Ruogu Li

Delay-Aware Cross-Layer Design for Network Utility Maximization in Multi-Hop Networks

We investigate the problem of designing delay-aware joint flow control, routing, and scheduling algorithms in general multi-hop networks for maximizing network utilization. Since the end-to-end delay performance has a complex dependence on the high-order statistics of cross-layer algorithms, earlier optimization-based design methodologies that optimize the long term network utilization are not immediately well-suited for delay-aware design. This motivates us in this work to develop a novel design framework and alternative methods that take advantage of several unexploited design choices in the routing and the scheduling strategy spaces. In particular, we reveal and exploit a crucial characteristic of back pressure-type controllers that enables us to develop a novel link rate allocation strategy that not only optimizes long-term network utilization, but also yields loop free multi-path routes between each source-destination pair. Moreover, we propose a regulated scheduling strategy, based on a token-based service discipline, for shaping the per-hop delay distribution to obtain highly desirable end-to-end delay performance. We establish that our joint flow control, routing, and scheduling algorithm achieves loop-free routes and optimal network utilization. Our extensive numerical studies support our theoretical results, and further show that our joint design leads to substantial end-to-end delay performance improvements in multi-hop networks compared to earlier solutions.

Scheduling for end-to-end deadline-constrained traffic with reliability requirements in multihop networks

We attack the challenging problem of designing a scheduling policy for end-to-end deadline-constrained traffic with reliability requirements in a multihop network. It is well known that the end-to-end delay performance for a multihop flow has a complex dependence on the high-order statistics of the arrival process and the algorithm itself. Thus, neither the earlier optimization-based approaches that aim to meet the long-term throughput demands nor the solutions that focus on a similar problem for single-hop flows directly apply. Moreover, a dynamic programming-based approach becomes intractable for such multi-timescale quality-of-service (QoS)-constrained traffic in a multihop environment. This motivates us in this paper to develop a useful architecture that enables us to exploit the degree of freedom in choosing appropriate service discipline. Based on the new architecture, we propose three different approaches, each leading to an original algorithm. We study the performance of these algorithms in different scenarios to show both optimality characteristics and to demonstrate the favorable service discipline characteristics they possess. We provide extensive numerical results to compare the performance of all of these solutions to throughput-optimal back-pressure-type schedulers and to longest waiting-time-based schedulers that have provably optimal asymptotic performance characteristics. Our results reveal that the dynamic choice of service discipline of our proposed solutions yields substantial performance improvements compared to both of these types of traditional solutions under nonasymptotic conditions.

A unified approach to optimizing performance in networks serving heterogeneous flows

We study the optimal control of communication networks in the presence of heterogeneous traffic requirements. Specifically, we distinguish the flows into two crucial classes: inelastic for modeling high-priority, delay-sensitive, and fixed-throughput applications; and elastic for modeling low-priority, delay-tolerant, and throughput-greedy applications. We note that the coexistence of such diverse flows creates complex interactions at multiple levels (e.g., flow and packet levels), which prevent the use of earlier design approaches that dominantly assume homogeneous traffic. In this work, we develop the mathematical framework and novel design methodologies needed to support such heterogeneous requirements and propose provably optimal network algorithms that account for the multilevel interactions between the flows. To that end, we first formulate a network optimization problem that incorporates the above throughput and service prioritization requirements of the two traffic types. We, then develop a distributed joint load-balancing and congestion control algorithm that achieves the dual goal of maximizing the aggregate utility gained by the elastic flows while satisfying the fixed throughput and prioritization requirements of the inelastic flows. Next, we extend our joint algorithm in two ways to further improve its performance: in delay through a virtual queue implementation with minimal throughput degradation and in utilization by allowing for dynamic multipath routing for elastic flows. A unique characteristic of our proposed dynamic routing solution is the novel two-stage queueing architecture it introduces to satisfy the service prioritization requirement.

Throughput-optimal wireless scheduling with regulated inter-service times

Motivated by the low-jitter requirements of streaming multi-media traffic, we focus on the development of scheduling strategies under fading conditions that not only maximize throughput performance but also provide regular inter-service times to users. Since the service regularity of the traffic is related to the higher-order statistics of the arrival process and the policy operation, it is highly challenging to characterize and analyze directly. We overcome this obstacle by introducing a new quantity, namely the time-since-last-service, which has a unique evolution different from a tradition queue. By combining it with the queue-length in the weight, we propose a novel maximum-weight type scheduling policy that is proven to be throughput-optimal and also provides provable service regularity guarantees. In particular, our algorithm can achieve a degree of service regularity within a constant factor of a fundamental lower bound we derive. This constant is independent of the higher-order statistics of the arrival process and can be as low as two. Our results, both analytical and numerical, exhibit significant service regularity improvements over the traditional throughput-optimal policies, which reveals the importance of incorporating the metric of time-since-last-service into the scheduling policy for providing regulated service.

Scheduling for end-to-end deadline-constrained traffic with reliability requirements in multi-hop networks

We attack the challenging problem of designing a scheduling policy for end-to-end deadline-constrained traffic with reliability requirements in a multi-hop network. It is well-known that the end-to-end delay performance for a multi-hop flow has a complex dependence on the high-order statistics of the arrival process and the algorithm itself. Thus, neither the earlier optimization based approaches that aim to meet the long-term throughput demands, nor the solutions that focus on a similar problem for single-hop flows directly apply. Moreover, a dynamic programming-based approach becomes intractable for such multi-time scale Quality-of-Service(QoS)-constrained traffic in a multi-hop environment. This motivates us in this work to develop an alternative model that enables us to exploit the degree of freedom in choosing appropriate service discipline. Based on the new model, we propose two alternative solutions, first based on a Lyapunov-drift minimization approach, and second based on a novel relaxed optimization-formulation. We provide extensive numerical results to compare the performance of both of these solutions to throughput-optimal back-pressure-type schedulers and to longest waiting time based schedulers that have provably optimal asymptotic performance characteristics. Our results reveal that the dynamic choice of service discipline of our proposed solutions yields substantial performance improvements compared to both of these types of traditional solutions under non-asymptotic conditions.

A Unified Approach to Optimizing Performance in Networks Serving Heterogeneous Flows

In this work, we study the control of communication networks in the presence of both inelastic and elastic traffic flows. The characteristics of these two types of traffic differ significantly. Hence, earlier approaches that focus on homogeneous scenarios with a single traffic type are not directly applicable. We formulate a new network optimization problem that incorporates the performance requirements of inelastic and elastic traffic flows. The solution of this problem provides us with a new queueing architecture, and distributed load balancing and congestion control algorithm with provably optimal performance. In particular, we show that our algorithm achieves the dual goal of maximizing the aggregate utility gained by the elastic flows while satisfying the demands of inelastic flows. Our base optimal algorithm is extended to provide better delay performance for both types of traffic with minimal degradation in throughput. It is also extended to the practically relevant case of dynamic arrivals and departures. Our solution allows for a controlled interaction between the performance of inelastic and elastic traffic flows. This performance can be tuned to achieve the appropriate design tradeoff. The network performance is studied both theoretically and through extensive simulations.

Throughput-optimal scheduling design with regular service guarantees in wireless networks

Motivated by the regular service requirements of video applications for improving quality of experience (QoE) of users, we consider the design of scheduling strategies in multihop wireless networks that not only maximize system throughput but also provide regular interservice times for all links. Since the service regularity of links is related to the higher-order statistics of the arrival process and the policy operation, it is challenging to characterize and analyze directly. We overcome this obstacle by introducing a new quantity, namely the time-since-last-service (TSLS), which tracks the time since the last service. By combining it with the queue length in the weight, we propose a novel maximum-weight-type scheduling policy, called Regular Service Guarantee (RSG) Algorithm. The unique evolution of the TSLS counter poses significant challenges for the analysis of the RSG Algorithm. To tackle these challenges, we first propose a novel Lyapunov function to show the throughput optimality of the RSG Algorithm. Then, we prove that the RSG Algorithm can provide service regularity guarantees by using the Lyapunov-drift-based analysis of the steady-state behavior of the stochastic processes. In particular, our algorithm can achieve a degree of service regularity within a factor of a fundamental lower bound we derive. This factor is a function of the system statistics and design parameters and can be as low as two in some special networks. Our results, both analytical and numerical, exhibit significant service regularity improvements over the traditional throughput-optimal policies, which reveals the importance of incorporating the metric of time-since-last-service into the scheduling policy for providing regulated service.

On the optimal convergence speed of wireless scheduling for fair resource allocation

In this paper, we study the design of joint flow-rate control and scheduling policies in multihop wireless networks for achieving maximum network utility with provably optimal convergence speed. Fast convergence is especially important in wireless networks that are dominated by the dynamics of incoming and outgoing flows as well as the time-sensitive applications. Yet, the design of fast converging policies in wireless networks is complicated by: 1) the interference-constrained communication capabilities, and 2) the finite set of transmission rates to select from due to operational and physical-layer constraints. We tackle these challenges by explicitly incorporating such discrete constraints to understand their impact on the convergence speed at which the running average of the received service rates and the network utility over a finite time horizon T converges to their limits. In particular, we establish a fundamental fact that the convergence speed of any feasible policy cannot be faster than Ω(1/T) under both the rate and utility metrics. Then, we develop an algorithm that achieves this optimal convergence speed in both metrics. We also show that the well-known dual algorithm can achieve the optimal convergence speed in terms of its utility value. These results reveal the interesting fact that the convergence speed of rates and utilities in wireless networks is dominated by the discrete choices of scheduling and transmission rates, which also implies that the use of higher-order flow-rate controllers with fast convergence guarantees cannot overcome the aforementioned fundamental limitation.

Wireless scheduling for network utility maximization with optimal convergence speed

In this paper, we study the design of joint flow rate control and scheduling policies in multi-hop wireless networks for achieving maximum network utility with provably optimal convergence speed. Fast convergence is especially important in wireless networks which are dominated by the dynamics of incoming and outgoing flows as well as the time sensitive applications. Yet, the design of fast converging policies in wireless networks is complicated by: (i) the interference-constrained communication capabilities, and (ii) the finite set of transmission rates to select from due to operational and physical-layer constraints. We tackle these challenges by explicitly incorporating such discrete constraints to understand their impact on the convergence speed at which the running average of the received service rates and the network utility converges to their limits. In particular, we establish a fundamental fact that the convergence speed of any feasible policy cannot be faster than Ω (1/T) under both the T rate and utility metrics. Then, we develop an algorithm that achieves this optimal convergence speed in both metrics. We also show that the well-known dual algorithm can achieve the optimal convergence speed in terms of its utility value. These results reveal the interesting fact that the convergence speed of rates and utilities in wireless networks is dominated by the discrete choices of scheduling and transmission rates, which also implies that the use of higher-order flow rate controllers with fast convergence guarantees cannot overcome the aforementioned fundamental limitation.

Optimal Dynamic Coding-Window Selection for Serving Deadline-Constrained Traffic Over Time-Varying Channels

We formulate and solve the problem of optimal channel coding and flow-rate control for serving deadline-constrained traffic with average delivery ratio requirements (typical of multimedia streaming and interactive real-time applications) over time-varying channels. To that end, we first characterize the largest set of arrival processes (rather than rates) whose deadline and delivery ratio requirements can be satisfied. Then, we propose a dynamic (channel) coding algorithm that provably satisfies the requirements of any arrival process in this region. This optimal dynamic algorithm evolves through simple iterations to utilize a combination of pricing and finite-horizon dynamic programming operations. Next, we proposed two low-complexity approximations of the algorithm that has provable performance. We also extend the setup to allow for a flow controller that adjusts the incoming flow rates to satisfy their delivery ratio constraints when the arrival process is unknown but controllable. We propose a joint dynamic coding and a rate control algorithm to solve this problem, and prove its stability under the stochastic system operation. We also apply these general results to an important wireless down-link broadcast scenario with and without random network coding capabilities. Our theoretical work is supported by extensive numerical studies, which also reveal that our dynamic coding strategy outperforms any static coding strategy by opportunistically exploiting the statistical variations in the arrival and channel processes.