An optimal routing policy for mesh-connected topologies

We address the problem of optimal routing in overlay networks. An overlay network is constructed by adding new overlay nodes on top of a legacy network. The overlay nodes are capable of implementing any dynamic routing policy, however, the legacy underlay has a fixed, single path routing scheme and uses a simple work-conserving forwarding policy. Moreover, the underlay routes are pre-determined and unknown to the overlay network. The overlay network can increase the achievable throughput of the underlay by using multiple routes, which consist of direct routes and indirect routes through other overlay nodes. We develop a throughput optimal dynamic routing algorithm for such overlay networks called the Optimal Overlay Routing Policy (OORP). OORP is derived using the classical dual subgradient descent method, and it can be implemented in a distributed manner. We show that the underlay queue-lengths can be used as a substitute for the dual variables. We also propose various schemes to gather the information about the underlay that is required by OORP and compare their performance via extensive simulations.

In multi-hop wireless networks, communication quality depends on the route from a source to a destination. In this paper, we consider a one-dimensional multi-hop wireless network where nodes are distributed randomly and theoretically analyze the relation between communication quality and routing policy using a measure called the Expected Transmission Count (ETX), which is the predicted number of data transmissions required to send a packet over that link, including retransmissions. First, we theoretically analyze the mean length of links, the mean number of hops, and the mean route ETX, which is the sum of the ETXs of all links in a route, of Longest Path Routing (LPR), and Shortest Path Routing (SPR). Second, we propose Adjustable Routing (AR), an approximation to Optimum Routing (OR), which minimizes route ETX. We theoretically compute the above characteristic values of AR. We also theoretically compute a lower bound of the mean route ETX of OR. We compare LPR, SPR, and OR using the results of analyses and show differences between these algorithms in the route ETX.

The Internet is a huge world-wide packet switching network comprised of more than 13,000 distinct subnetworks, referred to as Autonomous Systems (ASs) . They all rely on the Internet Protocol (IP) for transport of packets across the network. And most of them use shortest path routing protocols , such as OSPF or IS-IS, to control the routing of IP packets within an AS. The idea of the routing is extremely simple — every packet is forwarded on IP links along the shortest route between its source and destination nodes of the AS. The AS network administrator can manage the routing of packets in the AS by supplying the so-called administrative weights of IP links, which specify the link lengths that are used by the routing protocols for their shortest path computations. The main advantage of the shortest path routing policy is its simplicity, allowing for little administrative overhead. From the network engineering perspective, however, shortest path routing can pose problems in achieving satisfactory traffic handling efficiency. As all routing paths depend on the same routing metric , it is not possible to configure the routing paths for the communication demands between different pairs of nodes explicitly or individually; the routing can be controlled only indirectly and only as a whole by modifying the routing metric. Thus, one of the main tasks when planning such networks is to find administrative link weights that induce a globally efficient traffic routing configuration of an AS. It turns out that this task leads to very difficult mathematical optimization problems. In this chapter, we discuss and describe exact integer programming models and solution approaches as well as practically efficient smart heuristics for such shortest path routing problems .Keywordstelecommunication networksshortest path routingthe InternetOSPFECMPinteger linear programmingheuristics

We study end-to-end delay performance of different routing algorithms in networks with random failures. Specifically, we compare delay performances of differential backlog (DB) and shortest path (SP) routing algorithms and show that DB routing outperforms SP routing in terms of throughput when the network is heavily loaded and/or the failure rate is high while SP routing achieves better delay performance in the low load regime. Then, we investigate delay performance of a hybrid routing algorithm that combines principles of both SP and DB routing algorithms and show that it outperforms both of these routing algorithms. Finally, we demonstrate improvements in delay performance of DB routing through the use of a digital fountain approach which was originally proposed for multicast applications. In addition, our results show that there exists an optimal coding rate where digital fountain based DB routing achieves minimum end-to-end delay. To the best of our knowledge, this is the first work which investigates delay performance of DB routing and its enhanced versions for networks with link failures.

Recently, the merits of cooperative communication in the physical layer have been explored. However, the impact of cooperative communication on the design of the higher layers has not been well-understood yet. Cooperative routing in wireless networks has gained much interest due to its ability to exploit the broadcast nature of the wireless medium in designing power efficient routing algorithms. Most of the existing cooperation based routing algorithms are implemented by finding a shortest path route first and then improving the route using cooperative communication. As such, these routing algorithms do not fully exploit the merits of cooperative communications, since the optimal cooperative route might not be similar to the shortest path route. In this paper, we propose a cooperation-based routing algorithm, namely, the minimum power cooperative routing (MPCR) algorithm, which makes full use of the cooperative communications while constructing the minimum-power route. The MPCR algorithm constructs the minimum-power route, which guarantees certain throughput, as a cascade of the minimum-power single-relay building blocks from the source to the destination. Thus, any distributed shortest path algorithm can be utilized to find the optimal cooperative route with polynomial complexity. Using analysis, we show that the MPCR algorithm can achieve power saving of 65.61% in regular linear networks and 29.8% in regular grid networks compared to the existing cooperation-based routing algorithms, where the cooperative routes are constructed based on the shortest-path routes. From simulation results, MPCR algorithm can have 37.64% power saving in random networks compared to those cooperation-based routing algorithms.

Adaptive route choice models are studied that explicitly capture travelers’ route choice adjustments according to information on realized network conditions in stochastic time-dependent networks. Two types of adaptive route choice models are explored: an adaptive path model in which a sequence of path choice models are applied at intermediate decision nodes and a routing policy choice model in which the alternatives correspond to routing policies rather than paths at the origin. A routing policy in this study is a decision rule that maps from all possible pairs (e.g., node, time) to the next links out of the node. Existing route choice models that can be estimated on disaggregate revealed preferences assume a deterministic network setting from the traveler's perspective and cannot capture the traveler's proactive adaptive behavior under uncertain traffic conditions. The literature includes a number of algorithmic studies of optimal routing policy problems, but the estimation of a routing policy choice model is a new research area. The specifications of estimating the two adaptive route choice models are established and the feasibility of estimation from path observations is demonstrated on an illustrative network. Prediction results from three models–nonadaptive path model, adaptive path model, and routing policy model–are compared. The routing policy model is shown to better capture the option value of diversion than the adaptive path model. The difference between the two adaptive models and the nonadaptive model is larger in terms of expected travel time if the network is more stochastic, indicating that the benefit of adaptivity is more significant in a more unpredictable network.

In the context of modern high-speed Internet network, routing is often complicated by the notion of guaranteed quality of service (QoS), which can either be related to time, packet loss or bandwidth requirements: constraints related to various types of QoS make some routing inacceptable. Due to emerging real-time and multimedia applications, efficient routing of information packets in dynamically changing communication network requires that as the load levels, traffic patterns and topology of the network change, the routing policy also adapts. We focused in this paper on QoS based routing by developing a neuro-dynamic programming to construct dynamic state-dependent routing policies. In this paper, we propose an approach based on adaptive algorithm for packet routing using reinforcement learning called N best optimal path Q routing algorithm (NOQRA) which optimizes two criteria: cumulative cost path (or hop count if each link cost =1) and end-to-end delay. A load balancing policy depending on a dynamical traffic path probability distribution function is also defined and embodied in NOQRA to characterize the distribution of the traffic over the N Best Paths. Numerical results obtained with OPNET simulator for different levels of traffic's load show that NOQRA gives better results compared to standard optimal path routing and Q-routing algorithm based on Q-learning paradigm.

Machine learning is expected to be a key enabler in 5G wireless self-organizing networks (SONs) that will be significantly more autonomous, smarter, adaptable and user-centric than current networks. This paper proposes a methodology, User Specific-Optimal Capacity Shortest Path (US-OCSP) routing, that uses machine learning to determine the resource-based optimum-capacity shortest path for a user between source and destination. The methodology takes into account two primary metrics, available capacity at network nodes (eNodeBs/gNodeBs) and distance, that are critical in determining the optimal path for an end-user. An ns-3 simulation determines the capacity, which is measured by the availability of resources [i.e., Physical Resource Blocks (PRBs)] at all possible serving network nodes between the source and destination, that is followed by implementation of Q-learning, a reinforcement type of machine learning algorithm that determines the shortest path avoiding congested network nodes so as to achieve the required throughput and/or bit rate. The ability to determine the optimal-capacity shortest path route will facilitate effective resource allocation that will optimize end-user satisfaction in a 5G SON network.

Field Based Routing (FBR) is the next promising class of routing algorithms especially for wireless mesh networks. The inherent nature of shared medium wireless mesh networks, however, poses fundamental challenges to the design of effective routing policies that are optimal with respect to speed, time and resource utilization. In this paper, globally optimized routing algorithm for multiple subscribers in wireless mesh networks is proposed. Mesh network with multiple nodes will serve as an environment that optimizes some global utility function limited by the mobile nodes position in underlying MAC (Media Access Control) layer. By solving the optimization problem, the network is brought to a point of efficient operation with a certain routing policy for each node. This information will be the operating point that can be used to find better ways adaptive, which is able to steer the network towards the optimal routing. Global optimization of FBR is depicted through path estimation using PSO (Particle Swarm Optimization).

This paper considers the problem of throughput optimal routing/scheduling in\na multi-hop constrained queueing network with random connectivity whose special\ncase includes opportunistic multi-hop wireless networks and input-queued switch\nfabrics. The main challenge in the design of throughput optimal routing\npolicies is closely related to identifying appropriate and universal Lyapunov\nfunctions with negative expected drift. The few well-known throughput optimal\npolicies in the literature are constructed using simple quadratic or\nexponential Lyapunov functions of the queue backlogs and as such they seek to\nbalance the queue backlogs across network independent of the topology. By\nconsidering a class of continuous, differentiable, and piece-wise quadratic\nLyapunov functions, this paper provides a large class of throughput optimal\nrouting policies. The proposed class of Lyapunov functions allow for the\nrouting policy to control the traffic along short paths for a large portion of\nstate-space while ensuring a negative expected drift. This structure enables\nthe design of a large class of routing policies. In particular, and in addition\nto recovering the throughput optimality of the well known backpressure routing\npolicy, an opportunistic routing policy with congestion diversity is proved to\nbe throughput optimal.\n

Reinforcing probabilistic selective Quality of Service routes in dynamic irregular networks

This paper introduces the concept of time slot synchronization in time-wave division multiplexed (TWDM) multihop lightwave networks. It is shown that the time slot assignments of the intermediate nodes in a multihop path have significant effect on the end-to-end message delay. This is different from traditional notions in routing, where the hop count and congestion control are the primary concerns. Assuming a TWDM embedding of a given logical topology already exists, we formulate the optimal routing problem for arbitrary propagation delays. We propose a graph unfolding technique which converts this problem into the shortest path routing problem for weighted graphs with well known solutions. We show a method to estimate the buffering cost at the intermediate nodes (in multihop routing) to accommodate high-bandwidth traffic (e.g., video). Next, we address the question: given a logical topology what should the TWDM embedding be so that the routing delays are optimized P This leads us to an iterative approach for TWDM embedding. Given an initial embedding an optimal route is estimated for each pair of nodes. A weighted average of these optimal route distances is used as a metric to evaluate the TWDM embedding. Using a heuristic the TWDM embedding is modified and the process iterated to improve along this metric. Preliminary performance results illustrating the improvement in routing delay are provided. For example, for a 4-cube network on average delay minimization of 10% to 20% is observed.

Double-loop networks are widely used in computer networks. In this paper, we present an optimal message routing algorithm and an optimal fault-tolerant message routing algorithm for weighted bidirectional double-loop networks. The algorithms presented are novel, and they do not use routing tables. After a precalculation of O(log N) steps to determine network parameters, the algorithms can route messages using constant time at each node along the route. The algorithm presented can route messages in the presence of up to three faulty nodes or links. The fault-tolerant routing algorithm guarantees an optimal route in the presence of one node failure.

The border gateway protocol, BGP, is currently the only interdomain routing protocol employed on the Internet. As required of any interdomain protocol, BGP allows policy-based metrics to override distance-based metrics and enables each autonomous system to independently define its routing policies with little or no global coordination. Varadhan et al. (1996) have shown that there are collections of routing policies that together are not safe in the sense that they can cause BGP to diverge. That is, an unsafe collection of routing policies can result in some autonomous systems exchanging BGP routing messages indefinitely, without ever converging to a set of stable routes. In this paper we present sufficient conditions on routing policies that guarantee BGP safety. We use a new formalism, called the simple path vector protocol (SPVP), that is designed to capture the underlying semantics of any path vector protocol such as BGP. We identify a certain circular set of relationships between routing policies at various autonomous systems that we call a dispute cycle. We show that systems with no dispute cycles are guaranteed to be safe. While these include systems whose policies are consistent with shortest paths under some link metric, the class of systems with no dispute cycles is strictly larger.

Routing is a critical component in wireless mesh networks. The inherent shared-medium nature of the wireless mesh networks, however, poses fundamental challenges to the design of effective routing policies that are optimal with respect to the resource utilization. Node churns and traffic fluctuations exacerbate such a problem. In this paper, we propose a novel adaptive routing algorithm for multiple subscribers in wireless mesh networks. We view a mesh network with multiple nodes as an entity that optimizes some global utility function constrained by the underlying MAC layer interference. By solving the optimization problem, the network is driven to an efficient operating point with a certain routing policies for each node. We then use this operating point information to adaptively find better paths, which is able to gear the network towards optimal routing. Further, we take the fluctuations of the network into consideration and thus render our algorithm more robust for a variety of network situations. Simulations demonstrate the efficiency and efficacy of our algorithm.