Deterministic Routing Research Articles

Probing-based anypath forwarding routing algorithms in wireless mesh networks

Existing routing protocols for Wireless Mesh Networks (WMNs) are generally optimized with statistical link measures, without focusing on the intrinsic uncertainty of wireless links. We show evidence that, with the transient link uncertainties at PHY and MAC layers, a pseudo-deterministic routing protocol that relies on average or historic statistics can hardly explore the full potentials of a multi-hop wireless mesh.We study optimal WMN routing using probing-based anypath forwarding, with explicit consideration of transient link uncertainties. Starting from a two-state link capacity model, we show the underlying connection between WMN routing and the classic Canadian Traveller Problem (CTP) [1]. Inspired by a stochastic recoverable version of CTP (SRCTP), we develop an practical SRCTP-based online routing algorithm under link uncertainties. We study how dynamic next-hop selection can be done with low cost, and derive a systematic selection order for minimizing transmission delay. We further extend our solution to a general multi-rate link model, and present a Stopping Theory (ST) based solution, which naturally degrades to the SRCTP algorithm in the two-state link model. We conduct simulation studies to verify the effectiveness of the SRCTP and ST algorithms under diverse network configurations. In particular, compared to deterministic routing, reduction of end-to-end delay (51.15–73.02% for two-state links, 5.16% for multi-rate links) and improvement on packet delivery ratio (99.76% for two-state links, 94.44% for multi-rate links) are observed. By using RTS/CTS as the online probing tool in ns3 simulator, we observed both significant goodput improvements (29.9% than EXOR, 61.8% than HWMP) and much less packet arriving jitter (14.27 times less than EXOR, 45% less than HWMP) as compared to EXOR and HWMP routing protocols.

A Novel Adaptive Routing Algorithm for Network-On-Chip

In this paper, we propose a novel adaptive routing algorithm to solve the communication congestion problem for Network-on-Chip (NoC). The strategy competing for output ports in both X and Y directions is employed to utilize the output ports of the router sufficiently, and to reduce the transmission latency and improve the throughput. Experimental results show that the proposed algorithm is very effective in relieving the communication congestion, and a reduction in average latency by 45.7% and an improvement in throughput by 44.4% are achieved compared with the deterministic XY routing algorithm and the simple XY adaptive routing algorithm.

Robust on-demand routing mechanism for wireless multi-hop networks

All traditional on-demand routing protocols for wireless networks perform well if routing is provided with few optimised fixed routes before transmissions, and each hop uses a fixed neighbour for forwarding a packet. This strategy, however, cannot be adopted effectively in practical dynamic environments with frequent transmission failures. By taking advantage of the broadcast nature of wireless media the authors propose a novel opportunistic routing scheme to overcome the drawbacks of wireless transmission called ‘network layer broadcast with confirmed opportunity routing’ (NBC-OPP). NBC-OPP features a forwarding list built between source and destination upon the route request and route reply messages. Using the simulation of various network scenarios the authors have demonstrated the superior performance of this new method over traditional deterministic routing schemes for packet delivery, end-to-end delay and route control message load, especially for large node density, bad channel state and low traffic rate conditions.

Analysis of Buffer Arrangements in Low and High Dimensional Networks

Virtual channels have been introduced to enhance the performance of wormhole-switched networks. They are formed by arranging the buffer space dedicated to a given physical channel into multiple parallel buffers that share the physical bandwidth on a demand driven time-multiplexed manner. The question to be answered is: given a fixed amount of finite buffer what is the optimal way to arrange it into virtual channels. There have been few studies attempting to address this issue, however, these studies have so far resorted to simulation experiments and focused on deterministic routing algorithms. In this paper we use analytical performance models to investigate the optimal arrangement of the available buffer space into multiple virtual channels when adaptive routing is used in wormhole-switched k-ary ncubes.

Strategic Thinking and Risk Attitudes in Route Choice

This research investigates route choice behavior in networks with risky travel times and real-time information. A stated preference survey is conducted. In it subjects use a PC-based interactive map to choose routes link by link in various scenarios. The scenarios include two types of maps: the first map presents a choice between one stochastic route and one deterministic route, and the second contains real-time information and an available detour. The first type of map measures the basic risk attitude of the subject. The second type allows for strategic planning and measures the effect of this opportunity on subjects’ choice behavior. Results from each subject are analyzed to determine whether the subject planned strategically for the en route information or simply selected fixed paths from origin to destination. The full data set is used to estimate several choice models with expected travel times and standard deviations as explanatory variables. Estimation results are used to assess whether models that incorporate strategic behavior more accurately reflect route choice than do simpler path-based models.

Calibrated Labeling Method for Generating Bicyclist Route Choice Sets Incorporating Unbiased Attribute Variation

Discrete choice model estimation requires specification of the alternatives considered for each observed choice. In route choice problems based on real-world travel observations, generally only the chosen route is observed, and the rest of the choice set remains hidden from the analyst. In dense travel networks, thousands of paths may connect a given origin or destination, necessitating methods for generating a reasonable subset of options. A new method is proposed for generating deterministic route choice sets. The technique modifies the labeled routes method, in which multiple criteria are optimized individually to generate attractive routes. The proposed method offers two potential improvements: (a) multiple routes are generated for each label by allowing a sensitivity parameter to vary and (b) a calibration step fits the alternative shortest path deviation distribution to observed behavior. The resulting process is more flexible than traditional labeled routes, yet it maintains strong links to behavior and reduces potential attribute bias. The proposed calibrated labeling method is applied to bicyclist route choice in a dense urban network. Results suggest that the proposed technique outperforms existing methods on several key criteria. In addition, explicitly linking choice set generation to observed travel patterns creates a more intuitive behavioral link than existing strategies. The proposed method should be immediately useful for route choice modeling in similar contexts. Furthermore, the basic framework could be more broadly applicable for route choice set generation.

Performance Modelling of Torus Interconnection Networks with Deep Buffers

Analytical models of deterministic routing in wormhole-switched networks have been widely reported in the literature. However, all of these models have assumed no, or neglectable, buffers at each switching element of the network. This paper proposes a new analytical model for wormhole-switched torus with finite buffers and multiple virtual channels. The validity of the model has been demonstrated by comparing analytical results with those obtained from simulation experiments.

Oblivious Routing in Fat-Tree Based System Area Networks With Uncertain Traffic Demands

We study oblivious routing in fat-tree-based system area networks with deterministic routing under the assumption that the traffic demand is uncertain. The performance of a routing algorithm under uncertain traffic demands is characterized by the oblivious performance ratio that bounds the relative performance of the routing algorithm with respect to the optimal algorithm for any given traffic demand. We consider both single-path routing, where only one path is used to carry the traffic between each source-destination pair, and multipath routing, where multiple paths are allowed. For single-path routing, we derive lower bounds of the oblivious performance ratio for different fat-trees and develop routing schemes that achieve the optimal oblivious performance ratios for commonly used topologies. Our evaluation results indicate that the proposed oblivious routing schemes not only provide the optimal worst-case performance guarantees but also outperform existing schemes in average cases. For multipath routing, we show that it is possible to obtain an optimal scheme for all traffic demands (an oblivious performance ratio of 1). These results quantitatively demonstrate the performance difference between single-path routing and multipath routing in fat-trees.

Scalable Routing in Cyclic Mobile Networks

The nonexistence of an end-to-end path poses a challenge in adapting traditional routing algorithms to delay-tolerant networks (DTNs). Previous works have covered centralized routing approaches based on deterministic mobility, ferry-based routing with deterministic or semideterministic mobility, flooding-based approaches for networks with general mobility, and probability-based routing for semideterministic mobility models. Unfortunately, none of these methods can guarantee both scalability and delivery. In this paper, we extend the investigation of scalable deterministic routing in DTNs with repetitive mobility based on our previous works. Instead of routing with global contact knowledge, we propose a routing algorithm that routes on contact information compressed by three combined methods. We address the challenge of efficient information aggregation and compression in the time-space domain while maintaining critical information for efficient routing. Then, we extend it to handle a moderate level of uncertainty in contact prediction. Analytical studies and simulation results show that the performance of our proposed routing algorithm, DTN hierarchical routing (DHR), is comparable to that of the optimal time-space Dijkstra algorithm in terms of delay and hop count. At the same time, the per-node storage overhead is substantially reduced and becomes scalable.

Randomized Shortest-Path Problems: Two Related Models

This letter addresses the problem of designing the transition probabilities of a finite Markov chain (the policy) in order to minimize the expected cost for reaching a destination node from a source node while maintaining a fixed level of entropy spread throughout the network (the exploration). It is motivated by the following scenario. Suppose you have to route agents through a network in some optimal way, for instance, by minimizing the total travel cost-nothing particular up to now-you could use a standard shortest-path algorithm. Suppose, however, that you want to avoid pure deterministic routing policies in order, for instance, to allow some continual exploration of the network, avoid congestion, or avoid complete predictability of your routing strategy. In other words, you want to introduce some randomness or unpredictability in the routing policy (i.e., the routing policy is randomized). This problem, which will be called the randomized shortest-path problem (RSP), is investigated in this work. The global level of randomness of the routing policy is quantified by the expected Shannon entropy spread throughout the network and is provided a priori by the designer. Then, necessary conditions to compute the optimal randomized policy-minimizing the expected routing cost-are derived. Iterating these necessary conditions, reminiscent of Bellman's value iteration equations, allows computing an optimal policy, that is, a set of transition probabilities in each node. Interestingly and surprisingly enough, this first model, while formulated in a totally different framework, is equivalent to Akamatsu's model ( 1996 ), appearing in transportation science, for a special choice of the entropy constraint. We therefore revisit Akamatsu's model by recasting it into a sum-over-paths statistical physics formalism allowing easy derivation of all the quantities of interest in an elegant, unified way. For instance, it is shown that the unique optimal policy can be obtained by solving a simple linear system of equations. This second model is therefore more convincing because of its computational efficiency and soundness. Finally, simulation results obtained on simple, illustrative examples show that the models behave as expected.

A memetic algorithm for the multi-compartment vehicle routing problem with stochastic demands

The multi-compartment vehicle routing problem (MC-VRP) consists of designing transportation routes to satisfy the demands of a set of customers for several products that, because of incompatibility constraints, must be loaded in independent vehicle compartments. Despite its wide practical applicability the MC-VRP has not received much attention in the literature, and the few existing methods assume perfect knowledge of the customer demands, regardless of their stochastic nature. This paper extends the MC-VRP by introducing uncertainty on what it is known as the MC-VRP with stochastic demands (MC-VRPSD). The MC-VRPSD is modeled as a stochastic program with recourse and solved by means of a memetic algorithm. The proposed memetic algorithm couples genetic operators and local search procedures proven to be effective on deterministic routing problems with a novel individual evaluation and reparation strategy that accounts for the stochastic nature of the problem. The algorithm was tested on instances of up to 484 customers, and its results were compared to those obtained by a savings-based heuristic and a memetic algorithm (MA/SCS) for the MC-VRP that uses a spare capacity strategy to handle demand fluctuations. In addition to effectively solve the MC-VRPSD, the proposed MA/SCS also improved 14 best known solutions in a 40-problem testbed for the MC-VRP.

Electrostatic deposition of graphene in a gaseous environment: a deterministic route forsynthesizing rolled graphenes?

The synthesis of single-wall carbon nanotubes of desired diameters and chiralities is criticalto the design of nanoscale electronic devices with desired properties. The existing methodsare based on self-assembly, therefore lacking control over the diameters and chiralities. Thepresent work reports a direct route for rolling graphene. Specifically, we found that theelectrostatic deposition of graphene yielded: (i) flat graphene layers under high vacuum(10−7 Torr), (ii) completely scrolled graphene under hydrogen atmosphere, (iii) partially scrolledgraphene under nitrogen atmosphere, and (iv) no scrolling for helium atmospheres. Ourstudy shows that the application of the electrostatic field facilitates the rolling of graphenesheets exposed to appropriate gases and allows the rolling of any size of graphene. Thetechnique proposed here, in conjunction with a technique that produces graphenenanoribbons of uniform widths, will have significant impact on the development of carbonnanotube based devices. Furthermore, the present technique may be applied to obtaintubes/scrolls of other layered materials.

A Comment on "Beyond Fat-tree: Unidirectional Load-Balanced Multistage Interconnection Network"

A recent work proposed to simplify fat-trees with adaptive routing by means of a load-balancing deterministic routing algorithm. The resultant network has performance figures comparable to the more complex adaptive routing fat-trees when packets need to be delivered in order. In a second work by the same authors published in IEEE CAL, they propose to simplify the fat-tree to a unidirectional multistage interconnection network (UMIN), using the same load-balancing deterministic routing algorithm. They show that comparable performance figures are achieved with much lower network complexity. In this comment we show that the proposed load-balancing deterministic routing is in fact the routing scheme used by the butterfly network. Moreover we show that the properties of the simplified UMIN network proposed by them are intrinsic to the standard butterfly and other existing UMINs.

On routing and diameter of metacyclic graphs

Metacyclic graphs, which include supertoroids as a subclass, have been shown to possess interesting properties and potential applications in implementing moderate- to large-size parallel processors with fairly small node degrees. Wu, Lakshmivarahan, and Dhall (J. Parallel Distrib. Comput. 60 (2000), pp. 539–565) have described a deterministic, distributed routing scheme for certain subclasses of metacyclic graphs. However, they offer no proof that the scheme is a shortest-path routing algorithm and do not indicate whether or how their scheme may be extended to the entire class of metacyclic graphs. In this paper, we provide a near-shortest-path, deterministic routing algorithm that is applicable to any metacyclic graph and derive a bound for the diameter of such graphs.

Performance analysis of deterministically-routed bi-directional torus with non-uniform traffic distribution

Existing research has most often relied on simulation and considered the uniform traffic distribution when investigating the performance properties of multicomputer networks (e.g. the torus). However, there are numerous parallel applications that generate non-uniform traffic patterns, such as hot-spot. Furthermore, much more attention has been paid to capturing the impact of non-uniform traffic on network performance, resulting in the development of a number of analytical models for predicting message latency in the presence of hot-spots in the network. For instance, analytical models have been reported for the adaptively-routed torus with uni-directional as well as bi-directional channels. However, models for the deterministically-routed torus have considered uni-directional channels only. In an effort to fill in this gap, this paper describes an analytical model for the deterministically-routed torus with bi-directional channels when subjected to hot-spot traffic. The modelling approach adopted for deterministic routing is totally different from that for adaptive routing due to the inherently different nature of the two types of routing. The validity of the model is demonstrated by comparing analytical results against those obtained through extensive simulation experiments.

Beyond Fat--tree: Unidirectional Load--Balanced Multistage Interconnection Network

The fat-tree is one of the most widely-used topologies by interconnection network manufacturers. Recently, it has been demonstrated that a deterministic routing algorithm that optimally balances the network traffic can not only achieve almost the same performance than an adaptive routing algorithm but also outperforms it. On the other hand, fat-trees require a high number of switches with a non-negligible wiring complexity. In this paper, we propose replacing the fat--tree by a unidirectional multistage interconnection network (UMIN) that uses a traffic balancing deterministic routing algorithm. As a consequence, switch hardware is almost reduced to the half, decreasing, in this way, the power consumption, the arbitration complexity, the switch size itself, and the network cost. Preliminary evaluation results show that the UMIN with the load balancing scheme obtains lower latency than fat--tree for low and medium traffic loads. Furthermore, in networks with a high number of stages or with high radix switches, it obtains the same, or even higher, throughput than fat-tree.

Stochastic Physical Synthesis Considering Prerouting Interconnect Uncertainty and Process Variation for FPGAs

Process variation and prerouting interconnect delay uncertainty affect timing and power for modern VLSI designs in nanometer technologies. This paper presents the first in-depth study on stochastic physical synthesis algorithms leveraging statistical static timing analysis (SSTA) with process variation and prerouting interconnect delay uncertainty for field-programmable gate arrays (FPGAs). Evaluated by SSTA using the placed and routed circuits, the stochastic clustering, placement, and routing reduce the mean delay by 5.0%, 4.0%, and 1.4%, respectively, and reduce the standard deviation of delay by 6.4%, 6.1%, and 1.4%, respectively for MCNC designs. The majority of improvements come from modeling interconnect delay uncertainty for clustering and from considering process variation for placement, while routing has less improvement on delay. In addition, we study the interaction between each individual design stage. When applying all stochastic algorithms concurrently, the mean delay and standard deviation are reduced by 6.2% and 7.5%, respectively. On the other hand, stochastic clustering with deterministic placement and routing is a good flow with little change to the entire flow, but the mean delay is reduced by 5.0%, the standard deviation is reduced by 6.4%, and the runtime is slightly reduced compared to the deterministic flow. Finally, while its improvement over timing is small, stochastic routing is able to reduce the total wire length by 4.5% and to reduce the overall runtime by 4.2% compared to deterministic routing.

Network-on-chip architecture design based on mesh-of-tree deterministic routing topology

Network-on-Chip (NoC) is a new paradigm for designing future System-on-Chips (SoCs) where large numbers of Intellectual Property (IP) cores are connected through an interconnection network. The communication between the nodes is achieved by routing packets rather than wires. It supports high degree of reusability, scalability, and parallelism in communication. Here, we present NoC architecture based on Mesh-of-Tree (MoT) deterministic routing. MoT interconnection has the advantage of having small diameter as well as large bisection width. It is known as the fastest network when considered solely in terms of speed. The routing algorithm ensures that the packet will always reach the destination through the shortest path and it is deadlock free. We also present how Globally Asynchronous Locally Synchronous (GALS) style of communication has been implemented by using FIFO in mixed clock system.

Adaptive routing strategies for fault-tolerant on-chip networks in dynamically reconfigurable systems

An investigation into an effective and low-complexity adaptive routing strategy based on stochastic principles for an asynchronous network-on-chip platform that includes dynamically reconfigurable computing nodes is presented. The approach is compared with classic deterministic routing and it is shown to have good properties in terms of throughput and excellent fault-tolerance capabilities. The challenge of how to deliver reliability is one of the problems that multiprocessor system architects and manufactures will face as feature sizes and voltage supplies shrink and deep-submicron effects reduce the ability to carry out deterministic computing. It is likely that a new type of deep-submicron complex multicore systems will emerge which will be required to deliver high performance within strict energy and area budgets and operate over unreliable silicon. Within this context, the paper studies an on-chip communication infrastructure suitable for these systems.

Combinatorial performance modelling of toroidal cubes

Although several analytical models have been proposed in the literature for deterministic routing in different interconnection networks, very few of them have considered the effects of virtual channel multiplexing on network performance. This paper proposes a new analytical model to compute message latency in a general n-dimensional torus network with an arbitrary number of virtual channels per physical channel. Unlike the previous models proposed for toroidal-based networks, this model uses a combinatorial approach to consider all different possible cases for the source-destination pairs, thus resulting in an accurate prediction. The results obtained from simulation experiments confirm that the proposed model exhibits a high degree of accuracy for various network sizes, under different operating conditions, compared to a similar model proposed very recently, which considers virtual channel utilization in the k-ary n-cube network.