1. B. Malakooti, I. Thomas, S.K.Tanguturi, S. Gajurel, Hyun Kim and K. Bhasin, “Multiple Criteria Network Routing
with Simulation Results,” IERC, May 2006.
Multiple Criteria Network Routing with Simulation Results
Behnam Malakooti, Ivan Thomas, Siva Kumar Tanguturi, Sanjaya Gajurel and Hyun Kim
Electrical Engineering and Computer Science
Case Western Reserve University, Cleveland, OH 44106
Kul Bhasin
NASA Glenn Research Center, Cleveland, OH 44135
Abstract
In this paper, we develop Multiple Criteria Routing for wireless networks. Unlike wired network, wireless
networks require consideration of multiple criteria such as energy, latency and reliability. Routing criteria are
conflicting in nature, and our multiple criteria routing method finds the best compromise solution among the
chosen criteria. We utilize Normalized Weighted Additive Utility Function to perform the analysis. We
develop Global Multiple Criteria Routing and Distributed Multiple Criteria Routing, and then compare the
results by performing simulation on 5X5 grid network. The results show that the Distributed Multiple
Criteria Routing produces similar outcome as the Global Multiple Criteria Routing.
Keywords —Routing Protocol, Weighted Normalized Addictive Utility Function, Multiple Criteria Routing
Algorithm
1. INTRODUCTION
THE conventional routing algorithm finds the optimal route based on one criterion while taking into account quality of
service constraints [3]. Such approach suffices to produce reasonable results in wired static networks where there
exists plethora of source for energy, and links are reliable. For wireless networks [4,5], however, such approaches are
not suitable since the nodes possess limited amount of energy to carry out network operations, and the quality of the
link is significantly less than that of the wired and static networks. In such network settings, it is essential not only to
consider end-to-end latency, but also to consider other objectives such as minimization of the total energy
consumption and maximization of the link reliability.
In order to create a network routing protocol that accommodates multiple routing objectives, we have developed
Multiple Criteria Routing (MCR) algorithm. Our proposed Multiple Criteria Routing approach considers several
criteria including total energy consumption, end-to-end latency, and bit error rates. Routing criteria are usually
conflicting and competing, (i.e. one cannot find a route that minimizes total energy consumption, minimizes total
latency, and minimizes bit error rate). We develop a systematic Multiple Criteria Routing approach to identify
efficient routing solutions and to choose the most preferred solution based on user’s preference on importance of each
criterion.
Some of the previous work on realization of multiple criteria/objective routing is presented as follows. Climaco et al.
7] implemented bi-criteria routing approach for multimedia networks with the routing objectives of minimizing
resource consumption and the cost of negative impact on traffic flows in the network. Marwaha et al. [8] applied
multi-objective routing for mobile ad hoc network routing applications. Roy et al. [9] utilized multi-objective routing
approach for real-time wireless multicasting. Yuan [10] incorporated bi-criteria optimization technique for OSPF
routing to minimize network congestion and the impact of link failures. None of these techniques, however, solve
Multiple Criteria Routing problems considering simultaneous objectives that we have developed in this paper. Our
approach is unique,computationally efficient, and solves Multiple Criteria Routing problems in a distributed fashion.
The structure of Multiple Criteria Routing can be implemented in wireless networks to overcome the constraints on
energy and bandwidth. This paper presents techniques for both global and distributed Multiple Criteria Routing. In the
global routing algorithm, each node possesses complete knowledge of the entire network topology and the link costs.
In the distributed routing algorithm, each node only possesses knowledge of its neighboring nodes similar to distance
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2. B. Malakooti, I. Thomas, S.K.Tanguturi, S. Gajurel, Hyun Kim and K. Bhasin, “Multiple Criteria Network Routing
with Simulation Results,” IERC, May 2006.
vector routing algorithm. We have specified the three main routing criteria in mobile/wireless/space networks:
energy, latency and quality. For Distributed Multiple Criteria Routing, it is assumed that each node knows all criteria
values for its adjacent nodes at all times. We show how Distributed Multiple Criteria Routing generates a Multiple
Criteria Routing table at each node.
The rest of the paper is structured as follows: in Section 2, we provide general information on Normalized Weighted
Additive Utility Function (NWAUF). In Section 3, we develop global Multiple Criteria Routing algorithm and
Distributed Multiple Criteria Routing algorithm. In section 4 we perform numerical comparisons of Global Multiple
Criteria Routing and Distributed Multiple Criteria Routing. Lastly in Section 5 we conclude our work.
2. MULTIPLE CRITERIA ROUTING BACKGROUND
2.1 General Background NWAUF
The process of decision making involves choosing from various alternatives. These alternatives often can be ranked
on the basis of several criteria using different Multiple Criteria Decision Making (MCDM) methods. General MCDM
methodology involves five steps:
1. Identify and assess criteria values.
2. Identify the set of alternatives.
3. Choose a method for ranking alternatives.
4. Apply the method for ranking alternatives and choose the best alternative.
MCDM methods have been used to help solve a wide variety of problems in many different applications such as
tele-communications, manufacturing, transportations, etc. For purpose of simplicity and illustration, this work
focuses on one particular MCDM method: Normalized Weighted Additive Utility Function (NWAUF). However,
other complex MCDM methods (e.g. see [1,2]) can be used. The NWAUF method is based on normalizing criteria
(objective) values and using weights of importance ranging from 0 to 1, with a cumulative sum of one. Consider the
weighted additive utility function with a discrete set of alternatives, a j for j=1,2, …, n.:
k
U(a j ) = ∑ wi fij for alternative j.
i =1
Where w1, w2,…,wk are the weights of importance for each objective. All weights are positive numbers, i.e. w1 > 0, w2
> 0,.. wk > 0. The above weighted utility function can be used to determine the best (most preferred or the most
compromised) alternative for the given additive utility function. However, it is much easier to assess the weights of
importance (w1, w2, …, wk) when all criteria (objective) values are normalized to the same scale (e.g. 0 for worst and 1
for best). In this case, weights correspond clearly to the significance of each objective. The approach requires few
additional steps to normalize objectives.
The NWAUF is given as:
U(aj) = w1f1’ + w2f2’ + … + wkfk’ (1)
Where f1’, f2’, …, fk’ are normalized values of f1, f2, …, fk and w1, w2, …, wk are weights of importance.
Note that in a standard weighted utility function, the utility (U) value can take on any value. A normalized weighted
utility function, however, has a utility value ranging from 0 to 1. Hence, by normalizing the objectives, the U values
are normalized as well.
2.2 The Steps of NWAUF Method
The NWAUF consists of five steps. They are:
1) For each objective, find the range of objective function values:
Define: fi,min = min {fij, j = 1, 2, …, n}, for each objective fi, i = 1, 2,…k and fi,max = max {fij, j = 1, 2, …, n}, for each
objective fi, i = 1, 2,…k (fi,min and fi,max can be defined by the decision-maker to be values other than those found above)
f ij − f i min
2) Normalize each fi according to: f ' ij =
f i max − f i min
Note that each objective value is normalized between 0 (worst) and 1 (best).
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3. B. Malakooti, I. Thomas, S.K.Tanguturi, S. Gajurel, Hyun Kim and K. Bhasin, “Multiple Criteria Network Routing
with Simulation Results,” IERC, May 2006.
If the criteria are not normalized, situations can arise that skew the utility function if the scales of each criterion are
different. For example, if criteria f1 is given in thousandths (e.g. 0.003, 0.007, 0.004) and criteria f2 is given in
thousands (e.g. 11,000, 23,000, 17,000), the utility function results will depend much more heavily on f1, even if f2 is
considered more important than f1 (e.g. w2 > w1).
3) Assess weights of importance for each objective, (w1,... wk), where:
∑
k
i =1
wi = 1 and wi > 0 for all i. (2)
4) Calculate the utility for each alternative aj:
∑
k
U(aj) = i =1
wi f ij' , for all j = 1,2,…n. (3)
5) Rank alternatives in descending order of U(aj). The alternative with the highest U is the best alternative.
More complex utility functions that are non-additive can also be used for solving MCDM problems (e.g. see [1,2]).
Other methods such as pairwise comparison of alternatives and lexicographic ordering of criteria can also be used for
ranking alternatives. Above procedure is based on the assumption that each objective is being maximized. However,
it is possible to maximize or minimize each objective while using the additive utility function for a given problem. A
simple way to do this is to replace minimizing + fi by maximizing - fi.
3. OVERVIEW OF MULTIPLE CRITERIA ROUTING FORMULATION
Each link in a route can be associated with some criteria measurements. The Multiple Criteria Routing measurement is
a function of all of the links’ multi-criteria measurements that compose the route. The types of multi-criteria
measurements for wireless networks include energy, latency, quality, bandwidth and throughput.
3.1 Global Multiple Criteria Routing
A straightforward method of Multiple Criteria Routing for small networks is based on the assumption that global
knowledge of the network is available at all nodes; including all possible noncyclic routes for a given (source,
destination) pair and the criteria for each route. Then the routes correspond directly to alternatives a1 · · ·an , can be
chosen based on a NWAUF. Enumerating all possible non-cycle routes for a given source-destination pair is an
exponential-time algorithm, becoming computationally impossible for medium or large networks. Global Multiple
Criteria Routing is only applicable to small problems and presented here to show how Multiple Criteria Routing can
be used as a source route selection method.
The weights w1 · · ·wk are all set and stored at the source node for the given user. If the weights change, then the U(a)
function must be recalculated for all alternatives (routes) a1 · · · an. If any criteria changes for any link in the network,
the U(a) function must be recalculated since the normalized criteria values may also change. It is considered global
and source based because the source node stores a database of all links and their criteria, and performs all Multiple
Criteria Routing calculations necessary to choose the source routes, and the intermediate routers do not perform any
calculations. The Global Multiple Criteria Routing is a static algorithm because once a route to a given destination is
set at the source node, all packets will follow that route through the network until they are changed.
3.2 Distributed Multiple Criteria Routing
The Multiple Criteria Routing table at a given router shows Multiple Criteria information for the next hop (an adjacent
router) for the given destination. This table is used by the router for forwarding packets. The routing table must be
updated more frequently and systematically for mobile/wireless/space networks. We propose a new Distributed
Multiple Criteria Routing approach for identifying and updating routing tables for mobile/wireless/space networks.
Multiple Criteria Routing will be applied to the Distance Vector (DV) routing algorithm. DV routing algorithm uses
a single measurement metric. To expand DV to MCR, each node is required to store Multiple Criteria tables. Each
table represents a criterion, or “a type of measurement”. Each node also stores given weights of criteria for NWAUF.
In the DV routing table maintained at each node, the rows correspond to all the possible destinations and the columns
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4. B. Malakooti, I. Thomas, S.K.Tanguturi, S. Gajurel, Hyun Kim and K. Bhasin, “Multiple Criteria Network Routing
with Simulation Results,” IERC, May 2006.
correspond to the directly connected neighbors. The “Weighted Multiple Criteria” forwarding table is then derived
from the given weights and the given Multiple Criteria tables. We assume that all nodes in the network have the same
number and type of criteria. We formulated the Energy objective function as follows:
Energy, f1:
EX(Y,Z) = e(X,Z) + minv{EZ(Y,w)}
X
Where E (Y,Z) is the total energy consumption from node X to destination Y via node X’s directly attached neighbor,
node Z, e(X,Z) is the energy consumption using direct link from node X to node Z, and minw{EZ(Y,w)} gives node Z’s
currently known minimum energy path from itself to destination Y taken over all of node Z’s directly attached
neighbors denoted by v. Similarly, we formulated the objective functions for latency, Bit Error Rate (Quality).
Latency, f2:
LX(Y,Z) = l(X,Z) + minv{LZ(Y,w)}
Bit Error Rate (Quality),f3:
QX(Y,Z) = 1-( (1-q(X,Z)) x (1- minv{QZ(Y,w)}))
We refer to the combination of MCR and DV as DISTRIBUTED MCR. The difference between DV and
DISTRIBUTED MCR algorithms is that in DISTRIBUTED MCR, the alternatives are not entire routes, but rather the
next hop in a route. This is in contrast to Global Multiple Criteria Routing, where the alternatives are routes, rather
than hops.
Since Distributed Multiple Criteria Routing involves multiple distance tables (each representing a single criteria), the
process of calculating the forwarding table is not as simple as in DV. First, each distance table must be normalized for
the reasons stated in Section II. The normalization for Distributed Multiple Criteria Routing is done over each row of
each distance table. This is because the columns in the distance tables represent the alternatives (the possible next
hops) to get to each destination (the rows). The normalized values are stored in separate tables, one for each criterion,
called “normalized multi-criteria tables”. Next, the combined distance table is created from the normalized distance
tables. This is done with a NWAUF. Each normalized distance table is assigned a weight, wi, based on the criteria of
the normalized distance table, f’i. Then, the combined distance table is created for each element by executing the
NWAUF over corresponding entries in all the individual normalized distance tables.
4. NUMERICAL COMPARISON OF GLOBAL AND DISTRIBUTED MULTIPLE CRITERIA ROUTING
A program in C++ was written to further analyze Multiple Criteria Routing. It creates 5×5 grid networks, with the
source node in the upper left corner and the destination node in the lower right corner. Grid networks are used for
simplicity. Each link is assigned random Energy (f1), Delay (f2), and Bit Error Rate (f3). The pseudo-random number
generator (PRNG) developed by L’Ecuyer [6] was used to generate multiple independent streams of random numbers.
−8 −8
The value ranges are 1 to 100µJ, 1 to 100ms, and 1 × 10 to 100 × 10 for energy, delay, and bit error rates,
respectively. The graph is then exhaustively searched for all possible non-cyclic routes from Source to Destination,
with values given for the total f1, f2, and f3 for each route. f1, f2and f3 are then normalized.
Global MCR is then used to rank the routes from best to worst based on U(a) for the three criteria case (energy, delay,
and BER). To compare Distributed MCR with Global MCR, we run the Distributed algorithm on the grid test
networks with the same assortment of weights. The resulting routes are then compared to the Global MCR route
rankings. A “match” occurs if the best Global MCR route (ranked first) is the same route chosen by Distributed MCR.
The Distributed MCR algorithm was implemented in ns-2 [11]. The Global MCR C++ program (described
previously) outputs an ns-2 script file that defines the grid topology and link criteria for a static wired network in ns-2.
The network specified for ns-2 is the exact same network used by the C++ program to enumerate all possible routes, so
it can provide a basis for comparing Distributed MCR to the exact (global) results.
The ns-2 script defines a single flow consisting of a UDP traffic source (with a constant bit rate of 100 1000-byte
packets per second) at the source node; this traffic source sends packets to a UDP sink at the destination node. ns-2
runs for five simulated seconds. The ns-2 trace files are then analyzed to determine the most popular route taken by the
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5. B. Malakooti, I. Thomas, S.K.Tanguturi, S. Gajurel, Hyun Kim and K. Bhasin, “Multiple Criteria Network Routing
with Simulation Results,” IERC, May 2006.
packets of the UDP flow. It is this route which is compared to the best route determined by Global MCR. In the
following, we describes experiments performed for grid size of 5 X 5.
The experiment was performed on a 5 × 5 grid network shown in Fig. 1. The source node is A, and the destination
node is Y. To compare Global MCR with Distributed MCR, we run the Distributed MCR algorithm using the
assortment of weights in Table 1. The detailed results are shown in Table1 and Fig. 2.
Fig. 1. 5 X 5 Network Configuration
This experiment was performed on 5 × 5 networks for a total of 50 runs each with randomly generated link criteria.
The route rankings across all weight groupings for Distributed MCR are shown in Fig. 2 for three criteria.
TABLE 1. RESULTS FOR 50 RUNS ON THE 5 X 5 NETWORK WITH THREE
CRITERIA
Fig. 2. Results for 50 runs on the 5x5 network – three
criteria
The results from Table 1shows that the average energy, latency, and packet drop rate varies in accordance to the
weights assigned for each criterion, e.g. the criterion with a high assigned weight results in high average value. The
experimental results from Fig. 2. prove that in most of the cases, Distributed MCR generates optimal path. What
optimal path signifies in this case is that the results from the Global MCR match that of the Distributed MCR. The
reason that Distributed MCR may not produce optimal results in some cases is due to the fact that the minimum of each
criterion value exchanged by every node to reach a given destination may not be from the same next hop. Also, when
the weight assignment for the each criteria is very close (see Table VII), we observe Distributed MCR slightly deviates
from the optimal solution. To produce optimal results, we developed a work for this algorithm that uses one extra RTT
for correcting the criterion values in the table.
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6. B. Malakooti, I. Thomas, S.K.Tanguturi, S. Gajurel, Hyun Kim and K. Bhasin, “Multiple Criteria Network Routing
with Simulation Results,” IERC, May 2006.
5. CONCLUSION
In this paper, we have defined methods of Global and Distributed MCR and analyzed the effectiveness of Distributed
MCR. Our experiments demonstrated two important results. First, the average results of each criterion vary according
to the assigned weights. This implies that the user can control the routing process by adjusting values of weights
assigned to each criterion. Second, for most problems, the results obtained from Distributed MCR closely follow the
results from the Global MCR. This is important since Global MCR routing does not work on large or dense networks
as the computational cost becomes unmanageably large. Since Distributed MCR is performed in a distributed fashion
on each node, it can operate on larger networks. In this paper, we formulated and solved Multiple Criteria Decision
Making for routing problems to optimize several criteria simultaneously. We illustrated the basic characteristics of
MCR by developing a Global MCR method. Global MCR finds the optimal solution; however, it can only be used for
small problems. For medium and large size problems, we developed Distributed MCR. Distributed MCR is
computationally efficient and effectively uses the advantages of distance vector algorithm.
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