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223
Scaling Internet Routers Using Optics
 ACM SIGCOMM
, 2003
"... Routers built around a singlestage crossbar and a centralized scheduler do not scale, and (in practice) do not provide the throughput guarantees that network operators need to make efficient use of their expensive longhaul links. In this paper we consider how optics can be used to scale capacity a ..."
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Cited by 75 (14 self)
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Routers built around a singlestage crossbar and a centralized scheduler do not scale, and (in practice) do not provide the throughput guarantees that network operators need to make efficient use of their expensive longhaul links. In this paper we consider how optics can be used to scale capacity and reduce power in a router. We start with the promising loadbalanced switch architecture proposed by CS. Chang. This approach eliminates the scheduler, is scalable, and guarantees 100% throughput for a broad class of traffic. But several problems need to be solved to make this architecture practical: (1) Packets can be missequenced, (2) Pathological periodic traffic patterns can make throughput arbitrarily small, (3) The architecture requires a rapidly configuring switch fabric, and (4) It does not work when linecards are missing or have failed. In this paper we solve each problem in turn, and describe new architectures that include our solutions. We motivate our work by designing a 100Tb/s packetswitched router arranged as 640 linecards, each operating at 160Gb/s. We describe two different implementations based on technology available within the next three years.
Scheduling efficiency of distributed greedy scheduling algorithms in wireless networks
 in INFOCOM
, 2006
"... Abstract — We consider the problem of distributed scheduling in wireless networks subject to simple collision constraints. We define the efficiency of a distributed scheduling algorithm to be the largest number (fraction) such that the throughput under the distributed scheduling policy is at least e ..."
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Cited by 73 (1 self)
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Abstract — We consider the problem of distributed scheduling in wireless networks subject to simple collision constraints. We define the efficiency of a distributed scheduling algorithm to be the largest number (fraction) such that the throughput under the distributed scheduling policy is at least equal to the efficiency multiplied by the maximum throughput achievable under a centralized policy. For a general interference model, we prove a lower bound on the efficiency of a distributed scheduling algorithm by first assuming that all the traffic only uses onehop of the network. We also prove that the lower bound is tight in the sense that for any fraction larger than the lower bound, we can find a topology and an arrival rate vector within the fraction of the capacity region, such that the network is unstable under a greedy scheduling policy. We then extend our results to a more general multihop traffic scenario and show that similar scheduling efficiency results can be established by introducing prioritization or regulators to the basic greedy scheduling algorithm. Index Terms — Multihop wireless networks, scheduling, greedy algorithms, resource allocation
Maximum pressure policies in stochastic processing networks
, 2005
"... Complex systems like semiconductor wafer fabrication facilities (fabs), networks of data switches, and largescale call centers all demand efficient resource allocation. Deterministic models like linear programs (LP) have been used for capacity planning at both the design and expansion stages of s ..."
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Cited by 71 (6 self)
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Complex systems like semiconductor wafer fabrication facilities (fabs), networks of data switches, and largescale call centers all demand efficient resource allocation. Deterministic models like linear programs (LP) have been used for capacity planning at both the design and expansion stages of such systems. LPbased planning is critical in setting a medium range or longterm goal for many systems, but it does not translate into a daytoday operational policy that must deal with discreteness of jobs and the randomness of the processing environment. A stochastic processing network, advanced by J. Michael Harrison (2000, 2002, 2003), is a system that takes inputs of materials of various kinds and uses various processing resources to produce outputs of materials of various kinds. Such a network provides a powerful abstraction of a wide range of realworld systems. It provides highfidelity stochastic models in diverse economic sectors including manufacturing, service, and information technology. We propose a family of maximum pressure service policies for dynamically allocating service capacities in a stochastic processing network. Under a mild assumption on network structure, we prove that a network operating under a maximum pressure policy achieves maximum throughput predicted by LPs. These policies are semilocal in the sense that each
On the Stability of InputQueued Switches with SpeedUp
 IEEE/ACM TRANSACTIONS ON NETWORKING
, 2001
"... We consider cellbased switch and router architectures whose internal switching matrix does not provide enough speed to avoid input buffering. These architectures require a scheduling algorithm to select at each slot a subset of input buffered cells which can be transferred toward output ports. In t ..."
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Cited by 70 (6 self)
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We consider cellbased switch and router architectures whose internal switching matrix does not provide enough speed to avoid input buffering. These architectures require a scheduling algorithm to select at each slot a subset of input buffered cells which can be transferred toward output ports. In this paper, we propose several classes of scheduling algorithms whose stability properties are studied using analytical techniques mainly based upon Lyapunov functions. Original stability conditions are also derived for scheduling algorithms that are being used today in highperformance switch and router architectures.
Throughput and fairness guarantees through maximal scheduling in wireless networks
 IEEE Transactions on Information Theory
, 2008
"... We address the question of providing throughput guarantees through distributed scheduling, which has remained an open problem for some time. We consider a simple distributed scheduling strategy, maximal scheduling, and prove that it attains a guaranteed fraction of the maximum throughput region in a ..."
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Cited by 56 (2 self)
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We address the question of providing throughput guarantees through distributed scheduling, which has remained an open problem for some time. We consider a simple distributed scheduling strategy, maximal scheduling, and prove that it attains a guaranteed fraction of the maximum throughput region in arbitrary wireless networks. The guaranteed fraction depends on the “interference degree ” of the network, which is the maximum number of transmitterreceiver pairs that interfere with any given transmitterreceiver pair in the network and do not interfere with each other. Depending on the nature of communication, the transmission powers and the propagation models, the guaranteed fraction can be lower bounded by the maximum link degrees in the underlying topology, or even by constants that are independent of the topology. We prove that the guarantees are tight in that they can not be improved any further with maximal scheduling. Our results can also be generalized to endtoend multihop sessions. Finally, we enhance maximal scheduling to guarantee fairness of rate allocation among different sessions. I.
Practical Algorithms for Performance Guarantees in Buffered Crossbars
, 2005
"... Network operators would like high capacity routers that give guaranteed throughput, rate and delay guarantees. Because they want high capacity, the trend has been towards input queued or combined input and output queued (CIOQ) routers using crossbar switching fabrics. But these routers require impra ..."
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Cited by 50 (2 self)
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Network operators would like high capacity routers that give guaranteed throughput, rate and delay guarantees. Because they want high capacity, the trend has been towards input queued or combined input and output queued (CIOQ) routers using crossbar switching fabrics. But these routers require impractically complex scheduling algorithms to provide the desired guarantees. In this paper, we explore how a buffered crossbar  a crossbar switch with a packet buffer at each crosspoint  can provide guaranteed performance (throughput, rate, and delay), with less complex, practical scheduling algorithms. We describe scheduling algorithms that operate in parallel on each input and output port, and hence are scalable. With these algorithms, buffered crossbars with a speedup of two can provide 100% throughput, rate, and delay guarantees. Index Terms system design, combinatorics, packet switching, buffered crossbar, scheduling algorithm, performance guarantees, throughput, mimic, quality of service. I. BACKGROUND Network operators would like high capacity routers that give guaranteed performance. First, they prefer routers that guarantee throughput so they can maximize the utilization of their expensive longhaul links. Second, they want routers that can allocate to each flow a guaranteed rate. Third, they want the capability to control the delay for packets of individual flows for realtime applications. Because they want high capacity, the trend has been towards input queued or combined input and output queued (CIOQ) routers. Most of these routers use a crossbar switching fabric with a centralized scheduler. While it is theoretically possible to build crossbar schedulers that give 100% throughput [1] or rate and delay guarantees [2][3] they are considered too complex to b...
Maintaining Packet Order in TwoStage Switches
, 2002
"... High performance packet switches frequently use a centralized scheduler (also known as an arbiter) to determine the configuration of a nonblocking crossbar. The scheduler often limits the scalability of the system because of the frequency and complexity of its decisions. A recent paper by C.S. Cha ..."
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Cited by 50 (6 self)
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High performance packet switches frequently use a centralized scheduler (also known as an arbiter) to determine the configuration of a nonblocking crossbar. The scheduler often limits the scalability of the system because of the frequency and complexity of its decisions. A recent paper by C.S. Chang et al. introduces an interesting twostage switch, in which each stage uses a trivial deterministic sequence of configurations. The switch is simple to implement at high speed and has been proved to provide 100% throughput for a broad class of traffic. Furthermore, there is a bound between the average delay of the twostage switch and that of an ideal outputqueued switch. However, in its simplest form, the switch missequences packets by an arbitrary amount. In this paper, building on the twostage switch, we present an algorithm called Full Frames First (FFF), that prevents missequencing while maintaining the performance benefits (in terms of throughput and delay) of the basic twostage switch. FFF comes at some additional cost, which we evaluate in this paper.
Queueing dynamics and maximal throughput scheduling in switched processing systems
 QUEUEING SYSTEMS
, 2003
"... We study a processing system comprised of parallel queues, whose individual service rates are specified by a global service mode (configuration). The issue is how to switch the system between various possible service modes, so as to maximize its throughput and maintain stability under the most workl ..."
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Cited by 49 (14 self)
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We study a processing system comprised of parallel queues, whose individual service rates are specified by a global service mode (configuration). The issue is how to switch the system between various possible service modes, so as to maximize its throughput and maintain stability under the most workloadintensive input traffic traces (arrival processes). Stability preserves the job inflow–outflow balance at each queue on the traffic traces. Two key families of service policies are shown to maximize throughput, under the mild condition that traffic traces have longterm average workload rates. In the first family of cone policies, the service mode is chosen based on the system backlog state belonging to a corresponding cone. Two distinct policy classes of that nature are investigated, MaxProduct and FastEmpty. In the second family of batch policies (BatchAdapt), jobs are collectively scheduled over adaptively chosen horizons, according to an asymptotically optimal, robust schedule. The issues of nonpreemptive job processing and nonnegligible switching times between service modes are addressed. The analysis is extended to cover feedforward networks of such processing systems/nodes. The approach taken unifies and generalizes prior studies, by developing a general tracebased modeling framework (samplepath approach) for addressing the queueing stability problem. It treats the queueing structure as a deterministic dynamical system and analyzes directly its evolution trajectories. It does not require any probabilistic superstructure, which is
Delay Bounds for Approximate Maximum Weight Matching Algorithms for Input Queued Switches
 Proc. IEEE INFOCOM
, 2002
"... Input Queued(IQ) switch architecture has been of recent interest due to its low memory bandwidth requirement. A scheduling algorithm is required to schedule the transfer of packets through crossbar switch fabric at everytime slot. The performance, that is throughput and delay, of a switch depends o ..."
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Cited by 46 (5 self)
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Input Queued(IQ) switch architecture has been of recent interest due to its low memory bandwidth requirement. A scheduling algorithm is required to schedule the transfer of packets through crossbar switch fabric at everytime slot. The performance, that is throughput and delay, of a switch depends on the scheduling algorithm. The Maximum weight matching(MWM) algorithm is known to deliver 100% throughput under any admissible traffic [2][3][4]. In [5], Leonardi et. al. obtained nontrivial bound on the delay for MWM algorithm under admissible Bernoulli i.i.d. traffic. There has been a lot of interesting work done over time to analyze throughput of scheduling algorithms. But apart from [5], there has not been any work done to obtain bounds on delay of scheduling algorithms. The MWM algorithm is perceived to be very good scheduling algorithm in general and simulations have suggested that it performs better than most of the known algorithms in terms of delay. But it is very complex to implement. Hence many simple to implement approximations to MWM are proposed.
Order optimal delay for opportunistic scheduling in multiuser wireless uplinks and downlinks
 Proc. of Allerton Conf. on Communication, Control, and Computing (invited paper
, 2006
"... Abstract — We consider a onehop wireless network with independent time varying channels and N users, such as a multiuser uplink or downlink. We first show that general classes of scheduling algorithms that do not consider queue backlog necessarily incur average delay that grows at least linearly wi ..."
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Cited by 45 (6 self)
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Abstract — We consider a onehop wireless network with independent time varying channels and N users, such as a multiuser uplink or downlink. We first show that general classes of scheduling algorithms that do not consider queue backlog necessarily incur average delay that grows at least linearly with N. We then construct a dynamic queuelength aware algorithm that stabilizes the system and achieves an average delay that is independent of N. This is the first analytical demonstration that O(1) delay is achievable in such a multiuser wireless setting. The delay bounds are achieved via a technique of queue grouping together with basic Lyapunov stability and statistical multiplexing concepts.