IP fast reroute methods are used to recover packets in the data plane upon link failures. Previous work provided methods that guarantee failure recovery from at most two-link failures. We develop an IP fast reroute method that employs rooted arc-disjoint spanning trees to guarantee recovery from up to k-1 link failures in a k-edge-connected network. As arc-disjoint spanning trees may be constructed in sub-quadratic time in the size of the network, our approach offers excellent scalability. Through experimental results, we show that employing arc-disjoint spanning trees to recover from multiple failures reduces path stretch in comparison with previously known techniques.

We develop approaches for disjoint multipath routing and fast recovery in IP networks that guarantee recovery from arbitrary two link failures. We achieve this by developing the first known algorithm to construct three edge-independent spanning trees, which has a running time complexity of O(V2). The property of these trees is that the paths from a source to the destination on the trees are mutually link-disjoint. We illustrate how the three edge-independent trees rooted at a destination may be employed to achieve multipath routing and IP fast recovery. We discuss different ways of employing the trees. The routing of packets is based on the destination address and the input interface over which the packet was received. If the trees are employed exclusively for multipath routing, then no packet overhead is required. If the trees are employed for failure recovery, then the overhead bits will range from 0 to 2 bits depending on the flexibility sought in routing. We evaluate the performance of the trees in fast recovery by comparing the path lengths provided under single- and dual-link failures with an earlier approach based on tunneling. We also evaluate the performance of the trees when used for multipath routing and compare it to equal-cost multipaths (ECMP).

The introduction of coherent optics and wavelength division multiplexing (WDM) in telecommunication networks has led to unprecedented gains in backbone capacity. The increase in optical layer capacity inadvertently exacerbates the problem of traffic loss due to optical component failures. IP networks are designed over optical backbone networks, where each IP link traverses a multihop optical lightpath. Therefore, the failure of optical components often lead to multiple link failures in the IP network. In this paper, we develop an IP fast reroute mechanism using rooted arc-disjoint spanning trees that guarantees recovery from (k-1) link failures in a k-edge-connected network. As arc-disjoint spanning trees may be constructed in sub-quadratic time in the size of the network, our approach offers excellent scalability. Through experimental results, we show that employing arc-disjoint spanning trees to recover from multiple failures reduces path stretch in comparison with previously known techniques.

Central to network tomography is the problem of identifiability, the ability to identify internal network characteristics uniquely from end-to-end measurements. This problem is often underconstrained even when internal network characteristics such as link delays are modeled as additive constants. While it is known that the network topology can play a role in determining the extent of identifiability, there is a lack in the fundamental understanding of being able to quantify it for a given network. In this paper, we consider the problem of identifying additive link metrics in an arbitrary undirected network using measurement nodes and establishing paths/cycles between them. For a given placement of measurement nodes, we define and derive the “link rank” of the network-the maximum number of linearly independent cycles/paths that may be established between the measurement nodes. We achieve this in linear time. The link rank helps quantify the exact extent of identifiability in a network. We also develop a quadratic time algorithm to compute a set of cycles/paths that achieves the maximum rank.

Fast-recovery from link failures is a well-studied topic in IP networks. Employing fast-recovery in Ethernet networks is complicated as the forwarding is based on destination MAC addresses, which do not have the hierarchical nature similar to those exhibited in Layer 3 in the form of IP-prefixes. Moreover, switches employ backward learning to populate the forwarding table entries. Thus, any fast recovery mechanism in Ethernet networks must be based on undirected spanning trees if backward learning is to be retained. In this paper, we develop three alternatives for achieving fast recovery from single link failures in Ethernet networks. All three approaches provide guaranteed recovery from single link failures. The approaches differ in the technologies required for achieving fast recovery, namely VLAN rewrite or mac-in-mac encapsulation or both. We study the performance of the approaches developed on five different networks.

In this paper, we propose multicast protection trees that provide instantaneous failure recovery from single node failures. For a given node v, the multicast protection tree spans all the neighbors v and does not include v. Thus, when node v fails, its neighbors are connected through the multicast protection tree instead of node v, and the neighbors of node v forward the traffic over this tree. The multicast protection trees are constructed a priori, without the knowledge of the multicast traffic in the network. This facilitates protocol independent single node failure recovery in multicast networks. These trees are used when a new multicast tree is being formed after a node failure has occurred. We analyze the effectiveness of the proposed fast rerouting technique using three practical networks.

The Internet access may not be a reality in many scenarios such as poor communities and disaster-hit areas. A mesh network is a solution for such scenarios, where a wireless backbone will enable communication and needed services. In this paper we propose the design of a self-forming, self-healing infrastructure wireless mesh network architecture, composed using 802.11 based multi-radio network nodes. The design incorporates the peculiarities of these scenarios in a lean scheme based on well-established DHCP protocol and reduces auto-configuration as well as routing overhead.

In this paper, we study strategies for allocating and managing friendly jammers, so as to create virtual barriers that would prevent hostile eavesdroppers from tapping sensitive wireless communication. Our scheme precludes the use of any encryption technique. Applications include domains such as (i) protecting the privacy of storage locations where RFID tags are used for item identification, (ii) secure reading of RFID tags embedded in credit cards, (iii) protecting data transmitted through wireless networks, sensor networks, etc. By carefully managing jammers to produce noise, we show how to reduce the SINR of eavesdroppers to below a threshold for successful reception, without jeopardizing network performance.

In order to achieve resilient multipath routing, we introduce the concept of independent directed acyclic graphs (IDAGs) in this paper. Link-independent (node-independent) DAGs satisfy the property that any path from a source to the root on one DAG is link-disjoint (node-disjoint) with any path from the source to the root on the other DAG. Given a network, we develop polynomial-time algorithms to compute link-independent and node-independent DAGs. The algorithm developed in this paper: 1) provides multipath routing; 2) utilizes all possible edges; 3) guarantees recovery from single link failure; and 4) achieves all these with at most one bit per packet as overhead when routing is based on destination address and incoming edge. We show the effectiveness of the proposed IDAGs approach by comparing key performance indices to that of the independent trees and multiple pairs of independent trees techniques through extensive simulations.

In this paper, we study the problem of identifying constant additive link metrics using linearly independent monitoring cycles and paths. A monitoring cycle starts and ends at the same monitoring station, while a monitoring path starts and ends at distinct monitoring stations. We show that three-edge connectivity is a necessary and sufficient condition to identify link metrics using one monitoring station and employing monitoring cycles. We develop a polynomial-time algorithm to compute the set of linearly independent cycles. For networks that are less than three-edge-connected, we show how the minimum number of monitors required and their placement may be computed. For networks with symmetric directed links, we show the relationship between the number of monitors employed, the number of directed links for which metric is known a priori, and the identifiability for the remaining links. To the best of our knowledge, this is the first work that derives the necessary and sufficient conditions on the network topology for identifying additive link metrics and develops a polynomial-time algorithm to compute linearly independent cycles and paths.

This paper develops a new resilient multipath routing technique, referred to as SPT-DAG, that has the following characteristics: (1) provides multipath routing over directed acyclic graphs (DAG); (2) the shortest path tree is guaranteed to be part of the DAG; and (3) provides guaranteed recovery from single link failures. We develop polynomial time algorithm to compute the SPT-DAG and a routing protocol to forward packets over the SPT-DAG using one overhead bit in the packet. We consider different load-balancing approaches for forwarding a packet when the packet has not encountered a failure. Through extensive flow-based simulations, we show that the SPT-DAG performs significantly better than those approaches that exclusively target load balancing or resiliency.

We introduce the concepts of monitoring paths (MPs) and monitoring cycles (MCs) for unique localization of shared risk linked group (SRLG) failures in all-optical networks. An SRLG failure causes multiple links to break simultaneously due to the failure of a common resource. MCs (MPs) start and end at the same (distinct) monitoring location(s). They are constructed such that any SRLG failure results in the failure of a unique combination of paths and cycles. We derive necessary and sufficient conditions on the set of MCs and MPs needed for localizing any single SRLG failure in an arbitrary graph. When a single monitoring location is employed, we show that a network must be (k+2)-edge connected for localizing all SRLG failures, each involving up toklinks. For networks that are less than (k+2)-edge connected, we derive necessary and sufficient conditions on the placement of monitoring locations for unique localization of any single SRLG failure of up toklinks. We use these conditions to develop an algorithm for determining monitoring locations. We show a graph transformation technique that converts the problem of identifying MCs and MPs with multiple monitoring locations to a problem of identifying MCs with a single monitoring location. We provide an integer linear program and a heuristic to identify MCs for networks with one monitoring location. We then consider the monitoring problem for networks with no dedicated bandwidth for monitoring purposes. For such networks, we use passive probing of lightpaths by employing optical splitters at various intermediate nodes. Through an integer linear programming formulation, we identify the minimum number of optical splitters that are required to monitor all SRLG failures in the network. Extensive simulations are used to demonstrate the effectiveness of the proposed monitoring technique.

Multi-channel wireless networks are increasingly being employed as infrastructure networks in metro areas. In addition, nodes in these networks employ directional antennas to improve spatial throughput. In such networks, we consider the problem of finding a broadcast tree from a given root with channel assignment such that all the links in the broadcast tree can be active simultaneously without interfering with each other. We prove that finding such a tree is an NP-hard problem. Hence, we formulate the problem as an integer linear program (ILP) and develop heuristics to find the broadcast tree with channel assignment. We evaluate and compare the performances of the developed heuristics with respect to their success rate, average depth of the obtained tree, and average path length from root to a node in the network.

In this paper, we introduce the concept of Independent Directed Acyclic Graphs (IDAGs) to achieve resilient multipath routing. Link- independent (Node-independent) DAGs satisfy the property that any path from a source to the root on one DAG is link-disjoint (node-disjoint) with any path from the source to the root on the other DAG. Given a network, we develop polynomial time algorithms to compute link-independent and node-independent DAGs. The algorithm developed in this paper: (1) achieves multipath routing; (2) guarantees recovery from single link failure; (3) utilizes all possible edges; and (4) achieves all these with at most one bit per packet as overhead when routing is based on destination address and incoming link. We demonstrate the effectiveness of the proposed IDAGs approach by comparing key performance indices to that of the independent trees technique.

Multi-channel wireless networks are increasingly being employed as infrastructure networks, e.g.\ in metro areas. Nodes in these networks frequently employ directional antennas to improve spatial throughput. In such networks, given a source and destination, it is of interest to compute an optimal path and channel assignment on every link in the path such that the path bandwidth is the same as that of the link bandwidth and such a path satisfies the constraint that no two consecutive links on the path are assigned the same channel, referred to as "Channel Discontinuity Constraint" (CDC). CDC-paths are also quite useful for TDMA system, where preferably every consecutive links along a path are assigned different time slots. This paper contains several contributions. We first present an O(N2) distributed algorithm for discovering the shortest CDC-path between given source and destination. For use in wireless networks, we explain how spatial properties can be used for dramatically expedite the algorithm. This improves the running time of the O(N3) centralized algorithm of Ahuja et al. for finding the minimum-weight CDC-path. Our second result is a generalized t-spanner for CDC-path; For any ¿>0 we show how to construct a sub-network containing only O(N/¿) edges, such that that length of shortest CDC-paths between arbitrary sources and destinations increases by only a factor of at most 1/(1-2 sin (¿/2))2. This scheme can be implemented in a distributed manner with a message complexity of O(n log n) and it is highly dynamic, so addition/deletion of nodes are easily handled in a distributed manner. An important conclusion of this scheme is in the case of directional antennas are used. In this case, it is enough to consider only the two closest nodes in each cone.

Wireless infrastructure networks that provide ubiquitous connectivity to mobile nodes in metro areas are becoming increasingly popular. The nodes in such backbone networks are often equipped with multiple transceivers to allow for simultaneous transmissions in multiple non-overlapping channels. In this paper, we develop an analytical model for evaluating the throughput and delay performance of wireless infrastructure networks employing Slotted Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA) over multiple channels. The analytical model, which takes into account the correlation due to multi-hop transmissions, approximates the performance observed through simulations accurately.

This paper develops novel mechanisms for recovering from failures in IP networks with proactive backup path calculations and Internet Protocol (IP) tunneling. The primary scheme provides resilience for up to two link failures along a path. The highlight of the developed routing approach is that a node reroutes a packet around the failed link without the knowledge of the second link failure. The proposed technique requires three protection addresses for every node, in addition to the normal address. Associated with every protection address of a node is a protection graph. Each link connected to the node is removed in at least one of the protection graphs, and every protection graph is guaranteed to be two-edge-connected. The network recovers from the first failure by tunneling the packet to the next-hop node using one of the protection addresses of the next-hop node; the packet is routed over the protection graph corresponding to that protection address. We prove that it is sufficient to provide up to three protection addresses per node to tolerate any arbitrary two link failures in a three-edge-connected graph. An extension to the basic scheme provides recovery from single-node failures in the network. It involves identification of the failed node in the packet path and then routing the packet to the destination along an alternate path not containing the failed node. The effectiveness of the proposed techniques were evaluated by simulating the developed algorithms over several network topologies.

This paper develops a novel mechanism for recovering from dual link failures in IP networks. The highlight of the developed routing approach is that a node re-routes a packet around the failed link without the knowledge of the second link failure. The proposed technique requires three protection addresses for every node, in addition to the normal address. Associated with every protection address of a node is a protection graph. Each link connected to the node is removed in at least one of protection graphs and every protection graph is guaranteed to be two-edge connected. The network recovers from the first failure by tunneling the packet to the next-hop node using one of the protection addresses of the next-hop node; and the packet is routed over the protection graph corresponding to that protection address. We prove that it is sufficient to provide up to three protection addresses per node to tolerate any arbitrary two link failures in a three-edge connected graph. We evaluate the effectiveness of the proposed technique over several network topologies.

Multi-channel wireless networks are increasingly being employed as infrastructure networks in metro areas. In addition, nodes in these networks employ directional antennas to improve spatial throughput. In such networks, given a source and destination, it is of interest to compute a path and channel assignment on every link in the path such that the path bandwidth is the same as that of the link bandwidth. Such a path must satisfy the constraint that no two consecutive links on the path are assigned the same channel, referred to as "channel discontinuity constraint." In this paper, we develop two graph expansion techniques to compute the minimum cost path between a given node pair that satisfy the channel discontinuity constraint. The first expansion provides the exact solution in polynomial time using minimum cost perfect matching algorithm. The second expansion results in a lesser complexity algorithm compared to the former and is amenable to distributed implementation, while it may result in infeasible paths at times. Through extensive simulations, we study the effectiveness of the routing algorithms developed based on the two expansion techniques and the benefits of employing the minimum cost perfect matching based solution. We show that the lesser complexity algorithm may not be able to compute a path for less than 2% of the calls in the networks considered.

We introduce the concepts of monitoring paths (MPs) and monitoring cycles (MCs) for unique localization of shared risk linked group (SRLG) failures in all-optical networks. An SRLG failure is a failure of multiple links due to a failure of a common resource. MCs (MPs) start and end at same (distinct) monitoring location(s). They are constructed such that any SRLG failure results in the failure of a unique combination of paths and cycles. We derive necessary and sufficient conditions on the set of MCs and MPs needed for localizing an SRLG failure in an arbitrary graph. When a single monitoring location is employed, we show that a network must be (k + 2)-edge connected for localizing all SRLG failures with up to k links. For networks that are less than (k + 2)-edge connected, we derive necessary and sufficient condition on the placement of monitoring locations for unique localization of any SRLG failure of up to k links. We use these conditions to develop an algorithm for the placement of monitoring locations. We show a graph transformation technique that converts the problem of identifying MCs and MPs with multiple monitoring locations to a problem of identifying MCs with single monitoring location. We provide an integer linear program and a heuristic to identify MCs for networks with one monitoring location. Through extensive simulations, we demonstrate the effectiveness of the proposed monitoring technique.

In this paper, we analyze the blocking performance of a channel assignment scheme in a multi-channel wireless line network. We assume that the existing calls in the network may be rearranged on different channels to accommodate an incoming call. The analysis is limited to single-hop calls with different transmission ranges. Through extensive simulations, we demonstrate that the developed analytical model closely approximates the values obtained through simulations.

In this paper, we show that minimizing the product of path lengths results in minimizing the probability of connection failure between a source and destination given two links have failed in the network. We, therefore, analyze the problem of finding disjoint paths between two nodes with the minimum path length product. We formulate the problem as a mixed integer quadratic programming (MIQP) problem. We develop an iterative heuristic based on k-shortest path approach. We demonstrate through extensive simulations that only a few iterations are sufficient to obtain paths whose path length product is comparable to that of optimal obtained by solving the MIQP.

When sensors are redundantly deployed, a subset of senors should be selected to actively monitor the field (referred to as a "cover"), while the rest of the sensors should be put to sleep to conserve their batteries. We consider networks in which all the nodes are not aware of their locations or the relative directions of neighbors. We develop several geometric and density-based tests for deciding whether a sensor should turn itself off without degrading the quality of field coverage. These tests rely on estimated neighbor distances and locally advertised two-hop neighborhood information. We design an algorithm (LUC) that exploits these tests for computing covers. Based on LUC, we propose two distributed protocols (LUC-I and LUC-P) that periodically select covers and switch between them to extend "coverage time" and tolerate unexpected failures. Our protocols are highly efficient in terms of message overhead and processing complexity. We implement LUC-I in TinyOS and evaluate it using the TOSSIM simulator. Experimental results indicate that our approach significantly prolongs coverage time.

Wireless sensor networks (WSN) are typically employed for monitoring applications that require data collection at specific nodes, called drains. In order to improve the robustness of data collection, multiple drains may be employed. Data from every sensor is required to be logged into two distinct sensors for data collection to be resilient to any single drain failures. In this paper, we develop a routing mechanism based on colored trees. Every node forwards the packets based on the drain address and one additional bit. The number of routing table entries at each node is 2|D|, where |D| denotes the number of drains in the network. The construction of the colored trees guarantees that every node has two node-disjoint paths to two distinct drains. The running time complexity of the algorithm is O(|D||L|), where |L| denotes the number of links in the network. Through extensive simulations, we demonstrate that employing multiple drains and disjoint routing to two distinct drains reduces the average path length compared to disjoint routing to one of the multiple drains.

Efficient routing and wavelength assignment (RWA) in wavelength-routed all-optical networks is critical for achieving high efficiency over the backbone links. Extensive research has been conducted to find strategies to solve the RWA problem with exact network state available at the time of path selection. We consider the problem of minimizing the blocking probability in an all-optical network with partial wavelength conversion and with imprecise network state information. We model imprecision in link-state information (wavelength availability) probabilistically and use Markovian analysis to predict the availability of each link based on its previous advertisement and the estimated average traffic over the link. The estimated probabilities are then used to find the most probable path between a source destination pair. We also consider the problem of lightpath establishment with 1+1 protection. We use the same Markovian model to predict the link availability and then use the probabilistic estimate and a modified version of flow algorithm to find two link-disjoint paths between the source and destination. Simulations are conducted to compare the performance of random-fit and the proposed wavelength assignment schemes. We have also performed extensive simulations to study the performance of the proposed flow algorithm. It is observed that the proposed wavelength assignment scheme performs significantly better in terms of blocking probability than conventional wavelength assignment schemes.

This work proposes new retransmission and backoff strategies for network-wide broadcasting in multi-hop wireless networks. A comparative analysis is presented between existing algorithms as well as the ones proposed herein. Simulation experiments and analysis are used throughout this work to study or demonstrate the properties and performance of specific strategies as well as other properties or results of a more general nature. Several topics not considered in previous work are also studied. The broadcasting strategies are evaluated with respect to their impact on routing protocols that rely on flooding to perform path discovery, and research is conducted in designing schemes that maximize the route lifetime. Different backoff strategies are proposed and their performance is examined.

Wireless sensor networks (WSNs) employed in monitoring applications require data collected by the sensors to be deposited at specific nodes, referred to as drains. To improve robustness in data collection, we consider a dual homing network in which two drains are employed and every node is required to send data to the two drains over link- or node-disjoint paths. One approach to reduce the number of routing table entries at a node is to construct two trees, namely red and blue, each rooted at a particular drain such that the paths from any node to the two drains on the trees are link- or node-disjoint. In this paper, we develop the first distributed algorithm for constructing colored trees in a dual-homing network whose running time is linear in the number of links. In addition, we show that the average path length may be optimized by employing the generalized low-point concept rather than the traditional low-point concept.

This paper considers a distribution/aggregation network that employs optical code division multiple access (OCDMA) to transmit information to a head-end node in a metropolitan area network. The head-end node transmits synchronization pulses and the nodes employ ranging techniques to offset the propagation delay, resulting in a quasi-synchronous reception at the receiver. The paper develops a methodology to design orthogonal OCDMA codes for such quasi-synchronous communication systems. The paper also describes the receiver design and computes the bit error rate of such systems.

This paper presents a broadcasting algorithm that considerably reduces the number of retransmissions in applications such as onroad vehicular broadcasting where nodes are assumed to be arranged on a strip. Analysis and simulation results are presented to describe the overhead, coverage and latency characteristics of the algorithm.

Multi-path routing (MPR) is an effective strategy to achieve robustness, load balancing, congestion reduction, and increased throughput by transmitting data over multiple paths. Disjoint multi-path routing (DMPR) requires the multiple paths to be link- or node-disjoint. Implementation of both MPR and DMPR poses significant challenges in obtaining loop-free multiple (disjoint) paths and effectively forwarding the data over the multiple paths, the latter being significant in data-gram networks. In this paper, we develop a disjoint multipath routing strategy using colored trees with an objective to minimize the total cost of the routing paths in a network. Two trees, namely red and blue, rooted at a given drain is formed. We demonstrate through extensive simulations that the developed technique is extremely effective in optimizing the average cost of the paths. In addition, we also observe that the developed approach minimizes the average minimum (minimum of the two paths) cost, which is lower than that obtained by earlier algorithms. The colored tree approach simply doubles the size of the routing table when two link- or node-disjoint paths to a specific node is needed.

We study the problem of coverage of a given area for a maximum duration using a set of battery-operated sensors. Each sensor has a fixed sensing range and a limited lifetime due to the finite battery capacity. Sensors can be activated and deactivated at any time. The goal of this paper is to a find a schedule, determining when to activate and deactivate each sensor, to maximize the time for which every point in the area is covered by at least one sensor. We present several algorithms for this problem and show experimental and theoretical evidences to their efficiency. We also present an algorithm for a new model of coverage, called weak coverage, that does not require each point of the region to be covered all times, as long as the regions that are not covered are small

One of the strategies to recover from dual-link failures is to employ link protection for the two failed links independently which requires that two links may not use each other in their backup paths if they may fail simultaneously. Such a requirement is referred to as backup link mutual exclusion (BLME) constraint and the problem of identifying a backup path for every link that satisfies the above requirement is referred to as the BLME problem. This paper explores the BLME problem in depth by: (1) formulating the backup path selection as an integer linear program; and (2) developing a pseudo-polynomial time approximation algorithm based on minimum cost path routing. The ILP formulation and heuristic are applied to six networks and their performance is compared to approaches that assume precise knowledge of dual-link failure. The heuristic approach is shown to obtain feasible solutions that are resilient to most dual-link failures, although the backup path lengths may be significantly higher than optimal. In addition, the paper demonstrates the significance of the knowledge of failure location by illustrating that network with higher connectivity may require lesser capacity than one with a lower connectivity to recover from arbitrary dual-link failures.

This paper develops a connection establishment framework for protecting connections against single-link failures using link protection at the granularity of a connection, referred to as connection switched link protection (CSLP). As a connection is routed only, around a failed link, the channel assignment for the connection on the backup path of the failed link must be consistent with that of the primary path. Such a consistency is guaranteed at the time of call admission. The advantages of employing link protection at the connection level is established by comparing its performance through extensive simulations against link protection at the granularity of a fiber, referred to as fiber switched link protection (FSLP). Link protection at the connection level is shown to significantly outperform that at the granularity of a fiber, specifically when some traffic requires protection while others do not.

Resiliency to link failures in optical networks is becoming increasingly important due to the increasing data rate in the fiber. Path protection schemes attempt to guarantee a backup path for a connection upon a failure in the network, thereby reducing the recovery time for a connection. In this paper, we develop a failure dependent path protection scheme that dynamically assigns a primary path and backup paths, one for each failure that would affect the primary path. A connection established on the primary path will be re-established on its backup path only if a failure in the network affects the connection. We evaluate the performance of our developed protocol and compare with an alternative approach based on sub-graph routing that achieves high network utilization and low blocking probability at the cost of re-establishing connections even if the failure in the network does not affect the primary path of the connection. We observe that up to a factor of eight reduction in the number of reconfiguration scenarios is achieved with less than 10% reduction in effective network utilization and less than 3% reduction in fairness metrics for tolerating any single link failure in NSFNET and ARPA-2 networks. The failure dependent protection approach developed in this paper is also applicable to any general failure scenarios that are modeled as shared risk link group failures.

Traffic grooming in optical networks employing wavelength division multiplexing (WDM) has gained prominence due to the prevailing disparity between the user requirement and wavelength capacity. Nodes in an optical network get upgraded to the latest grooming technology slowly with time. Hence, WDM grooming networks are expected to employ heterogeneous grooming architectures. In this paper, we develop an analytical model to evaluate the blocking performance of WDM grooming networks with heterogeneous grooming capabilities. We demonstrate the accuracy of the analytical model by comparing the analytical results with that of the simulation. We observe that analytical models with and without precise knowledge of the grooming architectures predict similar performance. The proposed analytical model can be employed by resource placement algorithms that identify a set of nodes and links that need to be upgraded when the resources are limited.