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194
The impact of imperfect scheduling on crosslayer congestion control in wireless networks
, 2005
"... In this paper, we study crosslayer design for congestion control in multihop wireless networks. In previous work, we have developed an optimal crosslayer congestion control scheme that jointly computes both the rate allocation and the stabilizing schedule that controls the resources at the under ..."
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Cited by 349 (32 self)
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In this paper, we study crosslayer design for congestion control in multihop wireless networks. In previous work, we have developed an optimal crosslayer congestion control scheme that jointly computes both the rate allocation and the stabilizing schedule that controls the resources at the underlying layers. However, the scheduling component in this optimal crosslayer congestion control scheme has to solve a complex global optimization problem at each time, and is hence too computationally expensive for online implementation. In this paper, we study how the performance of crosslayer congestion control will be impacted if the network can only use an imperfect (and potentially distributed) scheduling component that is easier to implement. We study both the case when the number of users in the system is fixed and the case with dynamic arrivals and departures of the users, and we establish performance bounds of crosslayer congestion control with imperfect scheduling. Compared with a layered approach that does not design congestion control and scheduling together, our crosslayer approach has provably better performance bounds, and substantially outperforms the layered approach. The insights drawn from our analyses also enable us to design a fully distributed crosslayer congestion control and scheduling algorithm for a restrictive interference model.
Fairness and optimal stochastic control for heterogeneous networks
 Proc. IEEE INFOCOM, March 2005. TRANSACTIONS ON NETWORKING, VOL
, 2008
"... Abstract — We consider optimal control for general networks with both wireless and wireline components and time varying channels. A dynamic strategy is developed to support all traffic whenever possible, and to make optimally fair decisions about which data to serve when inputs exceed network capaci ..."
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Cited by 266 (63 self)
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Abstract — We consider optimal control for general networks with both wireless and wireline components and time varying channels. A dynamic strategy is developed to support all traffic whenever possible, and to make optimally fair decisions about which data to serve when inputs exceed network capacity. The strategy is decoupled into separate algorithms for flow control, routing, and resource allocation, and allows each user to make decisions independent of the actions of others. The combined strategy is shown to yield data rates that are arbitrarily close to the optimal operating point achieved when all network controllers are coordinated and have perfect knowledge of future events. The cost of approaching this fair operating point is an endtoend delay increase for data that is served by the network.
A tutorial on crosslayer optimization in wireless networks
 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS
, 2006
"... This tutorial paper overviews recent developments in optimization based approaches for resource allocation problems in wireless systems. We begin by overviewing important results in the area of opportunistic (channelaware) scheduling for cellular (singlehop) networks, where easily implementable my ..."
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Cited by 248 (29 self)
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This tutorial paper overviews recent developments in optimization based approaches for resource allocation problems in wireless systems. We begin by overviewing important results in the area of opportunistic (channelaware) scheduling for cellular (singlehop) networks, where easily implementable myopic policies are shown to optimize system performance. We then describe key lessons learned and the main obstacles in extending the work to general resource allocation problems for multihop wireless networks. Towards this end, we show that a cleanslate optimization based approach to the multihop resource allocation problem naturally results in a “loosely coupled” crosslayer solution. That is, the algorithms obtained map to different layers (transport, network, and MAC/PHY) of the protocol stack are coupled through a limited amount of information being passed back and forth. It turns out that the optimal scheduling component at the MAC layer is very complex and thus needs simpler (potentially imperfect) distributed solutions. We demonstrate how to use imperfect scheduling in the crosslayer framework and describe recently developed distributed algorithms along these lines. We conclude by describing a set of open research problems.
Capacity and delay tradeoffs for adhoc mobile networks
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 2005
"... We consider the throughput/delay tradeoffs for scheduling data transmissions in a mobile adhoc network. To reduce delays in the network, each user sends redundant packets along multiple paths to the destination. Assuming the network has a cell partitioned structure and users move according to a s ..."
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Cited by 190 (12 self)
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We consider the throughput/delay tradeoffs for scheduling data transmissions in a mobile adhoc network. To reduce delays in the network, each user sends redundant packets along multiple paths to the destination. Assuming the network has a cell partitioned structure and users move according to a simplified independent and identically distributed (i.i.d.) mobility model, we compute the exact network capacity and the exact endtoend queueing delay when no redundancy is used. The capacity achieving algorithm is a modified version of the GrossglauserTse 2hop relay algorithm and provides O(N) delay (where N is the number of users). We then show that redundancy cannot increase capacity, but can significantly improve delay. The following necessary tradeoff is established: delay/rate ≥ O(N). Two protocols that use redundancy and operate near the boundary of this curve are developed, with delays of O(√ N) and O(log(N)), respectively. Networks with noni.i.d. mobility are also considered and shown through simulation to closely match the performance of i.i.d. systems in the O(√ N) delay regime.
Energy optimal control for time varying wireless networks
 IEEE Trans. Inform. Theory
, 2006
"... Abstract — We develop a dynamic control strategy for minimizing energy expenditure in a time varying wireless network with adaptive transmission rates. The algorithm operates without knowledge of traffic rates or channel statistics, and yields average power that is arbitrarily close to the minimum p ..."
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Cited by 184 (50 self)
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Abstract — We develop a dynamic control strategy for minimizing energy expenditure in a time varying wireless network with adaptive transmission rates. The algorithm operates without knowledge of traffic rates or channel statistics, and yields average power that is arbitrarily close to the minimum possible value achieved by an algorithm optimized with complete knowledge of future events. Proximity to this optimal solution is shown to be inversely proportional to network delay. We then present a similar algorithm that solves the related problem of maximizing network throughput subject to peak and average power constraints. The techniques used in this paper are novel and establish a foundation for stochastic network optimization.
MinimumCost Multicast over Coded Packet Networks
 IEEE TRANS. ON INF. THE
, 2006
"... We consider the problem of establishing minimumcost multicast connections over coded packet networks, i.e., packet networks where the contents of outgoing packets are arbitrary, causal functions of the contents of received packets. We consider both wireline and wireless packet networks as well as b ..."
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Cited by 164 (28 self)
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We consider the problem of establishing minimumcost multicast connections over coded packet networks, i.e., packet networks where the contents of outgoing packets are arbitrary, causal functions of the contents of received packets. We consider both wireline and wireless packet networks as well as both static multicast (where membership of the multicast group remains constant for the duration of the connection) and dynamic multicast (where membership of the multicast group changes in time, with nodes joining and leaving the group). For static multicast, we reduce the problem to a polynomialtime solvable optimization problem, ... and we present decentralized algorithms for solving it. These algorithms, when coupled with existing decentralized schemes for constructing network codes, yield a fully decentralized approach for achieving minimumcost multicast. By contrast, establishing minimumcost static multicast connections over routed packet networks is a very difficult problem even using centralized computation, except in the special cases of unicast and broadcast connections. For dynamic multicast, we reduce the problem to a dynamic programming problem and apply the theory of dynamic programming to suggest how it may be solved.
AdHoc Networks Beyond Unit Disk Graphs
, 2003
"... In this paper we study a model for adhoc networks close enough to reality as to represent existing networks, being at the same time concise enough to promote strong theoretical results. The Quasi Unit Disk Graph model contains all edges shorter than a parameter d between 0 and 1 and no edges longer ..."
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Cited by 140 (11 self)
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In this paper we study a model for adhoc networks close enough to reality as to represent existing networks, being at the same time concise enough to promote strong theoretical results. The Quasi Unit Disk Graph model contains all edges shorter than a parameter d between 0 and 1 and no edges longer than 1. We show that  in comparison to the cost known on Unit Disk Graphs  the complexity results in this model contain the additional factor 1/d&sup2;. We prove that in Quasi Unit Disk Graphs flooding is an asymptotically messageoptimal routing technique, provide a geometric routing algorithm being more efficient above all in dense networks, and show that classic geometric routing is possible with the same performance guarantees as for Unit Disk Graphs if d 1/ # 2.
On the Complexity of Scheduling in Wireless Networks
 MOBICOM '06
, 2006
"... We consider the problem of throughputoptimal scheduling in wireless networks subject to interference constraints. We model the interference using a family of Khop interference models. We define a Khop interference model as one for which no two links within K hops can successfully transmit at the ..."
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Cited by 129 (3 self)
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We consider the problem of throughputoptimal scheduling in wireless networks subject to interference constraints. We model the interference using a family of Khop interference models. We define a Khop interference model as one for which no two links within K hops can successfully transmit at the same time (Note that IEEE 802.11 DCF corresponds to a 2hop interference model.). For a given K, a throughputoptimal scheduler needs to solve a maximum weighted matching problem subject to the Khop interference constraints. For K = 1, the resulting problem is the classical Maximum Weighted Matching problem, that can be solved in polynomial time. However, we show that for K> 1, the resulting problems are NPHard and cannot be approximated within a factor that grows polynomially with the number of nodes. Interestingly, we show that for specific kinds of graphs, that can be used to model the underlying connectivity graph of a wide range of wireless networks, the resulting problems admit polynomial time approximation schemes. We also show that a simple greedy matching algorithm provides a constant factor approximation to the scheduling problem for all K in this case. We then show that under a setting with singlehop traffic and no rate control, the maximal scheduling policy considered in recent related works can achieve a constant fraction of the capacity region for networks whose connectivity graph can be represented using one of the above classes of graphs. These results are encouraging as they suggest that one can develop distributed algorithms to achieve near optimal throughput in case of a wide range of wireless networks.
The Complexity of Connectivity in Wireless Networks
 IN: PROC. OF THE 25 TH ANNUAL JOINT CONF. OF THE IEEE COMPUTER AND COMMUNICATIONS SOCIETIES (INFOCOM
, 2006
"... We define and study the scheduling complexity in wireless networks, which expresses the theoretically achievable efficiency of MAC layer protocols. Given a set of communication requests in arbitrary networks, the scheduling complexity describes the amount of time required to successfully schedule a ..."
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Cited by 115 (13 self)
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We define and study the scheduling complexity in wireless networks, which expresses the theoretically achievable efficiency of MAC layer protocols. Given a set of communication requests in arbitrary networks, the scheduling complexity describes the amount of time required to successfully schedule all requests. The most basic and important network structure in wireless networks being connectivity, we study the scheduling complexity of connectivity, i.e., the minimal amount of time required until a connected structure can be scheduled. In this paper, we prove that the scheduling complexity of connectivity grows only polylogarithmically in the number of nodes. Specifically, we present a novel scheduling algorithm that successfully schedules a strongly connected set of links in time O(log 4 n) even in arbitrary worstcase networks. On the other hand, we prove that standard MAC layer or scheduling protocols can perform much worse. Particularly, any protocol that either employs uniform or linear (a node’s transmit power is proportional to the minimum power required to reach its intended receiver) power assignment has a Ω(n) scheduling complexity in the worst case, even for simple communication requests. In contrast, our polylogarithmic scheduling algorithm allows many concurrent transmission by using an explicitly formulated nonlinear power assignment scheme. Our results show that even in largescale worstcase networks, there is no theoretical scalability problem when it comes to scheduling transmission requests, thus giving an interesting complement to the more pessimistic bounds for the capacity in wireless networks. All results are based on the physical model of communication, which takes into account that the signaltonoise plus interference ratio (SINR) at a receiver must be above a certain threshold if the transmission is to be received correctly.
Topology control meets sinr: the scheduling complexity of arbitrary topologies
 in Proceedings of ACM MobiHoc
, 2006
"... To date, topology control in wireless ad hoc and sensor networks—the study of how to compute from the given communication network a subgraph with certain beneficial properties—has been considered as a static problem only; the time required to actually schedule the links of a computed topology with ..."
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Cited by 103 (9 self)
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To date, topology control in wireless ad hoc and sensor networks—the study of how to compute from the given communication network a subgraph with certain beneficial properties—has been considered as a static problem only; the time required to actually schedule the links of a computed topology without message collision was generally ignored. In this paper we analyze topology control in the context of the physical SignaltoInterferenceplusNoiseRatio (SINR) model, focusing on the question of how and how fast the links of a resulting topology can actually be realized over time. For this purpose, we define and study a generalized version of the SINR model and obtain theoretical upper bounds on the scheduling complexity of arbitrary topologies in wireless networks. Specifically, we prove that even in worstcase networks, if the signals are transmitted with correctly assigned transmission power levels, the number of time slots required to successfully schedule all links of an arbitrary topology is proportional to the squared logarithm of the number of network nodes times a previously defined static interference measure. Interestingly, although originally considered without explicit accounting for signal collision in the SINR model, this static interference measure plays an important role in the analysis of link scheduling with physical link interference. Our result thus bridges the gap between static graphbased interference models and the physical SINR model. Based on these results, we also show that when it comes to scheduling, requiring the communication links to be symmetric may imply significantly higher costs as opposed to topologies allowing unidirectional links.