In this paper, we propose a cross-layer scheduling algorithm that achieves a throughput "epsilon-close" to the optimal throughput in multi-hop wireless networks with a tradeoff of O(1 epsilon) in delay guarantees. The algorithm aims to solve a joint congestion control, routing, and scheduling problem in a multi-hop wireless network while satisfying per-flow average end-to-end delay guarantees and minimum data rate requirements. This problem has been solved for both backlogged as well as arbitrary arrival rate systems. Moreover, we discuss the design of a class of low-complexity suboptimal algorithms, the effects of delayed feedback on the optimal algorithm, and the extensions of the proposed algorithm to different interference models with arbitrary link capacities.
Delay issues in single-hop wireless networks have been addressed in @cite_6 - @cite_1 . Especially, the scheduling algorithm in @cite_11 provides a throughput-utility that is inversely proportional to the delay guarantee. Authors of @cite_4 have obtained delay bounds for two classes of scheduling policies. A random access algorithm is proposed in @cite_28 for lattice and torus interference graphs, which is shown to achieve order-optimal delay in a distributed manner with optimal throughput. But these works are not readily extendable to multi-hop wireless networks, where additional arrivals from neighboring nodes and routing must be considered. Delay analysis for multi-hop networks with fixed-routing is provided in @cite_30 . Delay-related scheduling in multi-hop wireless networks have been proposed in @cite_0 @cite_32 @cite_8 @cite_16 @cite_23 . However, none of the above-mentioned works provide explicit end-to-end delay guarantees.
@cite_30 @cite_4 @cite_8 @cite_28 @cite_1 @cite_32 @cite_6 @cite_0 @cite_23 @cite_16 @cite_11
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We analyze the delay performance of a multi-hop wireless network with a fixed route between each source-destination pair. There are arbitrary interference constraints on the set of links that can be served simultaneously at any given time. These interference constraints impose a fundamental lower bound on the delay performance of any scheduling policy for the system. We present a methodology to derive such lower bounds. For the tandem queue network, where the delay optimal policy is known, the expected delay of the optimal policy numerically coincides with the lower bound. We conduct extensive numerical studies to suggest that the average delay of the back-pressure scheduling policy can be made close to the lower bound by using appropriate functions of queue length. We consider the question of obtaining tight delay guarantees for throughout-optimal link scheduling in arbitrary topology wireless ad-hoc networks. We consider two classes of scheduling policies: 1) a maximum queue-length weighted independent set scheduling policy, and 2) a randomized independent set scheduling policy where the independent set scheduling probabilities are selected optimally. Both policies stabilize all queues for any set of feasible packet arrival rates, and are therefore throughput-optimal. For these policies and i.i.d. packet arrivals, we show that the average packet delay is bounded by a constant that depends on the chromatic number of the interference graph, and the overall load on the network. We also prove that this upper bound is asymptotically tight in the sense that there exist classes of topologies where the expected delay attained by any scheduling policy is lower bounded by the same constant. Through simulations we examine the scaling of the average packet delay with respect to the overall load on the network, and the chromatic number of the link interference graph. The back-pressure algorithm is a well-known throughput-optimal algorithm. However, its delay performance may be quite poor even when the traffic load is not close to network capacity due to the following two reasons. First, each node has to maintain a separate queue for each commodity in the network, and only one queue is served at a time. Second, the back-pressure routing algorithm may route some packets along very long routes. In this paper, we present solutions to address both of the above issues, and hence, improve the delay performance of the back-pressure algorithm. One of the suggested solutions also decreases the complexity of the queueing data structures to be maintained at each node. In this paper, we consider CSMA policies for scheduling of multihop wireless networks with one-hop traffic. The main contribution of this paper is to propose Unlocking CSMA (U-CSMA) policy that enables to obtain high throughput with low (average) packet delay for large wireless networks. In particular, the delay under U-CSMA policy becomes order-optimal. For one-hop traffic, delay is defined to be order-optimal if it is O(1), i.e., it stays bounded, as the network-size increases to infinity. Using mean field theory techniques, we analytically show that for torus (grid-like) interference topologies with one-hop traffic, to achieve a network load of @math , the delay under U-CSMA policy becomes @math as the network-size increases, and hence, delay becomes order optimal. We conduct simulations for general random geometric interference topologies under U-CSMA policy combined with congestion control to maximize a network-wide utility. These simulations confirm that order optimality holds, and that we can use U-CSMA policy jointly with congestion control to operate close to the optimal utility with a low packet delay in arbitrarily large random geometric topologies. To the best of our knowledge, it is for the first time that a simple distributed scheduling policy is proposed that in addition to throughput utility-optimality exhibits delay order-optimality. 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. We study a mobile wireless network where groups or clusters of nodes are intermittently connected via mobile carriers'' (the carriers provide connectivity over time among different clusters of nodes). Over such networks (an instantiation of a delay tolerant network), it is well-known that traditional routing algorithms perform very poorly. In this paper, we propose a two-level Back- Pressure with Source-Routing algorithm (BP+SR) for such networks. The proposed BP+SR algorithm separates routing and scheduling within clusters (fast time-scale) from the communications that occur across clusters (slow time-scale), without loss in network throughput (i.e., BP+SR is throughput-optimal). More importantly, for a source and destination node that lie in different clusters, the traditional back-pressure algorithm results in large queue lengths at each node along its path. This is because the queue dynamics are driven by the slowest time-scale (i.e., that of the carrier nodes) along the path between the source and destination, which results in very large end-to-end delays. On the other-hand, we show that the two-level BP+SR algorithm maintains large queues only at a very few nodes, and thus results in order-wise smaller end-to-end delays. We provide analytical as well as simulation results to confirm our claims. While there has been much progress in designing backpressure based stabilizing algorithms for multihop wireless networks, end-to-end performance (e.g., end-to-end buffer usage) results have not been as forthcoming. In this paper, we study the end-to-end buffer usage (sum of buffer utilization along a flow path) over a network with general topology and with fixed, loop-free routes using a large-deviations approach. We first derive bounds on the best performance that any scheduling algorithm can achieve. Based on the intuition from the bounds, we propose a class of (backpressure-like) scheduling algorithms called &#945;&#946;-algorithms. We show that the parameters &#945; and &#946; can be chosen such that the system under the &#945;&#946;-algorithm performs arbitrarily closely to the best possible scheduler (formally the decay rate function for end-to-end buffer overflow is shown to be arbitrarily close to optimal in the large-buffer regime). We also develop variants which have the same asymptotic optimality property, and also provide good performance in the small-buffer regime. Our results are substantiated using both analysis and simulation. In a wireless network, a sophisticated algorithm is required to schedule simultaneous wireless transmissions while satisfying interference constraint that two neighboring nodes can not transmit simultaneously. The scheduling algorithm need to be excellent in performance while being simple and distributed so as to be implementable. The result of Tassiulas and Ephremides (1992) imply that the algorithm, scheduling transmissions of nodes in the 'maximum weight independent set' (MWIS) of network graph, is throughput optimal. However, algorithmically the problem of finding MWIS is known to be NP-hard and hard to approximate. This raises the following questions: is it even possible to obtain throughput optimal simple, distributed scheduling algorithm? if yes, is it possible to minimize delay of such an algorithm? Motivated by these questions, we first provide a distributed throughput optimal algorithm for any network topology. However, this algorithm may induce exponentially large delay. To overcome this, we present an order optimal delay algorithm for any non-expanding network topology. Networks deployed in geographic area, like wireless networks, are likely to be of this type. Our algorithm is based on a novel distributed graph partitioning scheme which may be of interest in its own right. Our algorithm for non-expanding graph takes O (n) total message exchanges or O(l) message exchanges per node to compute a schedule.