A joint scheduling, power control, and routing algorithm for ad hoc wireless networks

Ad Hoc Networks 5 (2007) 959–973

www.elsevier.com/locate/adhoc

A joint scheduling, power control, and routing algorithm forad hoc wireless networks q,qq

Yun Li a,*, Anthony Ephremides b

a Department of Electrical and Computer Engineering, Colorado State University, 1373 Campus delivery,

Fort Collins, CO 80521-1373, United Statesb Department of Electrical and Computer Engineering, University of Maryland, College Park, MD 20742, United States

Received 25 January 2005; received in revised form 23 January 2006; accepted 26 April 2006Available online 24 May 2006

Abstract

In wireless networks there is strong coupling among the traditional layers of the architecture, and these interactionscannot be ignored. One example is the interaction between routing in the network layer and access control in the MAClayer. Another one is the coupling between power control in the physical layer and scheduling in the MAC layer. In thispaper, we assume a TDMA-based wireless ad hoc network and provide a centralized algorithm of joint power control,scheduling, and routing. Simulation results show the improvement of the network performance, in terms of throughput,delay, and power consumption, through use of the joint algorithm. Energy efficiency is another important aspect of ad hocnetworking, and is considered in our algorithm. Our simulation also shows the trade-off between energy consumption andnetwork throughput or delay performance.� 2006 Elsevier B.V. All rights reserved.

Keywords: Ad hoc networks; Power control; Scheduling; Routing; TDMA

1570-8705/$ - see front matter � 2006 Elsevier B.V. All rights reserved

doi:10.1016/j.adhoc.2006.04.005

q Prepared through collaborative participation in the Commu-nications and Networks Consortium sponsored by the US ArmyResearch Laboratory under the Collaborative Technology Alli-ance Program, Cooperative Agreement DAAD19-01-2-0011. TheUS Government is authorized to reproduce and distributereprints for Government purposes notwithstanding any copyrightnotation thereon. This research has been supported also by NSFGrant No. ANI0205330 and ONR Grant No. N00014-03-1-0007.qq The views and conclusions contained in this document arethose of the authors and should not be interpreted as representingthe official policies, either expressed or implied, of the ArmyResearch Laboratory or the US Government.

* Corresponding author. Tel.: +1 970 491 3148; fax: +1 970 4912249.

E-mail address: [email protected] (Y. Li).

1. Introduction

An ad hoc wireless network is a collection of wire-less mobile nodes forming a temporary network. Itsclassical applications are in battlefield communica-tions, disaster recovery, and search and rescue oper-ations. More commercial applications are alreadybeing developed. In an ad hoc wireless network, con-nections among these mobile nodes occur via multi-hop wireless connections without the support from afixed infrastructure such as a base station. Due to themobility of nodes, the status of a communicationlink is a function of the location and the transmis-sion power of the source and destination nodes,

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960 Y. Li, A. Ephremides / Ad Hoc Networks 5 (2007) 959–973

and the channel interference from other links. Thusthe physical layer, the Medium Access Control(MAC) layer, and the network layer are allinterdependent.

MAC protocols are either contention-based orTDMA-scheduling-based. Here we focus on the lat-ter. The problem of scheduling in TDMA multihopwireless networks has been widely studied. In bothbroadcast scheduling [1–3] and link scheduling[1,4,5], it is common to assume that there is no inter-ference beyond two hops, and it is often assumedthat the receiver of one link should not be in thetransmission range of other transmitters. Thus thereis an unrealistic ‘‘range’’ notion. With the fixedrange assumption and the no-interference assump-tion beyond two hops, many graph-theory-basedalgorithms have been developed. However, in real-ity, interference exists beyond a fixed range, andaggregated interference from several nodes thatare ‘‘beyond range’’ may destroy the ongoing link.In addition, these assumptions eliminate the possi-bility of simultaneous successful transmissions byrequiring no interference at all receivers. In ourwork, we consider unicast link scheduling, wherethe links between transmitter and receiver pairsare scheduled. All interference generated from othernodes is considered in our model, and the success ofthe transmission depends on the value of the Signal-to-Interference and Noise-Ratio (SINR). Thus, it ispossible for the receiver to correctly receive a signalfrom a transmitter when it is within the transmissionrange of other nodes, as long as the intended trans-mission is powerful enough to overcome the inter-ference and to achieve the required SINR level.The SINR criterion leads directly to the problemof power control.

Power control for cellular systems has been stud-ied extensively since 1992. The purpose of powercontrol is to balance the received powers of theusers, so as to achieve the SINR requirements ofall the users with minimum total power. In previouswork [6,7], the optimum power vector was found byinversion of a non-negative matrix related to thechannel gains and the cross-correlation propertiesof CDMA sequences. Subsequently, in [8] iterativepower control algorithms were developed for manydifferent power control problems, and it was proventhat if the interference function satisfies certainconditions, these iterative power control algorithmsconverge to the optimum power vector. After that,it was shown that a distributed version of the powercontrol algorithm also converges [9]. In our work,

we also introduce power control in the schedulingalgorithm, and try to satisfy the SINR requirementsof transmissions by jointly allocating the power andthe time slots.

Routing for ad hoc network is also well-studied.Many routing protocols have been proposed in thepast years [10]. They all require the knowledge ofthe links that exist in the network, and they typicallylead to table-driven protocols, like Destination-Sequenced Distance-Vector routing (DSDV) andClusterhead Gateway Switch Routing (CGSR), orto on-demand protocols, like Ad Hoc On-DemandDistance Vector routing (AODV) and DynamicSource Routing (DSR). Using the informationabout the physical positions of nodes, geographicrouting has been studied [11]. Since our workfocuses on the interaction between routing andscheduling, and the performance gain by jointlyscheduling and routing, we will not make use of aspecific protocol like the above; rather, we will focuson an appropriate link metric and use the classicalBellman–Ford algorithm for shortest path routing.We know that the distributed asynchronousBellman–Ford algorithm converges [12] and thuswe can adapt its properties to our joint schedul-ing-routing approach without being limited by thedetails of specific routing protocol implementation(which, besides, are often based on Bellman–Fordas well).

Our focus is on cross-layer design which canimprove network performance [13–15]. We focuson the coupling between routing in the networklayer and bandwidth allocation in the MAC sub-layer. The selection of routes clearly affects theflows, and hence, the requirement of bandwidthallocation at each wireless link. On the other hand,the choice of bandwidth allocation and accesscontrol affects the accumulation of queuing at links,and therefore changes the distance of each link andthe route selection. Many works on routing in suchnetworks (see, e.g., [16,17]) assume a fixed underly-ing protocol for access control, and most of theresearches on multiple access assume fixed routesand flow requirements [18].

In the past several years, the problem of couplingrouting with access control in ad hoc wireless net-works has been variously addressed in many papers.In [19] a unified approach to scheduling and routingwas introduced, where a cluster-based schedulingalgorithm and a route assignment were iteratedevery frame. Girici and Ephremides [20] providedlink-metric-based distributed routing and schedul-

Y. Li, A. Ephremides / Ad Hoc Networks 5 (2007) 959–973 961

ing algorithms, and studied the trade-offs betweenenergy, delay, and network lifetime. In [21], thetransmission schedule that minimizes the time toevacuate a packet radio network was studied, andit was proved that the joint optimal routing andscheduling problem can be decomposed into a purerouting and a pure scheduling problem.

In a TDMA-based structure, the bandwidth allo-cation assumes the form of time-slot allocation andleads to link scheduling. We also focus on the cou-pling between power control in the physical layerand scheduling in the MAC layer. The powerassignments of links change the link status, andhence the topology of the network, and the resultingscheduling is affected. On the other hand, schedul-ing determines the link activation and the interfer-ence that results from it, and, therefore, changesthe power required at each link to achieve the SINRrequirements. In [22] joint scheduling and powercontrol problem was formulated in an optimizationframework. The optimal power allocation and linkactivation to minimize the total average transmis-sion power were obtained subject to the minimumaverage rate constraint and peak transmissionpower constraint. Heuristic joint power controland scheduling algorithms were studied in [23,24].Our paper employs the same concept as in [23,24],that is, that both link scheduling and power controlare used to manage the interference. However, thework in [23] is not directly comparable because itconsiders multicasting traffic. We will compare ourresults to the algorithm developed in [24].

In our paper, we assume a TDMA-based wirelessad hoc network, where each node has one receiverand one transmitter, and all nodes share the band-width by occupying different time slots. In schedul-ing, our algorithm gives priority to the links whichhave larger queue and which block less traffic inneighboring links. We study scheduling with jointpower control and without joint power control,and conclude that with joint power control, the net-work achieves significantly larger throughput andless delay. We also compare our algorithm withthe one developed in [24], and conclude that ouralgorithm achieves better throughput and delaywith less complexity, at the cost of slightly higherenergy consumption.

In the route selection, the minimum energy routecould be selected at the beginning of the networkoperation to save the energy. But for general andarbitrary topologies, bandwidth requirement maynot be satisfied by scheduling alone, and hence,

congestion occurs at some links in the network.Multipath routing [25–28] is one way to balancetraffic load and to achieve even distribution overthe network. Some examples are alternate pathrouting (APR) [25] and multiple source routing(MSR) [26] that distribute traffic into multiple avail-able paths. Here, we will not get into the compli-cated multipath finding, rather, we reroute thedata traffic periodically to lead packets throughalternative routes and relieve the congestion. Inour algorithm, routes are selected periodicallyaccording to both energy consumption and the traf-fic accumulation. Our simulation results show thatthere is a trade-off between energy consumptionand the network performance.

The organization of the paper is as follows. Thenetwork model is described in Section 2. Next weintroduce our joint scheduling and power controlalgorithm in Section 3. The centralized algorithmand the simulation results are provided in thissection. Then in Section 4, we discuss our jointscheduling and routing algorithm with accompany-ing simulation results. After that, some thoughts ofdistributed implementation are discussed in Section5. Finally, conclusions and possible extension of theresearch are given in Section 6.

2. Network model

For a wireless ad hoc network, there is no sup-port from a fixed infrastructure, and the networkis connected by wireless channels. In TDMA-basedstructure, all nodes share the same frequency band,and time is slotted. We assume there is a goodglobal time known to all users. We also assumethe same waveform for all the K nodes and nomultiuser detection. Moreover, a separate low datarate channel is used for network control, andgeneral overhead traffic that needs to be exchangedfor the implementation of scheduling and routing.

We assume that each node is supported by oneomni-directional antenna and has one receiver andone transmitter that cannot work simultaneously.Hence a node cannot receive from more than onenode at the same time and cannot transmit to morethan one node at the same time either. We assigntime slots to directed links. Notation (i, j) denotesthe link with transmitter i and receiver j. Each linkcan be either active or idle, and each node can eitherbe in a transmission mode, a receiving mode, or anidle mode. The parameters and variables used in thealgorithm and simulation are listed in Table 1.

Table 1List of parameters and variables

Number of nodes K

SINR requirement bRate for each source destination pair ke

Buffer size for each link Qmax

Maximal transmission power Pmax

Maximal transmission distance Rmax

Transmission power at node i Pi

Distance between nodes i and j Rij

Queue of link (i, j) Qij

Attenuation factor of link (i, j) Gij

Link metric of link (i, j) L(i, j)Routing distance of link (i, j) D(i, j)Marginal protection factor a1, a2, a3

Number of iterations in powercalculation

N


Power decay law is assumed to be inversely pro-portional to the cth order of the distance betweenthe transmitter and the receiver. Typically,2 6 c 6 4 is true. The attenuation factor from nodei to node j is thus given by

Gij ¼ ðRij=R0Þ�c: ð1Þ

Here Rij is the distance between node i and j, and R0

is a normalization constant.Node i can adjust its transmission power Pi

within the range 0 < Pi 6 Pmax <1. We assumethat each successful transmission has to satisfy anSINR requirement b, and then the maximal trans-mission distance can be defined as

Rmax ¼ ðP max=ðbr2ÞÞ1c � R0; ð2Þ

with r2 the power spectral density of the noise. HereRmax is the distance over which a transmission issuccessful when the maximum transmission poweris used and all other nodes are at the idle mode.Throughout this paper, the distance is in the unitof R0, and the power is in the unit of r2.

We assume that each node generates data packetsof fixed length (they need one slot for transmission)to every other node according to a Poisson process.The rates between any source destination pair arethe same, and are equal to ke packets per second.After routing, local rate of traffic from node i to j

is then given by

KiðjÞ ¼ ke

Xðm;nÞ

iðm; nÞ:

Here i(m,n) is the index function. It is 1 for all thesource destination pairs (m,n) whose route includelink (i, j), and is 0 for all other pairs.

3. Joint scheduling and power control

3.1. Scheduling rules

We assign time slots to directed links accordingto their priority defined by their link metrics. Thelink metric of link (i, j) is defined as follows:

Lði; jÞ ¼ a � 1

1þ Qij

þ b � Qblocked

1þ Qblocked

;

where Qblocked ¼X

ðk;lÞ: blocked by ði;jÞ:Qkl: ð3Þ

Here Qij is the queue size of link (i, j). A link (k, l) isblocked by (i, j) if k = i or j, or, l = i or j. The weightfactors a and b vary between 0 and 1 and satisfy a +b = 1.

The first term of this metric takes into accountthe delay by giving higher priority to larger queues.The second term takes care of the effects of conges-tion developing on neighboring links that areblocked by an activated link. We prefer assigninga slot to links that block fewer other links. Sinceboth terms are between 0 and 1, the total metricof link (i, j) is also between 0 and 1 since it is a com-bination of these two terms.

Clearly the choice of the weight factors affects theperformance of the network. We have run simula-tions to compare the performance of the networkfor different values of a and b, and found that forthe networks we simulated, the parameter paira = 0.5, b = 0.5 works better than most alternativesin terms of the combination of throughput, delay,and power assumption. Hence we choose a = 0.5,b = 0.5 for later use.

Originally we had a third term in the link metricdefinition. That third term was either equal to (Rij/Rmax)c (to favor the link which uses less power), orequal to (1 � Ki(j)/maxi,j(Ki(j))) (to favor the linkwith larger average rate). However we found thatthe best performance always occurred when thethird term had zero weight. Therefore, we droppedthat term from the metric.

Our scheduling rules are as follows. First, the linkwith the lowest link metric has the highest priorityand is scheduled to occupy the time slot. Next, sincea node cannot transmit and receive in the same timeslot, and since it cannot transmit to more than onenodes, or receive from more than one nodes, when alink (i, j) is active, all other links involving either i orj are blocked. After that, the link with the next low-est value of the metric is a candidate for simulta-

List 1: Simplified scheduling algorithm

1. Calculate metrics of links, and define thelink set as all links that have traffic, anddefine the activation set as an empty set.

2. Select the lowest metric link; and calculatethe power of this link by Eq. (5).

3. If the SINR of this link is not satisfied, orthe SINR of any link in the activation setis not satisfied, remove this link from thelink set, and go back to step 2.

4. If the SINR of this link and all other links inthe activation set are satisfied, add this linkto the activation set, and remove this linkand links blocked by this link from link set.

5. Repeat step 2 to 4 until the link set is empty.


neous activation, provided the SINR requirement issatisfied for itself as well as the already activatedlinks. That is,

P iGij

r2 þP

k 6¼iP kGkjP b; ð4Þ

must hold for all activated links (i, j).

3.2. Scheduling algorithms and power control

As is evident from the scheduling rules describedabove, power control is coupled with the schedulingprocess since it affects the validity of the SINR cri-terion. Clearly there are three alternative ways forhandling this coupling.

1. Power allocation before scheduling, that is, poweris first allocated to each link solely based on itsSINR requirement against noise alone and staysfixed. Then links are scheduled to maximize thenumber of links that can transmit at the sametime, provided the SINR requirements are satis-fied. This results in a simplified scheduling alter-native. We call this the simplified schedulingbecause there is no real power control.

2. Jointly power control and scheduling at the sametime, that is, power is updated when schedulingis going on (whenever a new link is added tothe activation set). The joint algorithm that wepropose below is of this type.

3. Scheduling before power control, that is, schedul-ing is done first to find the maximal number oflinks that can be activated at the same time with-out primary conflicts; then the power levels areallocated to link activation set to satisfy theSINR requirements. It is possible that the SINRrequirements cannot be satisfied for a particularlink activation set. Then the activation set needsto be adjusted (typically by removing links fromthe link activated set) and power allocation mustbe tried again. The algorithm provided in [24]belongs to this category.

In this section, we compare the following specificalgorithms.

3.2.1. Scheduling algorithm 1: Simplified

scheduling

We propose a simplified scheduling for usingwhen iterative power control is not achievable,and for comparing with the joint scheduling and

power control algorithms. First the power of link(i, j) is calculated according to the attenuation factorGij before scheduling, so that the SINR of link (i, j)is satisfied if there is no interference from otherlinks. Then we leave some marginal protection a1

(a1 > 1) to tolerate some interference from otherlinks. If we do not give marginal protection, the firstscheduled link will always be destroyed when thesecond link is added no matter how small the inter-ference is, and hence only one link would be activein any slot. The power of transmitter i for the link(i, j) is given by

P i ¼ min b � a1 �r2

Gij; P max

� �: ð5Þ

The first link scheduled is the one with the lowestmetric. Then links are tried one by one according totheir metric. If the new link does not introduceexcessive interference to the prescheduled links,and its own SINR requirement can be satisfied, thenit is accepted. Otherwise it is rejected. Each time anew link is accepted, the links that this link blockedare out of future consideration. The algorithm isoutlined in List 1.

The marginal protection factor a1 is essential tothe performance of this algorithm. If a1 is very small(the extreme case is a1 = 1, no marginal protection),it is difficult for the earlier added links to toleratethe interference from later added links. On the otherhand, if a1 is too large, then links tend to use Pmax totransmit, and cause very large interference for the


later added links. The practical value of a1 is slightlylarger than 1. We will discuss this later in conjunc-tion with the simulation results.

3.2.2. Scheduling algorithm 2: Our joint algorithm

We propose this joint power control and schedul-ing algorithm, where power control and schedulingare done alternately. We add link one by oneaccording to the lowest metric criterion. When anew link is tried, the iterative power control algo-rithm is run to calculate the required power to sat-isfy the SINR requirements for all hithertoactivated links. The algorithm is outlined in List 2.

List 2: Our joint scheduling and power controlalgorithm

1. Calculate metrics of links, and define thelink set as all links that have traffic, anddefine the activation set as an empty set.

2. Try iterative power control algorithm withthe lowest metric link added to the activa-tion set.

3. If SINR requirements cannot be satisfied,remove this link from the link set, and goback to step 2.

4. If SINR can be satisfied, add this link to theactivation set, and update power of sched-uled links, and remove this link and the linksblocked by this link from the link set.

5. Repeat step 2 to 4 until the link set is empty.

The iterative power control algorithm without amaximum power constraint is as follows [8]:

P ðnþ1Þi ¼ b r2 þ

Xk 6¼i

P ðnÞk Gkj

!,Gij; 8 linkði; jÞ:

ð6ÞIt has been shown that if there are power vectors

that satisfy the SINR requirements, this algorithmconverges fast to the minimum power vector. Sincewe have a maximum power constraint, there are twodifferent cases depends on the value of the minimumpower vector and the value of Pmax. If the minimumpower vector satisfies the maximum power con-straint P 6 1 Æ Pmax, then the SINR requirementscan be satisfied. Otherwise, some elements of thepower vector will exceed Pmax and the SINRrequirements cannot be satisfied. When there is no

solution of the power vector to satisfy the SINRrequirements, the algorithm diverges, and the ele-ments in the power vector will grow beyond Pmax

very fast. In conclusion, if there is any element inthe power vector which grows beyond Pmax, theSINR requirements cannot be satisfied, and if theconverged power vector satisfies P 6 1 Æ Pmax, thenSINR requirements are satisfied.

With the power constraint P 6 1 Æ Pmax, thepower control algorithm can also be written as

P ðnþ1Þi ¼ min b r2 þ

Xk 6¼i

P ðnÞk Gkj

! ,Gij; P max

!;

8 linkði; jÞ:

This also converges [8]. However, the convergedpower vector may not satisfy the SINR require-ments. (This happens when one or more of the ele-ments in the power vector are Pmax.) Therefore, inour joint power control and scheduling algorithm,we use (6) for the iteration, and use P 6 1 Æ Pmax

as the criterion for the success of power allocation.Since links are added one by one, the power ele-

ments always increase from step to step. It actuallyneeds infinity number of iterations for the powervector to satisfy SINR requirements. Fortunately,the behavior of the converging process of the powercontrol algorithm is such that j P nþ1

i � P ni j decreases

rapidly with the iteration index n. Hence, we can usesome marginal protection to let the power vectorsatisfy SINR requirements with finite number ofiterations, i.e., we use ba2 (a2 > 1) instead of b asin (6). A value of a2 slightly larger than one signifi-cantly reduces the required number of iterations to areasonable value. For the network model we stud-ied, our simulations find out that if a2 = 1.05, SINRrequirements can be satisfied within 10 iterationsmost of the time.

In the simulation, we have a limited number ofiterations N. If the power exceed Pmax within N iter-ations, then we know that SINR requirements can-not be satisfied. However, there is a possibility ofnon-satisfaction of the SINR requirements after N

iterations even if the power elements have notexceeded Pmax. Given more iterations, the powervector might eventually exceed the maximum trans-mission power. This usually happens when the min-imum power vector has components only slightlylarger than Pmax, and hence a large number of iter-ations are needed for them to exceed Pmax. If thiswere to happen the transmission will be consideredfailed.


3.2.3. Scheduling algorithm 3: Algorithm based on

[24]

ElBatt and Ephremides [24] provided a jointpower control and scheduling algorithm workingin two phases. It calls a transmission scenario Valid

if one node can only be associated with one activelink at a time, and any receiver is spatially separatedfrom other transmitters by at least a distance D.This algorithm first finds the valid scenario with max-imum number of links by a centralized schedulingalgorithm. Then, the power control algorithm is exe-cuted in a distributed fashion. If no power vector canbe found to satisfy the SINR requirements, the linkwith the smallest SINR is removed from the valid sce-nario. Then, the power control algorithm is executedagain, until the SINR requirements are satisfied.

An alternative way of joint power control andscheduling is based on the idea of [24]. We use thecentralized version of the algorithm from [24] withD = 0. The algorithm is described in List 3. Sameas for scheduling algorithm 2, we introduce amarginal protection factor a3 to help the conver-gence.

List 3: The joint scheduling and power controlalgorithm based on [24]

1. Calculate metrics of links, and define thelink set as all links that have traffic.

2. Select the lowest metric link to add to thevalid scenario, and remove this link andlinks blocked by this link from the link set.

3. Repeat step 2 until the link set is empty.4. Try iterative power control algorithm to the

valid scenario.5. If the iterative algorithm does NOT con-

verge, remove the link with largest link met-ric from the valid scenario, and go back tostep 4.

6. If the iterative algorithm converges, stop.

4

3

2

1

0

2.13.0

Fig. 1. A simple symmetric 5-node network.

3.3. Comparison of scheduling algorithms

Scheduling algorithm 1 is simple and easy toimplement. But without power control, its through-put will not be optimal. Notice that every power andtime-slot allocation that is accepted by schedulingalgorithm 1 or 3 is also accepted by algorithm 2.Algorithm 2 achieves the optimal throughputamong all the algorithms that schedule links accord-ing to the same link metric.

Both the algorithm 1 and 2 work ‘‘from the bot-tom up’’, that is, they add links to the activation setone by one. But algorithm 3 works ‘‘from the topdown’’, i.e., it has a valid scenario first, then linksare removed from the set until the SINR require-ments can be reached. Therefore, if a link is notselected into the valid scenario, it will not have achance to be active, even when it is acceptable aftersome of the links are removed from the set. Thiscauses the suboptimal throughput of algorithm 3.We will use a simple topology, as shown in Fig. 1,to illustrate this through the operation of the threealgorithms.

In this network, there is one node (node 0) at thecenter and 4 nodes (nodes 1–4) at the outside. The 4outer nodes locate at the north, west, south, andeast of the center node, with the same distance of2.1 to the center node. We assume the maximumpower is 256 and the maximum distance that twonodes can communicate is 4. Therefore, there arelinks between any two adjacent outer nodes sincethe distance is 3.0 < 4, and there is no links betweennode 1 and 3, or node 2 and 4, since the distance is2.1 · 2 > 4.

Suppose at one slot, there are three links waitingto be activated. They are, listed according to theirpriority given by their link metrics: (2, 1), (0, 3),and (3,4). We assume SINR requirement b = 1,attenuation parameter c = 4. The three schedulingalgorithms operate as the following:

Scheduling algorithm 1 with a1 = 1.3:
Accept (2,1) with power 105.3.Try link (0,3) and fail.

Table 2Simulation parameters

Attenuation parameter c = 4Maximal transmission distance Rmax = 4Buffer size Qmax = 10,000SINR requirement b = 1


Try Link (3, 4) and fail.Result: link (2, 1) is scheduled with power105.3.(Note that if a1 = 1.5, then link (2,1) and link(3, 4) are both accepted with power 113.4.)

Weight factors in link metric a = 0.5, b = 0.5Simulation time 100,000 slots
Scheduling algorithm 2 (a2 = 1.05): Parameter in simplified
schedulinga1 = 1.3

Parameters in our jointalgorithm

a2 = 1.05, N = 10

Parameters in algorithmbased on [24]

a3 = 1.05, N = 15

Accept (2,1) with power 81.Try link (0, 3) and fail.Try link (3, 4) and succeed.Result: link (2, 1) and link (3,4) both acceptedwith power 102.1.

Scheduling algorithm 3:
Find maximum valid scenario: link (2, 1) andlink (0,3).Try power control algorithm and failed.Link (0, 3) is removed from the valid scenario.Result: Only link (2, 1) is activated with power81.
In this example, using algorithm 3, link (3, 4) hasno chance at all since it is blocked by link (0,3),which has a higher priority and is added to the validset earlier. While if using algorithm 1 or 2, link (3, 4)is still possible if link (0,3) fails. Whether link (3.4)is accepted depends on the power allocation and theSINR requirement.

3.4. Simulation results for the centralized

algorithm

We study the centralized algorithm to evaluatethe performance gain of the joint algorithm, andto provide a reference point for the future distrib-uted version. It is also applicable to some networksthat might have a base station. We assume that thecontroller has access to the information of allqueues and the topology of the network.

The simulation is a packet-level simulation codewritten in computer language C. We assume that themaximal transmission distance is 4 units and the max-imal power is 256. Packets are generated by Poissonprocess at each node pair independently. We assumelarge buffer size Qmax at all nodes (packets are dis-carded if the buffer is full). Packets are failed if theSINR is not satisfied due to the inaccurate power cal-culation because of the finite number of iterations.Simulation parameters are listed in Table 2.

We first simulate the simple 5-node networkshown in Fig. 1. Its performance in terms ofthroughput, delay, and power versus ke is shown

in Fig. 2. In these figures, scheduling 1 is the simpli-fied algorithm, scheduling 2 is our joint schedulingand power control algorithm, and scheduling 3 isthe joint scheduling and power control algorithmbased on [24]. We use routing parameter (0.9,0.1)to show the different performance of the schedulingalgorithms. As will be explained in Section 4, if weuse the minimum energy route, then all the trafficwill go through node 0, and only one link couldbe active at any slot, and therefore, different sched-uling algorithms make no difference.

We notice that there is a threshold rate for eachof the scheduling algorithms. If the rate is largerthan the threshold rate, then the number of waitingpackets keeps increasing until the buffer is full andpackets are dropped. When the rate is larger thanthe threshold, the throughput no longer increaseswith the same slope, and the delay increases rapidly.The threshold rates for the three scheduling algo-rithms for this specific network are about 0.04,0.08, and 0.06 (packets/slot/source–destinationpair) respectively.

We find that scheduling algorithm 1 has smallestthroughput (and threshold rate) and largest delay. Itis clear that the joint power control and schedulingimproves the network performance significantly interms of throughput and delay. Comparing schedul-ing algorithm 2 and 3, it is clear that our joint algo-rithm outperforms the joint algorithm based on [24]in both throughput and delay.

The average power of the algorithm 1 does notchange significantly as the rate increases, becausethe power is preset, and is not related to the interfer-ence caused by a higher rate. On the contrary, thejoint scheduling and power control algorithms usemore power for larger rate. The reason is that moreinterference is generated when more links are active,and therefore larger power is needed to overcomethe interference and satisfy the SINR requirements.

Fig. 2. Throughput, power, and delay of scheduling algorithms,for the 5-node network.


Algorithm 2 needs slightly larger power than algo-rithm 3, due to the larger throughput it achieves.

To test the performance of the algorithm andhave a better idea of the trends, we then simulate10 randomly generated 10-node networks in a10 · 10 area. The average performance of the ran-domly generated networks is shown in Fig. 3. Thereis no joint routing and scheduling for this simula-tion, the route is selected to be the minimum energyroute. The results are discussed as follows.

Using scheduling algorithm 1, the averageperformance of these 10-node random networksdepends greatly on the factor a1 as listed in Table3. Obviously, transmission power increases witha1. The throughput also increases with a1, andachieves the maximum throughput when a1 � 1.3.There is an optimal a1 to maximize the through-put/power, which is around 1.1. The delay decreasesrapidly with a1. Although the optimal value of a1

depends on the traffic rate and network topology,the great news is that in average, the less than30% power increasing can improve the networkthroughput by more than 40%. In the followingcomparison with other scheduling algorithms, weuse a1 = 1.3 for the scheduling algorithm 1 toachieve the maximum throughput and small delay,at the cost of more energy consumption.

In the scheduling algorithm 2 and 3, the choicesof N and a are interdependent. The larger a is, thesmaller N need to be, but with the price of increasedpower consumption. From simulation, the mini-mum N needed to have 60.1% failure rate is listedin Table 4. We chose a2 = 1.05 and a3 = 1.05 inthe following simulations. To reach the same6 0.1% failure rate, we used N = 10 for algorithm2, and N = 15 for the algorithm 3.

Comparing to algorithm 3, algorithm 2 needs lessnumber of iterations to satisfy the SINR require-ments. The reason is that the links are added oneby one, so each time when the power control algo-rithm is run, the initial power vector, the one thatsatisfies the SINR requirements without the newlink, is not very far away from the solution. There-fore algorithm 3 has higher failure rate if the numberof iterations is the same, or higher complexity if thenumber of iteration is raised to achieve same failurerate.

Same as in the symmetric 5-node case, the aver-age power of algorithm 1 does not change signifi-cantly as the rate increases, while the algorithms 2and 3 use more power for larger rate.

The delay depends significantly on the rate. If therate is larger than the threshold rate, the queues keepgrowing, and the delay increases very fast. Algorithm

Fig. 3. Throughput, power, delay, and complexity of scheduling algorithms, average over 10 random 10-node networks.

Table 3The average throughput, delay, and power versus a1, averageover 10 randomly generated 10-node networks with schedulingalgorithm 1 and ke = 0.005

a1 Throughput(packets/slot)

Delay(slot)

Power (r2) Throughput/power

1.0 0.318 13523 52.2 6.08e�31.1 0.441 937 57.6 7.65e�31.3 0.449 11.9 66.2 6.78e�32.0 0.449 6.62 89.8 5.00e�3

10.0 0.449 5.60 160.4 2.80e�3

Table 4Minimum number of iterations needed for joint scheduling andpower control algorithms

a = 1.10 a = 1.05 a = 1.01

Scheduling algorithm 2 7 9 14Scheduling algorithm 3 10 12 21


2 achieves the best delay among the three schedulingalgorithms, while algorithm 1 has the largest delay.

We compare the calculation complexity of thethree scheduling algorithms by counting the numberof calculations (comparison and updating). Asshown in Fig. 3, scheduling algorithm 1 has thesmallest complexity at low rate. However, at highrate its complexity per packet transmission is notlow at all. The reason is that many links with highlink metric cannot be rejected at step 4 as blockedlinks (like in joint algorithms), and the SINR checkat step 3 has to be carried out many times. Compar-ing our joint algorithm with algorithm 3, our algo-rithm has less complexity since it needs lessnumber of iterations to converge.

To conclude, the simplified scheduling is the sim-plest one because there is no power control. But theamount of calculation is not less than that of the jointscheduling and power control algorithms, and the


performance in terms of delay and throughput issignificantly worse than other schemes. Our jointscheduling and power control algorithm gives themaximum use of the channel (i.e., maximum through-put and smallest delay). Our algorithm also has smal-ler complexity comparing to the algorithm based on[24], and needs only slightly larger total power.

4. Joint scheduling and routing

4.1. Routing

Since our work focuses on the interactionbetween routing and scheduling, we use the central-ized version of the Bellman–Ford algorithm forshortest path routing, and do not go into the detailsof the routing protocol implementation.

The routing distance of link (i, j) is defined as

Dði; jÞ ¼ d �Qij

Qmax

� �þ e � Rij

Rmax

� �c

: ð7Þ

Here d and e are weight factors satisfying d + e = 1.The first term is proportional to the queue size, toencourage the usage of less congested links. The sec-ond term is related to the power consumption, orphysical distance of the link, to encourage the trans-mission over short distances and hence expend lessenergy. A link between two nodes in close proximitynot only expends less power for the transmission,therefore prolonging the lifetime of the nodes andthe network, but also causes less interference to allother links in the network.

4.2. Joint routing and scheduling algorithm

When the traffic rate is fixed by routing, thescheduling algorithm tries to assign the required

P3=115.4

P2 =115.4

4

3

2

1

0

2.13.0

2

Fig. 4. Examples of simultaneous transmissi

traffic rate by giving higher priority to links with lar-ger queue. However, the rate achieved by the sched-uling algorithm may be different from the requiredrate. There are cases where the bandwidth require-ments cannot be satisfied by scheduling alone. Forexample, if a node is close to many nodes, and ison the routes of many source destination pairs,the bandwidth requirement to that node may justexceed the maximal possible value, even if it isassigned slots all the time.

Let us illustrate this by the simple network givenin Fig. 1. In the minimum energy routing, the outerlinks are not used. The route from node 1 to node 2will go through links (1, 0) and (0, 2), instead of link(1,2), to save energy because 2.1c + 2.1c < 3.0c istrue for any c > 2. Then all the traffic has to gothrough node 0, and make it a bottleneck. As aresult, at most one packet can be transmitted atany time slot. If the outer links can be used, thentwo packets can be transmitted at the same time,and double the throughput. Some examples ofsimultaneous transmissions are given in Fig. 4.

As time goes on, the difference between band-width requirement and assignment at some linksmay stay positive for a number of slots, and queuesstart building up at the buffers. These queues do notbuild up uniformly among all nodes and flows. Thusthe packets which are encountering long delay intheir current route need to be rerouted. As the linkdistance is changed by the building up of the queues,a shortest path routing algorithm can re-computeroutes using the updated information about thequeues sizes. The recomputed routes provide newvalues of the average rates on each link that thescheduling aims to satisfy. This is the problem ofjointly solving the access control problem and therouting problem in ad hoc networks.

P0 =37.0

P2=240.9

4

3

1

0

2.13.0

on for the symmetric 5-node network.

Fig. 5. Throughput, delay, and power for different routingparameters for the 5-node network.


At the beginning of the network operation, we setQij = 0. As long as e > 0, routes are optimized byenergy consumption. After that, routes are calcu-lated periodically by the Bellman–Ford algorithmbased on the updated link distance in (7). This suc-cessive interaction from frame to frame, betweenroute selection (that determines the required band-width) and bandwidth allocation (that determinesthe actually assigned bandwidth) is at the center ofthe joint routing/access resolution. The reroutinghelps in balancing the traffic throughout the linksand nodes in the network. Rerouting periodicallymay increase the throughput, and decrease the delayand the number of discarded packets. It is alsoimportant to take into account the mobility of usersand the topology changes in the network as rerout-ing is performed.

In the example we just showed, we start from theminimum energy route. The route from node 1 tonode 3 is (1, 0)(0,3), and the route from node 1 tonode 2 is (1, 0)(0,2). After periodical rerouting, thetraffic from node 1 to node 3 sometimes takes theroute (1,2)(2,3) or the route (1, 4)(4,3). The routefrom node 1 to node 2 now goes through the link(1,2) directly. As a result, the traffic is distributedmore evenly, and throughput is increased. There isa trade-off here between delay and power. If wewant to minimize the power, all traffic tends to gothrough node 0, this cause congestion and big delay.On the other hand, if we want to minimize the delay,the traffic will go through some outer links to avoidnode 0 that has a heavy load, and this cause largerpower consumption.

It may not be possible to recompute routes acrossthe network at the rate of every frame. In fact suchan update rate may lead the algorithm to unstableoscillations. Thus the time constant of route adjust-ment must be made large enough to include multipleframes and react only to the aggregate queue sizefluctuations over a sufficiently large number offrames.

4.3. Simulation results

In order to study the effect of joint routing andscheduling algorithm, we simulated the simple 5-node network shown in Fig. 1. The performance interms of throughput, delay, and power, is shown inFig. 5. For the joint scheduling and routing algo-rithm, we use our joint scheduling and power controlalgorithm (with a2 = 1.05, N = 10) to do scheduling,and the routes are updated every 1000 slots.

The curves for d = 0, e = 1 is the minimumenergy route without rerouting, and the curves for

Fig. 6. Throughput, delay, and power for different routingparameters, average over 10 random 10-node networks.


d = 1, e = 0 is the least congestion route without theconsideration of the power. We found that thepower consumption of d = 0, e = 1 is the smallest,and the power of d = 1, e = 0 is the largest. Allother curves lie in between as expected. The resultclearly shows the trade-off between the delay andthe power consumption. The larger the weight ofthe delay term, the smaller the delay is, with the costof larger power. Similarly, the larger the weight ofthe power term, the smaller the power consumptionis, with the cost of larger delay.

We also simulated 10 randomly generated 10-node networks in a 10 · 10 area, and the averageperformance is shown in Fig. 6. Here (0.9,0.1) is agood trade-off between the delay and the powerconsumption. It has almost as good delay as theminimum delay routing, with only slightly morepower consumption.

5. Thoughts on distributed version

Since ad hoc networks generally do not have a cen-tral controller, a distributed implementation is veryimportant for routing and scheduling algorithms.The distributed asynchronous routing that is basedon the Bellman–Ford algorithm is known to con-verge and has been well studied and documented[12]. Hence we need to focus on the distributed ver-sion of scheduling and power control algorithm. Herewe present only some thoughts and observationsregarding distributed implementation.

The distributed power control algorithm with theconstraint P 6 1 Æ Pmax uses the measured SINR toupdate the power, and its convergence is proved in[9]. However, it is possible that the power vectorconverges to a vector whose elements are Pmax, thatis, the SINR requirements cannot be satisfied, andsome links should be removed. Possible methods toreduce the number of iterations include using discretepower levels and set margin protection. The com-plexity of the asynchronous power control algorithmand the information that needs to be exchangedbetween neighbors are serious impediments.

The challenge is to perform distributed schedul-ing to find the conflict-free link activation set. Todo this there are some heuristic algorithms, likethe hand shaking protocol proposed in [29].Another difficulty is how to relate allocated slotsto the metric of the links. One possibility is to letnodes send requests at random times, and let thechoice of random times relate to the link metric.That is, the link with the lowest link metric is more

likely to send a request earlier than the links withhigher link metrics.


At this point we do not have a definite distributedversion to propose. The thoughts and heuristics wementioned have not been evaluated and hence, thequestion of how to implement our ideas in a distrib-uted fashion remains open.

6. Conclusions and extension

In this paper, we provided a centralized algo-rithm of joint power control, scheduling, and rout-ing. Simulation results show that the jointscheduling and power control algorithm improvesthe throughput and delay significantly, and thatthe joint scheduling and routing algorithm alsoimproves the network performance. Our simulationshows that there is a trade-off between energy con-sumption and the throughput and delay networkperformance.

This work has several possible extensions. Thespecification of a distributed algorithm and its eval-uation is one of them. The algorithms can also beeasily modified to accommodate multiple flow types.The only modification needed is to use bf,f = 1,2, . . . ,F, instead of b, when checking SINRrequirements in the case of F flow types. For someapplications, it may not be possible to do schedulingfor each slot; we may attempt scheduling for aframe consisting of multiple slots. The basic ideasremain the same. Finally this study can be extendedto CDMA-based systems by slightly changing thescheduling rules and by reflecting the CDMAsequence properties on the value of the SINRthreshold.

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Yun Li received the B.S. and M.S. degreein physics, from Tsinghua University,Beijiing, China, in 1993 and 1996respectively, and the M.S. and Ph.D.degree in electrical engineering fromUniversity of Maryland, College Park,Maryland, in 1998 and 2004, respec-tively.

She is now a postdoctoral fellow atColorado State University. Her researchinterests include wireless communica-

tions, ad hoc networks, and sensor management.

Anthony Ephremides received his B.S.degree from the National TechnicalUniversity of Athens (1967), and M.S.(1969) and Ph.D. (1971) degrees fromPrinceton University, all in ElectricalEngineering. He has been at the Uni-versity of Maryland since 1971, andcurrently holds a joint appointment asProfessor in the Electrical EngineeringDepartment and in the Institute of Sys-tems Research (ISR) of which he is a

founding member. He is co-founder of the NASA Center forCommercial Development of Space on Hybrid and Satellite
Communications Networks established in 1991 at Maryland asan off-shoot of the ISR. He served as Co-Director of that Centerfrom 1991 to 1994.
He was a Visiting Professor in 1978 at the National TechnicalUniversity in Athens, Greece, and in 1979 at the EECS Depart-ment of the University of California, Berkeley, and at INRIA,France. During 1985–1986 he was on leave at MIT and ETH inZurich, Switzerland. He was the General Chairman of the 1986IEEE Conference on Decision and Control in Athens, Greece andof the 1991 IEEE International Symposium on InformationTheory in Budapest, Hungary. He also organized two workshopson Information theory in 1984 (Hot Springs, VA) and in 1999(Metsovo, Greece). He was the Technical Program Co-Chair ofthe IEEE INFOCOM in New York City in 1999 and of the IEEEInternational Symposium on Information theory in Sorrento,Italy in 2000. He has also been the Director of the FairchildScholars and Doctoral Fellows Program, an academic andresearch partnership program in Satellite Communicationsbetween Fairchild Industries and the University of Maryland. Hewon the IEEE Donald E. Fink Prize Paper Award (1992) and hewas the first recipient of the Sigmobile Award of the ACM(Association of Computer Machinery) for contributions towireless communications in 1997. He has been the President ofthe Information Theory Society of the IEEE (1987) and hasserved on its Board of Governors almost continuously from 1981until the present. He was elected to the Board of Directors of theIEEE in 1989 and 1990.

He has authored or co-authored over 100 technical journalpapers and 300 technical conference presentations. He has alsocontributed chapters to several books and edited numerous spe-cial issues of scientific journals. He has also won awards from theMaryland Office of Technology Liaison for the commercializa-tion of products and ideas stemming from his research. He hasserved on the Editorial Boards of the IEEE Transactions onAutomatic Control, IEEE Transactions on Information theory,the Journal of Wireless Networks, and the International Journalof Satellite Communications.

He has been the Dissertation Supervisor of over twenty Ph.D.students who now hold prominent positions in academia,industry, and research labs. He is the founder and President ofPontos, Inc., a Maryland company that provides technical con-sulting services, since 1980.

His interests are in the areas of communication theory, com-munication systems and networks, queueing systems, signalprocessing, and satellite communications. His research has beencontinuously supported since 1971 by NSF, NASA, ONR, ARL,NRL, NSA, and Industry. In 2003, he was awarded the CynthiaKim Eminent Professorship in Information Technology at theUniversity of Maryland.

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A joint scheduling, power control, and routing algorithm for ad hoc wireless networks