowledge of the future. We show that the proposed deterministic (resp., randomized) algorithm incurs no more than 2-alpha (resp., e/(e-1+alpha)) times the minimum cost obtained by an optimal offline algorithm that knows the exact future a priori, where alpha is the entitled discount after reservation. Our online algorithms achieve the best possible competitive ratios in both the deterministic and randomized cases, and can be easily extended to cases when short-term predictions are reliable. Simulations driven by a large volume of real-world traces show that significant cost savings can be achieved with prevalent IaaS prices.

preprint2013arXiv

Understanding the Benefits of Open Access in Femtocell Networks: Stochastic Geometric Analysis in the Uplink

We introduce a comprehensive analytical framework to compare between open access and closed access in two-tier femtocell networks, with regard to uplink interference and outage. Interference at both the macrocell and femtocell levels is considered. A stochastic geometric approach is employed as the basis for our analysis. We further derive sufficient conditions for open access and closed access to outperform each other in terms of the outage probability, leading to closed-form expressions to upper and lower bound the difference in the targeted received power between the two access modes. Simulations are conducted to validate the accuracy of the analytical model and the correctness of the bounds.

preprint2012arXiv

Jointly Optimal Channel and Power Assignment for Dual-Hop Multi-channel Multi-user Relaying

We consider the problem of jointly optimizing channel pairing, channel-user assignment, and power allocation, to maximize the weighted sum-rate, in a single-relay cooperative system with multiple channels and multiple users. Common relaying strategies are considered, and transmission power constraints are imposed on both individual transmitters and the aggregate over all transmitters. The joint optimization problem naturally leads to a mixed-integer program. Despite the general expectation that such problems are intractable, we construct an efficient algorithm to find an optimal solution, which incurs computational complexity that is polynomial in the number of channels and the number of users. We further demonstrate through numerical experiments that the jointly optimal solution can significantly improve system performance over its suboptimal alternatives.

preprint2012arXiv

Optimal Unitary Linear Processing for Amplify-and-Forward Cooperative OFDM systems

In this paper, we consider the amplified-and-forward relaying in an OFDM system with unitary linear processing at the relay. We proposed a general analytical framework to find the unitary linear processing matrix that maximizes the system achievable rate. We show that the optimal processing matrix is a permutation matrix, which implies that a subcarrier pairing strategy is optimal. We further derived the optimal subcarrier pairing schemes for scenarios with and without the direct source-destination path for diversity. Simulation results are presented to demonstrate the achievable gain of optimal subcarrier pairing compared with non-optimal linear processing and non-pairing.

preprint2009arXiv

Dynamic Control of Tunable Sub-optimal Algorithms for Scheduling of Time-varying Wireless Networks

It is well known that for ergodic channel processes the Generalized Max-Weight Matching (GMWM) scheduling policy stabilizes the network for any supportable arrival rate vector within the network capacity region. This policy, however, often requires the solution of an NP-hard optimization problem. This has motivated many researchers to develop sub-optimal algorithms that approximate the GMWM policy in selecting schedule vectors. One implicit assumption commonly shared in this context is that during the algorithm runtime, the channel states remain effectively unchanged. This assumption may not hold as the time needed to select near-optimal schedule vectors usually increases quickly with the network size. In this paper, we incorporate channel variations and the time-efficiency of sub-optimal algorithms into the scheduler design, to dynamically tune the algorithm runtime considering the tradeoff between algorithm efficiency and its robustness to changing channel states. Specifically, we propose a Dynamic Control Policy (DCP) that operates on top of a given sub-optimal algorithm, and dynamically but in a large time-scale adjusts the time given to the algorithm according to queue backlog and channel correlations. This policy does not require knowledge of the structure of the given sub-optimal algorithm, and with low overhead can be implemented in a distributed manner. Using a novel Lyapunov analysis, we characterize the throughput stability region induced by DCP and show that our characterization can be tight. We also show that the throughput stability region of DCP is at least as large as that of any other static policy. Finally, we provide two case studies to gain further intuition into the performance of DCP.

preprint2009arXiv

On Stability Region and Delay Performance of Linear-Memory Randomized Scheduling for Time-Varying Networks

Throughput optimal scheduling policies in general require the solution of a complex and often NP-hard optimization problem. Related literature has shown that in the context of time-varying channels, randomized scheduling policies can be employed to reduce the complexity of the optimization problem but at the expense of a memory requirement that is exponential in the number of data flows. In this paper, we consider a Linear-Memory Randomized Scheduling Policy (LM-RSP) that is based on a pick-and-compare principle in a time-varying network with $N$ one-hop data flows. For general ergodic channel processes, we study the performance of LM-RSP in terms of its stability region and average delay. Specifically, we show that LM-RSP can stabilize a fraction of the capacity region. Our analysis characterizes this fraction as well as the average delay as a function of channel variations and the efficiency of LM-RSP in choosing an appropriate schedule vector. Applying these results to a class of Markovian channels, we provide explicit results on the stability region and delay performance of LM-RSP.