Showing papers on "Link-state routing protocol published in 1998"

Power-aware routing in mobile ad hoc networks

Abstract: b this paper we present a case for using new power-aware metn.cs for determining routes in wireless ad hoc networks. We present five ~erent metriw based on battery power consumption at nodw. We show that using th=e metrics in a shortest-cost routing algorithm reduces the cost/packet of routing packets by 5-30% over shortwt-hop routing (this cost reduction is on top of a 40-70% reduction in energy consumption obtained by using PAMAS, our MAC layer prtocol). Furthermore, using these new metrics ensures that the mean time to node failure is increased si~cantly. An interesting property of using shortest-cost routing is that packet delays do not increase. Fintiy, we note that our new metrim can be used in most tradition routing protocols for ad hoc networks.

A distance routing effect algorithm for mobility (DREAM)

Abstract: 1 Introduction h this paper we introduce a new routing protocol for ad hoc networks built around two novel observations. One, called the distance eflect, usw the fmt that the greater the distance separating two nodes, the slower they appear to be moving with respect to each other. Accor@gly, the location information in routing tables can be updated as a function of the distance separating nodes without compromising the routing accuracy. The second idea is that of triggering the sending of location updates by the moving nodes autonomously, based ody on a node's mobility rate. htuitively, it is clear that in a direction routing dgorithrn, routing information about the slower moving nodes needs to be updated less frequently than that about hig~y mobtie nodw. h this way e~ node can optimize the frequency at which it sends updates to the networks and correspondingly r~ duce the bandwidth and energy used, leading to a fully distributed and self-optimizing system. B~ed on thwe routing tablw, the proposed direction algorithm sends messages in the " recorded dwectionn of the destination node, guaranteeing detivery by following the direction with a given probability. We show by detailed simda-tion that our protocol always delivers more than 80% of the data messages by following the direction computed, without using any recovery procedure. In addition, it mintilzes the overhead used for maintaining routes using the two new principlw of update message frequency and distance. Lastly, the dgorithrn is fully distributed, provides loop-free paths, and is robust, since it suppfies multiple routes. Pemlissiontomakedigitalorhsrdcopiesof allorpartof this\vorkfor personal or classroom use is granted without fee provided that copies are not mzde or dis~.buted for prolit or commercial ad~arrtageand that copies bcwrthis notice and the full citation on the first page. To copy othm}tise, to republish, to post on senrers or to redistribute to lists, requires prior specific permission an&'ora fee. 76 Rom a routing perspective, an ad hoc network is a packet radio network in which the mobile nodes perform the routing functions. Generdy, routing is multi-hop since nodes may not be within the wireless transmission range of one another and thus depend on each other to forward packets to a given destination. Since the topology of an ad hoc network changes frequently, a routing protocol should be a distributed algorithm that computes multiple, cycle free routes while keeping the communication overhead to a minimum (see, e.g., [4]). One way to …

An overview of quality of service routing for next-generation high-speed networks: problems and solutions

Abstract: The upcoming gigabit-per-second high-speed networks are expected to support a wide range of communication-intensive real-time multimedia applications. The requirement for timely delivery of digitized audio-visual information raises new challenges for next-generation integrated services broadband networks. One of the key issues is QoS routing. It selects network routes with sufficient resources for the requested QoS parameters. The goal of routing solutions is twofold: (1) satisfying the QoS requirements for every admitted connection, and (2) achieving global efficiency in resource utilization. Many unicast/multicast QoS routing algorithms have been published, and they work with a variety of QoS requirements and resource constraints. Overall, they can be partitioned into three broad classes: (1) source routing, (2) distributed routing, and (3) hierarchical routing algorithms. We give an overview of the QoS routing problem as well as the existing solutions. We present the strengths and weaknesses of different routing strategies, and outline the challenges. We also discuss the basic algorithms in each class, classify and compare them, and point out possible future directions in the QoS routing area.

Routing lookups in hardware at memory access speeds

Abstract: The increased bandwidth in the Internet puts great demands on network routers; for example, to route minimum sized Gigabit Ethernet packets, an IP router must process about 1.5/spl times/10/sup 6/ packets per second per port. Using the "rule-of-thumb" that it takes roughly 1000 packets per second for every 10/sup 6/ bits per second of line rate, an OC-192 line requires 10/spl times/10/sup 6/ routing lookups per second; well above current router capabilities. One limitation of router performance is the route lookup mechanism. IP routing requires that a router perform a longest-prefix-match address lookup for each incoming datagram in order to determine the datagram's next hop. We present a route lookup mechanism that when implemented in a pipelined fashion in hardware, can achieve one route lookup every memory access. With current 50 ns DRAM, this corresponds to approximately 20/spl times/10/sup 6/ packets per second; much faster than current commercially available routing lookup schemes. We also present novel schemes for performing quick updates to the forwarding table in hardware. We demonstrate using real routing update patterns that the routing tables can be updated with negligible overhead to the central processor.

A Framework for QoS-based Routing in the Internet

Abstract: This document describes some of the QoS-based routing issues and requirements, and proposes a framework for QoS-based routing in the Internet. This memo provides information for the Internet community. It does not specify an Internet standard of any kind.

Internet routing instability

Abstract: This paper examines the network interdomain routing information exchanged between backbone service providers at the major US public Internet exchange points. Internet routing instability, or the rapid fluctuation of network reachability information, is an important problem currently facing the Internet engineering community. High levels of network instability can lead to packet loss, increased network latency and time to convergence. At the extreme, high levels of routing instability have led to the loss of internal connectivity in wide-area, national networks. We describe several unexpected trends in routing instability, and examine a number of anomalies and pathologies observed in the exchange of inter-domain routing information. The analysis in this paper is based on data collected from border gateway protocol (BGP) routing messages generated by border routers at five of the Internet core's public exchange points during a nine month period. We show that the volume of these routing updates is several orders of magnitude more than expected and that the majority of this routing information is redundant, or pathological. Furthermore, our analysis reveals several unexpected trends and ill-behaved systematic properties in Internet routing. We finally posit a number of explanations for these anomalies and evaluate their potential impact on the Internet infrastructure.

Adaptive wavelength routing in all-optical networks

Abstract: We consider routing and wavelength assignment in wavelength-routed all-optical networks (WAN) with circuit switching. The conventional approaches to address this issue consider the two aspects of the problem disjointly by first finding a route from a predetermined set of candidate paths and then searching for an appropriate wavelength assignment. We adopt a more general approach in which we consider all paths between a source-destination (s-d) pair and incorporate network state information into the routing decision. This approach performs routing and wavelength assignment jointly and adaptively, and outperforms fixed routing techniques. We present adaptive routing and wavelength assignment algorithms and evaluate their blocking performance. We obtain an analytical technique to compute approximate blocking probabilities for networks employing fixed and alternate routing. The analysis can also accommodate networks with multiple fibers per link. The blocking performance of the proposed adaptive routing algorithms are compared along with their computational complexity.

The performance of query control schemes for the zone routing protocol

Abstract: In this paper, we study the performance of route query control mechanisms for the recently proposed Zone Routing Protocol (ZRP) for ad-hoc networks. The ZRP proactively maintains routing information for a local neighborhood (routing zone), while reactively acquiring routes to destinations beyond the routing zone. This hybrid routing approach has the potential to be more efficient in the generation of control traffic than traditional routing schemes. However, without proper query control techniques, the ZRP can actually produce more traffic than standard flooding protocols.Our proposed query control schemes exploit the structure of the routing zone to provide enhanced detection (Query Detection (QD1/QD2)), termination (Loop-back Termination (LT), Early Termination (ET)) and prevention (Selective Bordercasting (SBC)) of overlapping queries. We demonstrate how certain combinations of these techniques can be applied to single channel or multiple channel ad-hoc networks to improve both the delay and control traffic performance of the ZRP. Our query control mechanisms allow the ZRP to provide routes to all accessible network nodes with only a fraction of the control traffic generated by purely proactive distance vector and purely reactive flooding schemes, and with a response time as low as 10% of a flooding route query delay.

OSPF: Anatomy of an Internet Routing Protocol

Abstract: From the Publisher: Written for TCP/IP network administrators, protocol designers, and network application developers, this book gives the most complete and practical view ever into the inner workings of Internet routing. The book focuses on OSPF (Open Shortest Path First), a common TCP/IP routing protocol that provides robust and efficient routing support in the most demanding Internet environments. A methodical and detailed description of the protocol is offered and OSPF's role within the wider context of a TCP/IP network is demonstrated. Practical throughout, the book provides not only a theoretical description of Internet routing, but also a real-world look into how theory translates into practice. It shows how algorithms are implemented, and how the routing protocols function in a working network where transmission lines and routers routinely break down. You will find clear explanations of such routing fundamentals as how a router forwards packets, IP addressing, CIDR (Classless Inter-Domain Routing), the routing table, Internet routing architecture, and the two main routing technologies: Distance Vector and link-state algorithms. OSPF is discussed in depth, with an examination of the rationale behind OSPF's design decisions and how it has evolved to keep pace with the rapidly changing Internet environment. OSPF topics covered by the book include the following: OSPF areas and virtual links NBMA (Nonbroadcast multi-access) and Point-to-MultiPoint network segments OSPF configuration and management Interaction with other routing protocols OSPF cryptographic authentication OSPF protocol extensions, including the Demand Circuit extensions and the multicast extensions to OSPF (MOSPF) An OSPF FAQ IP multicast and multicast routing are also discussed. Methods for debugging routing problems are explained, including a catalog of available debugging tools. The book also offers side-by-side comparisons of all the unicast and multicast routing protocols currently in use in the Internet. You will come away from this book with a sophisticated understanding of Internet routing and of the OSPF protocol in particular. Moreover, the book's practical focus will enable you to put this deeper understanding to work in your network environment.

Global state routing: a new routing scheme for ad-hoc wireless networks

Abstract: In an ad-hoc environment with no wired communication infrastructure, it is necessary that mobile hosts operate as routers in order to maintain the information about connectivity. However with the presence of high mobility and low signal/interference ratio (SIR), traditional routing schemes for wired networks are not appropriate, as they either lack the ability to quickly reflect the changing topology, or may cause excessive overhead, which degrades network performance. Considering these restrictions, we propose a new scheme especially designed for routing in an ad-hoc wireless environments. We call this scheme "global state routing" (GSR), where nodes exchange vectors of link states among their neighbors during routing information exchange. Based on the link state vectors, nodes maintain a global knowledge of the network topology and optimize their routing decisions locally. The performance of the algorithm, studied in this paper through a series of simulations, reveals that this scheme provides a better solution than existing approaches in a truly mobile, ad-hoc environment.

Routing and mobility management protocols for ad-hoc networks

Abstract: Two network communication protocols, one for routing and one for mobility management, are presented that are particularly suited for use with ad-hoc networks. The routing protocol is a proactive-reactive hybrid routing protocol that limits the scope of the proactive procedure to the node's local neighborhood. Routing zones are defined for each node that include nodes whose distance from the subject node in hops is at most some predefined number, referred to as the zone radius. Each node is required to know the topology of the network within its routing zone only. The reactive procedure is limited during route discovery to queries of only those nodes located on the periphery of routing zones. In this manner, the queries hop across nodes in distances of zone radius, thus limiting the scope of the reactive procedure. The zone radius is preferably adjustable to accommodate different and differing network topologies and network operational conditions in the most efficient manner. The mobility management protocol relies on some network nodes assuming the mobility management function. In this scheme, each network node is “associated” with one or more mobility management nodes. The mobility management nodes form a virtual network which is embedded within the actual ad-hoc network. Each mobility management node knows the location of all nodes within its zone, and communicates this information to any other mobility management node that requests it.

Quality of service based routing: a performance perspective

Abstract: Recent studies provide evidence that Quality of Service (QoS) routing can provide increased network utilization compared to routing that is not sensitive to QoS requirements of traffic. However, there are still strong concerns about the increased cost of QoS routing, both in terms of more complex and frequent computations and increased routing protocol overhead. The main goals of this paper are to study these two cost components, and propose solutions that achieve good routing performance with reduced processing cost. First, we identify the parameters that determine the protocol traffic overhead, namely (a) policy for triggering updates, (b) sensitivity of this policy, and (c) clamp down timers that limit the rate of updates. Using simulation, we study the relative significance of these factors and investigate the relationship between routing performance and the amount of update traffic. In addition, we explore a range of design options to reduce the processing cost of QoS routing algorithms, and study their effect on routing performance. Based on the conclusions of these studies, we develop extensions to the basic QoS routing, that can achieve good routing performance with limited update generation rates. The paper also addresses the impact on the results of a number of secondary factors such as topology, high level admission control, and characteristics of network traffic.

Forwarding Group Multicast Protocol (FGMP) for multihop, mobile wireless networks

Abstract: In this paper we propose a new multicast protocol for multihop mobile wireless networks Instead of forming multicast trees, a group of nodes in charge of forwarding multicast packets is designated according to members’ requests Multicast is then carried out via “scoped” flooding over such a set of nodes The forwarding group is periodically refreshed to handle topology/membership changes Multicast using forwarding group takes advantage of wireless broadcast transmissions and reduces channel and storage overhead, thus improving the performance and scalability The key innovation with respect to wired multicast schemes like DVMRP is the use of flags rather than upstream/downstream link state, making the protocol more robust to mobility The dynamic reconfiguration capability makes this protocol particularly suitable for mobile networks The performance of the proposed scheme is evaluated via simulation and is compared to that of DVMRP and global flooding

Comparative performance evaluation of routing protocols for mobile, ad hoc networks

Abstract: We evaluate several routing protocols for mobile, wireless, ad hoc networks via packet level simulations. The protocol suite includes routing protocols specifically designed for ad hoc routing, as well as more traditional protocols, such as link state and distance vector used for dynamic networks. Performance is evaluated with respect to fraction of packets delivered, end-to-end delay and routing load for a given traffic and mobility model. It is observed that the new generation of on-demand routing protocols use a much lower routing load. However the traditional link state and distance vector protocols provide, in general, better packet delivery and delay performance.

Mobile agents for adaptive routing

Abstract: This paper introduces AntNet, a new routing algorithm for telecommunication networks. AntNet is an adaptive, distributed, mobile-agents-based algorithm which was inspired by recent work on the ant colony metaphor. We apply AntNet in a datagram network and compare it with both static and adaptive state-of-the-art routing algorithms. We ran experiments for various paradigmatic temporal and spatial traffic distributions. AntNet showed both very good performances and robustness under all the experimental conditions with respect to its competitors.

On routes and multicast trees in the Internet

Abstract: Multicasting has an increasing importance for network applications such as groupware or videoconferencing. Several multicast routing protocols have been defined. However they cannot be used directly in the Internet since most inter-domain routers do no implement multicasting. Thus these protocols are mainly tested either on a small scale inside a domain, or through the Mbone, whose topology is not really the same as Internet topology. The purpose of this paper is to construct a graph using actual routes of the Internet, and then to use this graph to compare some parameters - delays, scaling in term of state or traffic concentration - of multicast routing trees constructed by different algorithms - source shortest path trees and shared trees.

Issues and trends in router design

Abstract: Future routers must not only forward packets at high speeds, but also deal with nontrivial issues such as scheduling support for differential services, heterogeneous link technologies, and backward compatibility with a wide range of packet formats and routing protocols. The authors outline the design issues facing the next generation of backbone, enterprise, and access routers. The authors also present a survey of advances in router design, identifying important trends, concluding with a selection of open issues.

Routing in a multi-layer distributed network element

Abstract: A multi-layer distributed network element (201) for relaying packets according to known routing protocols. A distributed architecture of multiple subsystems (410) delivers routing at wire-speed performance across subnetworks. Each subsystem (410) includes a forwarding memory (413) and an associated memory (414) and is configured to identify unicast and multicast packets for routing purposes, modify the packets in hardware, including replace VLAN information, and forward the packets to the next hop. The routing decisions are made in the inbound subsystem, and packets are forwarded, if necessary given the network topology, through a separate outbound subsystem.

QoS routing in ad hoc wireless networks

Abstract: The emergence of nomadic applications have generated a lot of interest in wireless network infrastructures which support multimedia services. We propose a bandwidth routing algorithm for multimedia support in a multihop wireless network. This network can be interconnected to wired networks (e.g. ATM or the Internet) or stand alone. Our bandwidth routing includes bandwidth calculation and reservation schemes. Under such a routing algorithm, we can derive a route to satisfy the bandwidth requirement for the QoS constraint. At a source node, the bandwidth information can be used to decide to accept a new call or not immediately. This is specially important to carry out a fast handoff when interconnecting to an ATM backbone infrastructure. It enables an efficient call admission control. The simulation results show that the bandwidth routing algorithm is very useful in extending the ATM virtual circuit service to the wireless network. Different types of QoS traffic can be integrated in such a dynamic radio network with high performance.

QoSMIC: quality of service sensitive multicast Internet protocol

Abstract: In this paper, we present, QoSMIC, a multicast protocol for the Internet that supports QoS-sensitive routing, and minimizes the importance of a priori configuration decisions (such as core selection). The protocol is resource-efficient, robust, flexible, and scalable. In addition, our protocol is provably loop-free.Our protocol starts with a resources-saving tree (Shared Tree) and individual receivers switch to a QoS-competitive tree (Source-Based Tree) when necessary. In both trees, the new destination is able to choose the most promising among several paths. An innovation is that we use dynamic routing information without relying on a link state exchange protocol to provide it. Our protocol limits the effect of pre-configuration decisions drastically, by separating the management from the data transfer functions; administrative routers are not necessarily part of the tree. This separation increases the robustness, and flexibility of the protocol. Furthermore, QoSMIC is able to adapt dynamically to the conditions of the network.The QoSMIC protocol introduces several new ideas that make it more flexible than other protocols proposed to date. In fact, many of the other protocols, (such as YAM, PIMSM, BGMP, CBT) can be seen as special cases of QoSMIC. This paper presents the motivation behind, and the design of QoSMIC, and provides both analytical and experimental results to support our claims.

Ant Colonies for Adaptive Routing in Packet-Switched Communications Networks

Abstract: In this paper we present AntNet, a novel adaptive approach to routing tables learning in packet-switched communications networks. AntNet is inspired by the stigmergy model of communication observed in ant colonies. We present compelling evidence that AntNet, when measuring performance by standard measures such as network throughput and average packet delay, outperforms the current Internet routing algorithm (OSPF), some old Internet routing algorithms (SPF and distributed adaptive Bellman-Ford), and recently proposed forms of asynchronous online Bellman-Ford (Q-routing and Predictive Q-routing).

A performance comparison of the temporally-ordered routing algorithm and ideal link-state routing

Abstract: We present a relative performance comparison of the temporally-ordered routing algorithm (TORA) with an ideal link state (ILS) routing algorithm. The performance metrics evaluated include bandwidth efficiency for both control and data, as well as end-to-end message packet delay and throughput. The routing algorithms are compared in the context of a dynamic, multihop, wireless network employing broadcast transmissions. The network parameters varied include network size, average rate of topological changes and average network connectivity. While the average network connectivity was found not to be a significant factor, the relative performance of TORA and ILS was found to be critically dependent on the network size, and the average rate of topological changes. The results further indicate that for a given available bandwidth-as either the size of network increases or the rate of network topological change increases, the performance of TORA eventually exceeds that of ILS.

A distributed algorithm of delay-bounded multicast routing for multimedia applications in wide area networks

Abstract: Multicast routing is to find a tree which is rooted from a source node and contains all multicast destinations. There are two requirements of multicast routing in many multimedia applications: optimal network cost and bounded delay. The network cost of a tree is defined as the sum of the cost of all links in the tree. The bounded delay of a routing tree refers to the feature that the accumulated delay from the source to any destination along the tree shall not exceed a prespecified bound. This paper presents a distributed heuristic algorithm which generates routing trees having a suboptimal network cost under the delay bound constraint. The proposed algorithm is fully distributed, efficient in terms of the number of messages and convergence time, and flexible in dynamic membership changes. A large amount of simulations have been done to show the network cost of the routing trees generated by our algorithm is similar to, or even better than, other existing algorithms.

A fast routability-driven router for FPGAs

Abstract: Three factors are driving the demand for rapid FPGA compilation. First, as FPGAs have grown in logic capacity, the compile computation has grown more quickly than the compute power of the available computers. Second, there exists a subset of users who are willing to pay for very high speed compile with a decrease in quality of result, and accordingly being required to use a larger FPGA or use more real-estate on a given FPGA than is otherwise necessary. Third, very high speed compile has been a long-standing desire of those using FPGA-based custom computing machines, as they want compile times at least closer to those of regular computers.This paper focuses on the routing phase of the compile process, and in particular on routability-driven routing (as opposed to timing-driven routing). We present a routing algorithm and routing tool that has three unique capabilities relating to very high-speed compile: For a “low stress” routing problem (which we define as the case where the track supply is at least 10% greater than the minimun number of tracks per channel actually needed to route a circuit) the routing time is very fast. For example, the routing phase (after the netlist is parsed and the routing graph is constructed) for a 20,000 LUT/FF pair circuit with 30% extra tracks is only 23 seconds on a 300 MHz Sparcstation.For low-stress routing problems the routing time is near-linear in the size of the circuit, and the linearity constant is very small: 1.1 ms per LUT/FF pair, or roughly 55,000 LUT/FF pairs per minute.For more difficult routing problems (where the track supply is close to the minimum needed) we provide a method that quickly identifies and subdivides this class into two sub-classes: (i) those circuits which are difficult (but possible) to route and will take significantly more time than low-stress problems, and (ii) those circuits which are impossible to route. In the first case the user can choose to continue or reduce the amount of logic; in the second case the user is forced to reduce the amount of logic or obtain a larger FPGA.

Quality of service based routing

Abstract: Recent studies provide evidence that Quality of Service (QoS) routing can provide increased network utilization compared to routing that is not sensitive to QoS requirements of traffic. However, th...

Routing area updating in packet radio network

Abstract: The invention relates to a cellular packet radio network and to a method for updating a routing area in a packet radio network. Packet radio support nodes (SGSN) are connected to a digital cellular radio network (BSS), which provides a radio interface for the support nodes for packet-switched data transmission between the support nodes and mobile stations. There is a logical link between a mobile station (MS) and a serving packet radio support node (SGSN). The packet radio network utilizes logical routing areas, each of which comprises one or more cells. Each cell broadcasts information on the routing area to which it belongs. The mobile station sends a routing area update request to the packet radio network when it roams to a new cell which belongs to a different routing area than the old cell. The update request includes the identifiers of the old and new routing area. When the packet radio node detects a routing area update carried out by an unknown mobile station, it initiates the establishment of a logical link by sending a link establishment message (LLC Subm, 21, 21') to the mobile station, the message including the same identifier the mobile station used for itself in the routing area update request. The mobile station initializes the logical link at its own end and sends and acknowledgement to the serving packet radio support node.

Wormhole routing techniques for directly connected multicomputer systems

Abstract: Wormhole routing has emerged as the most widely used switching technique in massively parallel computers. We present a detailed survey of various techniques for enhancing the performance and reliability of wormhole-routing schemes in directly connected networks. We start with an overview of the direct network topologies and a comparison of various switching techniques. Next, the characteristics of the wormhole routing mechanism are described in detail along with the theory behind deadlock-free routing. The performance of routing algorithms depends on the selection of the path between the source and the destination, the network traffic, and the router design. The routing algorithms are implemented in the router chips. We outline the router characteristics and describe the functionality of various elements of the router. Depending on the usage of paths between the source and the destination, routing algorithms are classified as deterministic, fully adaptive, and partially adaptive. We discuss several representative algorithms for all these categories. The algorithms within each category vary in terms of resource requirements and performance under various traffic conditions. The main difference among various adaptive routing schemes is the technique used to avoid deadlocks. We also discuss a few algorithms based on deadlock recovery techniques. Along with performance, fault tolerance is essential for message routing in multicomputers, and we thus discuss several fault-tolerant wormhole routing algorithms along with their fault-handling capabilities. These routing schemes enable a message to reach its destination even in the presence of faults in the network. The implementation details of wormhole routing algorithms in contemporary commercial systems are also discussed. We conclude by itemizing several future directions and open issues.

QoS routing in networks with uncertain parameters

Abstract: This article considers the problem of routing connections with QoS requirements across networks, when the information available for making routing decisions is inaccurate. This uncertainty about the actual state of a network component arises naturally in a number of different environments, which are reviewed in the paper. The goal of the route selection process is then to identify a path that is most likely to satisfy the QoS requirements. For end to end delay guarantees, this problem is intractable. However we show that by decomposing the end-to-end constraint into local delay constraints, efficient and tractable solutions can be established. We first consider the simpler problem of decomposing the end-to-end constraint into local constraints, for a given path. We show that, for general distributions, this problem is also intractable. Nonetheless, by defining a certain class of probability distributions, which posses a certain convexity property, and restricting ourselves to that class, we are able to establish efficient and exact solutions. Moreover, we show that typical distributions would belong to that class. We then consider the general problem, of combined path optimization and delay decomposition. We present an efficient solution scheme for the above class of probability distributions. Our solution is similar to that of the restricted shortest-path problem, which renders itself to near-optimal approximations of polynomial complexity. We also show that yet simpler solutions exist in the special case of uniform distributions.