Since Tassiulas and Ephremides proposed the maximum weight scheduling algorithm of throughput-optimality for constrained queueing networks in 1992, extensive research efforts have been made for resolving its high complexity issue under various directions. In this paper, we resolve the issue by developing a generic framework for designing throughput-optimal and low-complexity scheduling algorithms. Under the framework, an algorithm updates current schedules via an interaction with a given oracle system that can generate a solution of a certain discrete optimization problem in a finite number of interactive queries. Therefore, one can design a variety of scheduling algorithms under this framework by choosing different oracles, e.g., the exhaustive search (ES), the markov chain monte carlo (MCMC), the belief propagation (BP) and the cutting-plane (CP) algorithms. The complexity of the resulting algorithm is decided by the number of operations required for an oracle processing a single query, which is typically very small. Somewhat surprisingly, we prove that an algorithm using any such oracle is throughput-optimal for general constrained queueing network models that arise in the context of emerging large-scale communication networks. In particular, the pick-and-compare' algorithms developed by Tassiulas in 1998 and recently developed queue-based CSMA algorithms can be also understood as special cases of such algorithms using ES and MCMC oracles, respectively. To our best knowledge, our result is the first that establishes a rigorous connection between iterative optimization methods and low-complexity scheduling algorithms, which we believe provides various future directions and new insights in both areas.
Design and analysis of resource allocation algorithms in constrained queueing networks have been of great interest for last four decades across various research communities, where the contention resolution protocols in multiple-access broadcast channels have been studied since the mid-1970s @cite_23 . The broadcast channels induce a special constraint in resources usages among queues (i.e., every queue contend with all other queues), and simple distributed contention resolution protocols gained much attention in the ages. It is the year 1992 that the seminal work by Tassiulas and Ephremides proposed a throughput-optimal algorithm, referred to as MW, for general resource constraints. Its main appeal is that it does require only information on the current queue lengths (and instantaneous service rates) and does not rely on the knowledge of underlying system parameters. However, as we mentioned earlier, the MW algorithm suffers from the high implementation complexity, and a huge array of subsequent research has been made to develop algorithms with high performance guarantees and low-complexity.
@cite_23
2076915000
The popularity of Aloha-like algorithms for resolution of contention between multiple entities accessing common resources is due to their extreme simplicity and distributed nature. Example applications of such algorithms include Ethernet and recently emerging wireless multi-access networks. Despite a long and exciting history of more than four decades, the question of designing an algorithm that is essentially as simple and distributed as Aloha while being efficient has remained unresolved. In this paper, we resolve this question successfully for a network of queues where contention is modeled through independent-set constraints over the network graph. The work by Tassiulas and Ephremides (1992) suggests that an algorithm that schedules queues so that the summation of weight' of scheduled queues is maximized, subject to constraints, is efficient. However, implementing such an algorithm using Aloha-like mechanism has remained a mystery. We design such an algorithm building upon a Metropolis-Hastings sampling mechanism along with selection of weight' as an appropriate function of the queue-size. The key ingredient in establishing the efficiency of the algorithm is a novel adiabatic-like theorem for the underlying queueing network, which may be of general interest in the context of dynamical systems. Designing scheduling algorithms that work in synergy with TCP is a challenging problem in wireless networks. Extensive research on scheduling algorithms has focused on inelastic traffic, where there is no correlation between traffic dynamics and scheduling decisions. In this work, we study the performance of several scheduling algorithms in LTE networks, where the scheduling decisions are intertwined with wireless channel fluctuations to improve the system throughput. We use ns-3 simulations to study the performance of several scheduling algorithms with a specific focus on Max Weight (MW) schedulers with both UDP and TCP traffic, while considering the detailed behavior of OFDMA-based resource allocation in LTE networks. We show that, contrary to its performance with inelastic traffic, MW schedulers may not perform well in LTE networks in the presence of TCP traffic, as they are agnostic to the TCP congestion control mechanism. We then design a new scheduler called “Queue MW” (Q-MW) which is tailored specifically to TCP dynamics by giving higher priority to TCP flows whose queue at the base station is very small in order to encourage them to send more data at a faster rate. We have implemented Q-MW in ns-3 and studied its performance in a wide range of network scenarios in terms of queue size at the base station and round-trip delay. Our simulation results show that Q-MW achieves peak and average throughput gains of 37 and 10 compared to MW schedulers if tuned properly. We consider a cognitive radio network where multiple secondary users (SUs) contend for spectrum usage, using random access, over available primary user (PU) channels. Our focus is on SUs' queueing delay performance, for which a systematic understanding is lacking. We take a fluid queue approximation approach to study the steady-state delay performance of SUs, for cases with a single PU channel and multiple PU channels. Using stochastic fluid models, we represent the queue dynamics as Poisson driven stochastic differential equations, and characterize the moments of the SUs' queue lengths accordingly. Since in practical systems, a secondary user would have no knowledge of other users' activities, its contention probability has to be set based on local information. With this observation, we develop adaptive algorithms to find the optimal contention probability that minimizes the mean queue lengths. Moreover, we study the impact of multiple channels and multiple interfaces, on SUs' delay performance. As expected, the use of multiple channels and or multiple interfaces leads to significant delay reduction. We consider a class of queueing networks referred to as "generalized constrained queueing networks" which form the basis of several different communication networks and information systems. These networks consist of a collection of queues such that only certain sets of queues can be concurrently served. Whenever a queue is served, the system receives a certain reward. Different rewards are obtained for serving different queues, and furthermore, the reward obtained for serving a queue depends on the set of concurrently served queues. We demonstrate that the dependence of the rewards on the schedules alter fundamental relations between performance metrics like throughput and stability. Specifically, maximizing the throughput is no longer equivalent to maximizing the stability region; we therefore need to maximize one subject to certain constraints on the other. Since stability is critical for bounding packet delays and buffer overflow, we focus on maximizing the throughput subject to stabilizing the system. We design provably optimal scheduling strategies that attain this goal by scheduling the queues for service based on the queue lengths and the rewards provided by different selections. The proposed scheduling strategies are however computationally complex. We subsequently develop techniques to reduce the complexity and yet attain the same throughput and stability region. We demonstrate that our framework is general enough to accommodate random rewards and random scheduling constraints. We consider a communication network and study the problem of designing a high-throughput and low-delay scheduling policy that only requires a polynomial amount of computation at each time step. The well-known maximum weight scheduling policy, proposed by Tassiulas and Ephremides (1992), has favorable performance in terms of throughput and delay but, for general networks, it can be computationally very expensive. A related randomized policy proposed by Tassiulas (1998) provides maximal throughput with only a small amount of computation per step, but seems to induce exponentially large average delay. These considerations raise some natural questions. Is it possible to design a policy with low complexity, high throughput, and low delay for a general network? Does Tassiulas' randomized policy result in low average delay? In this paper, we answer both of these questions negatively. We consider a wireless network operating under two alternative interference models: (a) a combinatorial model involving independent set constraints and (b) the standard SINR (signal to interference noise ratio) model. We show that unless NP ⊆ BPP (or P = NP for the case of determistic arrivals and deterministic policies), and even if the required throughput is a very small fraction of the network's capacity, there does not exist a low-delay policy whose computation per time step scales polynomially with the number of queues. In particular, the average delay of Tassiulas' randomized algorithm must grow super-polynomially. To establish our results, we employ a clever graph transformation introduced by Lund and Yannakakis (1994). We consider the problem of resource allocation in downlink OFDMA systems for multi service and unknown environment. Due to users' mobility and intercell interference, the base station cannot predict neither the Signal to Noise Ratio (SNR) of each user in future time slots nor their probability distribution functions. In addition, the traffic is bursty in general with unknown arrival. The probability distribution functions of the SNR, channel state and traffic arrival density are then unknown. Achieving a multi service Quality of Service (QoS) while optimizing the performance of the system (e.g. total throughput) is a hard and interesting task since it depends on the unknown future traffic and SNR values. In this paper we solve this problem by modeling the multiuser queuing system as a discrete time linear dynamic system. We develop a robust H∞ controller to regulate the queues of different users. The queues and Packet Drop Rates (PDR) are controlled by proposing a minimum data rate according to the demanded service type of each user. The data rate vector proposed by the controller is then fed as a constraint to an instantaneous resource allocation framework. This instantaneous problem is formulated as a convex optimization problem for instantaneous subcarrier and power allocation decisions. Simulation results show small delays and better fairness among users. A model for wireless networks with slotted-Aloha-type random access and with multihop flow routes is considered. The goal is to devise distributed algorithms for utility-optimal end-to-end throughput allocation and queueing stability. A class of queue back-pressure random access algorithms (QBRAs), in which actual queue lengths of the flows in each node's close neighborhood are used to determine the nodes' channel access probabilities, is studied. This is in contrast to some previously proposed algorithms, which are based on deterministic optimization formulations and are oblivious to actual queues. QBRA is also substantially different from the well-studied ldquoMaxWeightrdquo type scheduling algorithms, even though both use the concept of back-pressure. For the model with infinite backlog at each flow source, it is shown that QBRA, combined with simple congestion control local to each source, leads to optimal end-to-end throughput allocation within the network saturation throughput region achievable by random access, without end-to-end message passing. This scheme is generalized to the case with minimum flow rate constraints. For the model with stochastic exogenous arrivals, it is shown that QBRA ensures stability of the queues as long as nominal loads of the nodes are within the saturation throughput region. Simulation comparison of QBRA and the queue oblivious random-access algorithms, shows that QBRA reduces end-to-end delays. We consider the problem of allocating resources (time slots, frequency, power, etc.) at a base station to many competing flows, where each flow is intended for a different receiver. The channel conditions may be time-varying and different for different receivers. It is well-known that appropriately chosen queue-length based policies are throughput-optimal while other policies based on the estimation of channel statistics can be used to allocate resources fairly (such as proportional fairness) among competing users. In this paper, we show that a combination of queue-length-based scheduling at the base station and congestion control implemented either at the base station or at the end users can lead to fair resource allocation and queue-length stability. A resource allocation model that has within its scope a number of computer and communication network architectures was introduced by Tassiulas and Ephremides (1992) and scheduling methods that achieve maximum throughput were proposed. Those methods require the solution of a complex optimization problem at each packet transmission time and as a result they are not amenable to direct implementations. We propose a class of maximum throughput scheduling policies for the model introduced by Tassiulas and Ephremides that have linear complexity and can lead to practical implementations. They rely on a randomized, iterative algorithm for the solution of the optimization problem arising in the scheduling, in combination with an incremental updating rule. The proposed policy is of maximum throughput under some fairly general conditions on the randomized algorithm. Age of information (AoI) is a recently proposed metric that measures the time elapsed since the generation of the last received information update. We consider the problem of AoI minimization for a network under general interference constraints, and time varying channel. We study the case where the channel statistics are known, but the current channel state is unknown. We propose two scheduling policies, namely, the virtual queue based policy and age-based policy. In the virtual queue based policy, the scheduler schedules links with maximum weighted sum of the virtual queue lengths, while in the age-based policy, the scheduler schedules links with maximum weighted sum of a function of link AoI. We prove that the virtual queue based policy is peak age optimal, up to an additive constant, while the age-based policy is at most factor 4 away from the optimal age. Numerical results suggest that both the proposed policies are, in fact, very close to the optimal. In this book, we consider the problem of achieving the maximum throughput and utility in a class of networks with resource-sharing constraints. This is a classical problem of great importance. In the context of wireless networks, we first propose a fully distributed scheduling algorithm that achieves the maximum throughput. Inspired by CSMA (Carrier Sense Multiple Access), which is widely deployed in today's wireless networks, our algorithm is simple, asynchronous, and easy to implement. Second, using a novel maximal-entropy technique, we combine the CSMA scheduling algorithm with congestion control to approach the maximum utility. Also, we further show that CSMA scheduling is a modular MAC-layer algorithm that can work with other protocols in the transport layer and network layer. Third, for wireless networks where packet collisions are unavoidable, we establish a general analytical model and extend the above algorithms to that case. Stochastic Processing Networks (SPNs) model manufacturing, communication, and service systems. In manufacturing networks, for example, tasks require parts and resources to produce other parts. SPNs are more general than queueing networks and pose novel challenges to throughput-optimum scheduling. We proposes a "deficit maximum weight" (DMW) algorithm to achieve throughput optimality and maximize the net utility of the production in SPNs. Table of Contents: Introduction Overview Scheduling in Wireless Networks Utility Maximization in Wireless Networks Distributed CSMA Scheduling with Collisions Stochastic Processing networks Middleboxes are widely deployed in today's enterprise networks. They perform a wide range of important network functions, including WAN optimizations, intrusion detection systems, network and application level firewalls, etc. Depending on the processing requirement of traffic, packet processing for different traffic flows may consume vastly different amounts of hardware resources (e.g., CPU and link bandwidth). Multi-resource fair queueing allows each traffic flow to receive a fair share of multiple middlebox resources. Previous schemes for multi-resource fair queueing, however, are expensive to implement at high speeds. Specifically, the time complexity to schedule a packet is O(log n), where n is the number of backlogged flows. In this paper, we design a new multi-resource fair queueing scheme that schedules packets in a way similar to Elastic Round Robin. Our scheme requires only O(1) work to schedule a packet and is simple enough to implement in practice. We show, both analytically and experimentally, that our queueing scheme achieves nearly perfect Dominant Resource Fairness. Consider N parallel queues competing for the attention of a single server. At each time slot each queue may be connected to the server or not depending on the value of a binary random variable, the connectivity variable. Allocation at each slot; is based on the connectivity information and on the lengths of the connected queues only. At the end of each slot, service may be completed with a given fixed probability. Such a queueing model is appropriate for some communication networks with changing topology. In the case of infinite buffers, necessary and sufficient conditions are obtained for stabilizability of the system in terms of the different system parameters. The allocation policy that serves the longest connected queue stabilizes the system when the stabilizability conditions hold. The same policy minimizes the delay for the special case of symmetric queues. In a system with a single buffer per queue, an allocation policy is obtained that maximizes the throughput and minimizes the delay when the arrival and service statistics of different queues are identical. > In packet-switched networks, resources are typically shared by a dynamic set of data flows. This dynamic resource sharing can be represented by a queueing network with state-dependent service rates. For a specific resource allocation we refer to as balanced fairness the corresponding queueing network is a Whittle network and has an explicit stationary distribution. We give some key properties satisfied by balanced fairness and compare the resulting throughput performance to those obtained under the max-min fair and proportional fair allocations. A novel media access control (MAC) protocol named carrier sense multiple access with idle detection (CSMA ID) is proposed to handle variable-length packets over an all-optical ring network. To evaluate optimal utilization of channel bandwidth, we study packet scheduling based on three transmitting queue discipline (TQD) architectures and four idle space allocation (ISA) algorithms with regard to their impact on performance. For numerical evaluation of performance, an analytical model is developed by a preclassification queue with weighted round-robin (PCQWRR) architecture and a random algorithm. Moreover, three related MAC protocols are examined and compared, namely, multitoken, carrier sense multiple access collision avoidance (CSMA CA) and carrier sense multiple access collision preemption (CSMA CP). Simulation results indicate that, of the TQDs, better performance is obtained by PCQWRR compared with first-in-first-out and preclassification queues. The first fit space (FFS) algorithm has the best performance of the ISAs. The 12 combinations of TQDs-ISAs are then considered. It is found that the combination of PCQWRR with FFS provides the greatest efficiency and has the lowest packet latency, providing better throughput than three different MAC protocols under either symmetric or asymmetric traffic load on all-optical ring networks. Scheduling is a critical and challenging resource allocation mechanism for multihop wireless networks. It is well known that scheduling schemes that favor links with larger queue length can achieve high throughput performance. However, these queue-length-based schemes could potentially suffer from large (even infinite) packet delays due to the well-known last packet problem, whereby packets belonging to some flows may be excessively delayed due to lack of subsequent packet arrivals. Delay-based schemes have the potential to resolve this last packet problem by scheduling the link based on the delay the packet has encountered. However, characterizing throughput optimality of these delay-based schemes has largely been an open problem in multihop wireless networks (except in limited cases where the traffic is single-hop). In this paper, we investigate delay-based scheduling schemes for multihop traffic scenarios with fixed routes. We develop a scheduling scheme based on a new delay metric and show that the proposed scheme achieves optimal throughput performance. Furthermore, we conduct simulations to support our analytical results and show that the delay-based scheduler successfully removes excessive packet delays, while it achieves the same throughput region as the queue-length-based scheme. Increasingly ubiquitous communication networks and connectivity via portable devices have engendered a host of applications in which sources, for example people and environmental sensors, send updates of their status to interested recipients. These applications desire status updates at the recipients to be as timely as possible; however, this is typically constrained by limited network resources. In this paper, we employ a time-average age metric for the performance evaluation of status update systems. We derive general methods for calculating the age metric that can be applied to a broad class of service systems. We apply these methods to queue-theoretic system abstractions consisting of a source, a service facility and monitors, with the model of the service facility (physical constraints) a given. The queue discipline of first-come-first-served (FCFS) is explored. We show the existence of an optimal rate at which a source must generate its information to keep its status as timely as possible at all its monitors. This rate differs from those that maximize utilization (throughput) or minimize status packet delivery delay. While our abstractions are simpler than their real-world counterparts, the insights obtained, we believe, are a useful starting point in understanding and designing systems that support real time status updates. Supporting ultra-reliable and low-latency communications (URLLC) is one of the major goals in 5G communication systems. Previous studies focus on ensuring end-to-end delay requirement by reducing transmission delay and coding delay, and only consider reliability in data transmission. However, the reliability reflected by overall packet loss also includes other components such as queueing delay violation. Moreover, which tools are appropriate to design radio resource allocation under constraints on delay, reliability, and availability is not well understood. As a result, how to optimize resource allocation for URLLC is still unclear. In this article, we first discuss the delay and packet loss components in URLLC and the network availability for supporting the quality of service of users. Then we present tools for resource optimization in URLLC. Last, we summarize the major challenges related to resource management for URLLC, and perform a case study. In this paper, a novel cognitive multiple-access strategy in the presence of a cooperating relay is proposed. Exploiting an important phenomenon in wireless networks, source burstiness, the cognitive relay utilizes the periods of silence of the terminals to enable cooperation. Therefore, no extra channel resources are allocated for cooperation and the system encounters no bandwidth losses. Two protocols are developed to implement the proposed multiple-access strategy. The maximum stable throughput region and the delay performance of the proposed protocols are characterized. The results reveal that the proposed protocols provide significant performance gains over conventional relaying strategies such as selection and incremental relaying, specially at high spectral efficiency regimes. The rationale is that the lossless bandwidth property of the proposed protocols results in a graceful degradation in the maximum stable throughput with increasing the required rate of communication. On the other hand, conventional relaying strategies suffer from catastrophic performance degradation because of their inherent bandwidth inefficiency that results from allocating specific channel resources for cooperation at the relay. The analysis reveals that the throughput region of the proposed strategy is a subset of its maximum stable throughput region, which is different from random access, where both regions are conjectured to be identical. This text presents a modern theory of analysis, control, and optimization for dynamic networks. Mathematical techniques of Lyapunov drift and Lyapunov optimization are developed and shown to enable constrained optimization of time averages in general stochastic systems. The focus is on communication and queueing systems, including wireless networks with time-varying channels, mobility, and randomly arriving traffic. A simple drift-plus-penalty framework is used to optimize time averages such as throughput, throughput-utility, power, and distortion. Explicit performance-delay tradeoffs are provided to illustrate the cost of approaching optimality. This theory is also applicable to problems in operations research and economics, where energy-efficient and profit-maximizing decisions must be made without knowing the future. Topics in the text include the following: - Queue stability theory - Backpressure, max-weight, and virtual queue methods - Primal-dual methods for non-convex stochastic utility maximization - Universal scheduling theory for arbitrary sample paths - Approximate and randomized scheduling theory - Optimization of renewal systems and Markov decision systems Detailed examples and numerous problem set questions are provided to reinforce the main concepts. Table of Contents: Introduction Introduction to Queues Dynamic Scheduling Example Optimizing Time Averages Optimizing Functions of Time Averages Approximate Scheduling Optimization of Renewal Systems Conclusions