Optimal Node Routing

High performance in advanced packet switches can be achieved by providing queuing both at the input and the output ports. The author studies the performance of this class of switches under nonuniform traffic. Two different output queuing arrangements are considered, namely, the case where dedicated queues are provided at each output port, and the case where the output queuing space is shared among all the output ports. An analytical approach is presented for the performance study of these two schemes in the case of operation with fixed-size packets and under various degrees of traffic imbalance at the inputs or the outputs. The measures investigated include the average delay, the maximum throughput of the switch in the case of output traffic imbalance, and the saturation load in the case of input traffic imbalance. Analytical results for these measures are derived for the case of a switch with a large number of input and output ports. Numerical results for the maximum throughput and the saturation load are presented. It is demonstrated that the scheme of output sharing performs better than the scheme of dedicated output queuing. >

This paper is about high capacity switches and routers that give guaranteed throughput, rate and delay guarantees. Many routers are built using input queueing or combined input and output queueing (CIOQ), using crossbar switching fabrics. But such routers require impractically complex scheduling algorithms to provide the desired guarantees. 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.

This paper considers the problem of secure packet routing at the maximum achievable rate in a Quantum key distribution (QKD) network. Assume that a QKD protocol generates symmetric private keys for secure communication over each link in a multi-hop network. The quantum key generation process, which is affected by noise, is assumed to be modeled by a stochastic counting process. Packets are first encrypted with the available quantum keys for each hop and then transmitted on a point-to-point basis over the communication links. A fundamental problem that arises in this setting is to design a secure and capacity-achieving routing policy that accounts for the time-varying availability of the quantum keys for encryption and finite link capacities for transmission. In this paper, by combining the QKD protocol with the Universal Max Weight (UMW) routing policy [1] – [3], we design a new secure throughput-optimal routing policy, called Tandem Queue Decomposition (TQD). TQD solves the problem of secure routing efficiently for a wide class of traffic, including unicast, broadcast, and multicast. One of our main contributions in this paper is to show that the problem can be reduced to the usual generalized network flow problem on a transformed network without the key availability constraints. Simulation results show that the proposed policy incurs a substantially smaller delay as compared to the state-of-the-art routing and key management policies. The proof of throughput-optimality of the proposed policy makes use of the Lyapunov stability theory along with a careful treatment of the key-storage dynamics.

Approximate Markov chains for the performance of banyan networks built with basic switches of arbitrary size containing input queues, output queues or a combination of input buffers and output queues are presented. These chains are also extended to model banyans where each link is replaced by a number of parallel links. Comparison with simulations indicates that the chains are reasonably accurate for practical network loads. It is shown that banyans built with switches containing a combination of single input buffers and output queues outperforms banyans built with switches containing only input queues or only output queues. Banyans built with larger nodes are shown to outperform banyans built with smaller nodes. It is shown that banyan-based networks with multiple links can be designed to have extremely low blocking probabilities. >

Performance analysis of packet switches with input and output buffers

We study a basic problem in Multi-Queue switches. A switch connectsm input ports to a single output port. Each input port is equipped with an incoming FIFO queue with bounded capacityB. A switch serves its input queues by transmitting packets arriving at these queues, one packet per time unit. Since the arrival rate can be higher than the transmission rate and each queue has limited capacity, packet loss may occur as a result of insufficient queue space. The goal is to maximize the number of transmitted packets. This general scenario models most current networks (e.g. IP networks) which only support a “best effort” service in which all packet streams are treated equally. A 2-competitive algorithm for this problem was designed in [5] for arbitraryB. Recently, a (17/9 ≈ 1.89)-competitive algorithm was presented forB>1 in [3]. Our main result in this paper shows that forB which is not too small our algorithm can do better than 1.89, and approach a competitive ratio ofe/(e − 1) ≈ 1.58.

In this paper we propose energy-aware scheduling algorithms that aim to optimize the tradeoff between energy consumption and traditional performance measures such as queue size and delay. We use the power-rate function f(x)= c+xα for x > 0 and f(0)= 0 to model the energy consumption. Scheduling algorithms have been studied in the past for the special case in which the base power c= 0. In general the base power c can be significant. We propose a batch-based scheduling algorithm that can keep the energy consumption to asymptotically optimal while paying for a logarithmic factor in the queue size. Such a tradeoff is best possible. We also characterize the energy-delay tradeoff for a rate-adaptive version of the Weighted Fair Queuing scheduling algorithm.

The author considers the problem of packet routing in a dynamic communication network as a problem of autonomous agent navigation in an uncertain environment, and proposes a novel method for network routing. The basic idea is that, instead of using an estimated constant, one uses a probability distribution to model the delay of link in a computer network, and computes routing tables based on such a probabilistic model of the network. Since the new model is no longer just a snapshot of the network at a particular time, but represents a probabilistic pattern which treats the changes of link delays as normal rather than as an exception, it is reasonable to expect that the routing tables based on the new model can be very robust against the dynamic changes of link delays. A computer network with such probabilistic information can be represented by a U-graph and the network routing problem is quite similar to mobile agent navigation in uncertain environments. >

Efficient routing strategy with transmission history information and its surrogate analysis

Although epsilon-near-zero (ENZ) media have emerged as a promising platform for power dividers, the majority of existing designs are confined to fixed power splitting. In this work, two dynamically tunable power dividers using waveguide ENZ media are proposed by precisely modulating the internal magnetic field and the widths of the output waveguides. The first approach features a mechanically reconfigurable ring-shaped ENZ waveguide. By continuously re-distributing the magnetic field within the ENZ tunneling channels utilizing rotatable copper plates, arbitrary power division among multiple output ports is constructed. The second design integrates a rectangular-loop ENZ cavity into a substrate-integrated waveguide, with four positive–intrinsic–negative diodes embedded to dynamically activate specific output ports. This configuration steers electromagnetic energy toward output ports with varying cross-sectional areas, enabling on-demand control over both the power division and the number of output ports. Both analytical and full-wave simulation results confirm dynamic power division, with transmission efficiencies exceeding 93%. Despite differences in structure and actuation mechanisms, both designs exhibit flexible field control, high reconfigurability, and excellent transmission performance, highlighting their potential in advanced applications such as real-time wireless communications, multi-input–multi-output systems, and reconfigurable antennas.

In the classical broadcast scheduling problem , there are n pages stored at a server, and requests for these pages arrive over time. Whenever a page is broadcast, it satisfies all outstanding requests for that page. The objective is to minimize average flow time of the requests. For any ϵ > 0, we give a (1+ϵ)-speed O (1/ϵ 3 )-competitive online algorithm for broadcast scheduling. This improves over the recent breakthrough result of Im and Moseley [2010], where they obtained a (1+ϵ)-speed O (1/ϵ 11 )-competitive algorithm. Our algorithm and analysis are considerably simpler than Im and Moseley [2010]. More importantly, our techniques also extend to the general setting of nonuniform page sizes and dependent requests . This is the first scalable algorithm for broadcast scheduling with varying size pages and resolves the main open question from Im and Moseley [2010].

The authors consider a discrete-time model of an access ATM switch with output buffers. A switch with output queueing has an optimum performance; however, it requires a switch fabric with speed N. However, the switch fabric may operate at L<N times the speed of the input/output links. The random traffic assumption underestimates the buffer size. Each input port of the switch is assumed to be driven by an interrupted Bernoulli process and every cell in a burst is directed to the same output port. An efficient aggregation method is applied for the performance analysis of the switch. The results prove to be very good.

Asynchronous Transfer Mode (ATM) is the recommended transport technique for the Broadband ISDN by CCITT (I.121). Many switches have been proposed to accommodate the ATM that requires fast packet switching capability [1-8]. The proposed switches for the Broadband ISDN can be cLassified as input queueing or output queueing type. The input queueing type have a throughput performance which is approximately 58 percent that of the output queueing type [1]. However, output queueing networks require larger amounts of hardware than input queueing networks [2]. In this paper, we propose a new multistage switch with internal buffering that approaches a maximum throughput of 100% as the buffering is increased. The switch is capable of broadcasting and self-routing. It consists of two switching planes which consist of packet processors, 2x2 switching elements, distributors and buffers located between stages and in the output ports. The internal data rate of the proposed switch is the same as that of the arriving information stream. In this sense, the switch does not require speedup. The switch has Iog2 N stages that forward packets in store-and-forward fashion, thus incurring a latency of log2 N time periods. Performance analysis shows additional delay is small.

Due to its simplicity and scalability, the differentiated services (DiffServ) model is expected to be widely deployed across the Internet. For each DiffServ compliant router, the scheduling algorithm is critical in implementing per hop behaviors (PHBs), according to which packets are forwarded. We propose a hierarchical DiffServ scheduling (HDS) algorithm to support DiffServ classes on input-queued switches. The proposed HDS algorithm features in a hierarchical scheduling scheme that consists of two levels of schedulers. One level is the central scheduler which is designed to maximize the switch throughput by computing a maximal size matching between input ports and output ports. The other level is formed by input port schedulers which provide differentiated services by serving cells belonging to different classes dynamically. Using such a hierarchical scheme, the implementation complexity and the amount of information needed to be transmitted between input ports and the central scheduler are dramatically reduced compared with existing maximal weight matching based DiffServ scheduling algorithms. The tradeoff of its slightly worse delay performance is acceptable.

We describe a novel method for scheduling highspeed network switches. The targeted architecture is an input-buffered switch with a non-blocking switch fabric. The input buffers are organized as virtual output queues to avoid head-of-line blocking. The task of the scheduler is to decide when the input ports can forward packets from the virtual output queues to the corresponding output ports. Our Least Choice First (LCF) scheduling method selects the input and output ports to be matched by prioritizing the input ports according to the number of virtual output queues that contain packets: The fewer virtual output queues with packets, the higher- the scheduling priority, of the input port. This way the number- of switch connections and, with it, switch throughput is maximized. Fairness is provided through the addition of a round-robin algorithm. We present two alternative implementations: A central implementation intended for narrow, switches and a distributed implementation based on an iterative algorithm intended for wide switches. The simulation results show that the LCF scheduler outperforms other scheduling methods such as the parallel iterative matcher, iSLIP, and the wave front arbiter.