Transportation Research Part C 21 (2012) 214–229

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Transportation Research Part C

journal homepage: www.elsevier .com/locate / t rc

Adaptive data dissemination for time-constrained messagesin dynamic vehicular networks

Kai Liu, Victor C.S. Lee ⇑Department of Computer Science, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong

a r t i c l e i n f o a b s t r a c t

Article history:Received 30 November 2010Received in revised form 12 July 2011Accepted 21 October 2011

Keywords:Roadside-to-vehicle communicationData disseminationAdaptive schedulingReal-time

0968-090X/$ - see front matter � 2011 Elsevier Ltddoi:10.1016/j.trc.2011.10.006

⇑ Corresponding author. Tel.: +852 27888617; faxE-mail addresses: kevin.liu@student.cityu.edu.hk

With the advent of emerging wireless communication technologies, tremendous effortshave been put on promoting the safety and efficiency of transportation services by devel-oping innovative applications. In particular, there has been significant interest in accessinginformation stored at RSUs (Roadside Units). The unique characteristics in vehicular net-works, such as dynamic traffic factors including vehicle arrival rate, dwell time and dataaccess patterns, bring us new challenges on data dissemination. This work dedicates tothe investigation of timely and adaptive data dissemination in the dynamically changingtraffic environment. Firstly, we derive an analytical model to explore and examine theeffects of the dynamic traffic factors. In light of the theoretical results, an on-line schedul-ing algorithm is proposed for adaptive data dissemination. Finally, we evaluate perfor-mance of the new algorithm in a variety of circumstances. The simulation resultsdemonstrate satisfactory performance of the proposed algorithm.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

The ITSs (Intelligent Transport Systems) encompass a broad range of advanced information and communication technol-ogies, which are applied in transport infrastructures and vehicular networks. They are expected to offer fundamental break-throughs in enhancing road safety, reducing congestion, improving driving comfort and protecting environment, to name afew. In general, there are two types of communication models in ITS: IVC (Inter-Vehicle Communication) and RVC (Roadside-to-Vehicle Communication) (Chang et al., 2007; Yanlin et al., 2006). In IVC, vehicles communicate with each other directlythrough the mounted OBUs (On Board Units) without the presence of any infrastructure. In RVC, on the other hand, vehiclescommunicate with RSUs (Roadside Units), which are installed at intersections or along the road. In practice, the two com-munication models are cooperated with each other in vehicular networks to provide a variety of services. The RSU can pro-vide information to passing vehicles within its service region, while the vehicles are also able to forward or exchangeinformation via vehicle-to-vehicle communication (Delot et al., 2010). In this study, we focus on the data disseminationin the RVC model.

Nowadays, different parties including manufacturers, governments and academia are actively engaged in developinginfrastructures and doing researches in ITS. In industry, numerous projects are developed worldwide. COOPERS (COOPERS,2010), SAFESPOT (SAFESPOT, 2010) and CVIS (CVIS, 2010) are integrated projects co-funded by the European CommissionInformation Society and Media. They are working on the design and development of cooperative systems for a safer, cleanerand smarter mobility in Europe. In Japan, the deployment of ITS devices and infrastructures has been spreading rapidly. Forexample, in Japan, the number of vehicles installed with an intelligent car navigation device, which is so called VICS (Vehicle

. All rights reserved.

: +852 27888614.(K. Liu), csvlee@cityu.edu.hk (V.C.S. Lee).

K. Liu, V.C.S. Lee / Transportation Research Part C 21 (2012) 214–229 215

Information and Communication System), has increased from 1.5 million in March 2006 to 27.6 million in June 2010 (VICS,2010). This project contributed significantly in improving the traffic efficiency in Japan. In US, California PATH (PATH, 2010)is one of the representative projects, which is administrated by the ITS at the UC Berkeley in collaboration with CaliforniaDepartment of Transportation. The general mission of the project is to develop innovative ITS strategies and technologiesto improve safety, flexibility, mobility, stewardship and delivery of transportation systems in US. Meanwhile, the USDOT(United States Department of Transportation) (ITSPLAN, 2010) also incorporates closely with the ITS projects and offers themwith tremendous financial support. According to the recently released ITS Strategic Research Plan (2010–2014), the ITS re-search programs will be funded $100 million per year in the coming 5 years.

In academia, the issue of effective communication in dynamic vehicular networks has received great attention. Generally,there are three categories of communication requirements (Morsi Mahmod et al., 2008): requirements on data traffic char-acteristics, communication functionality requirements and communication quality requirements. They are the problems tobe solved on different stack layers referring to the OSI protocol model. By far, studies concerning data access in vehicularnetworks have largely focused on the requirements of communication functionality and quality (Maeshima et al., 2007;Mak et al., 2005; Korkmaz et al., 2006; Jhang and Liao, 2008; Kuramoto et al., 2007), which are the issues typically residedon the network layer and the data link layer. Little work, however, has put effort on the investigation of data traffic charac-teristics in vehicular networks at the application level.

This work is dedicated to the evaluation of system performance from the application point of view. Specifically, we con-sider a RVC model in which vehicles access information provided by the RSU. Typical data traffic characteristics in vehicularnetworks (e.g. data access rates, access time-constraint and data access patterns) as well as their effects on system perfor-mance are intensively examined. The main contribution of this paper is twofold. First, based on the analytical results, weobserve that it is critical for the data dissemination to be adaptable to dynamic traffic environments. Second, we proposean adaptive channel and data allocation algorithm to implement efficient data dissemination in a hybrid data broadcastmodel.

The rest of this paper is organized as follows. Section 2 reviews the related works. Section 3 presents the system archi-tecture and formulates the problem. In Section 4, an analytical model is derived and analyzed. In Section 5, we propose anon-line algorithm to implement adaptive data and channel allocation. Section 6 illustrates the simulation environment anddiscusses the simulation results. Finally, we conclude this study in Section 7.

2. Related works

Data broadcast is an effective approach to disseminating data items in both conventional mobile computing applicationsand emerging vehicular network systems. Generally, there are two data broadcast mechanism: push-based and pull-basedbroadcast (Aksoy and Leung, 2004). In push-based broadcast, the server broadcasts whole or part of the database periodicallyaccording to certain static broadcast programs, which can be developed based upon historical data access statistics or a set ofpre-defined request profiles. All clients listen passively to the broadcast channel to retrieve data items of interest withoutsubmitting explicit queries. FLAT (Saxena and Pinottti, 2005) is the simplest push-based broadcast mechanisms whichbroadcasts data items in a ‘round robin’ manner. A more sophisticated mechanism called Broadcast Disk was introducedin Acharya et al. (1996), where popular data items are broadcast more frequently in fast disks than less popular data itemsin slow disks. GREEDY (Yee et al., 2002) is another representative push-based algorithm which aims to minimize the MCAED(Multi-Channel Average Expected Delay) in a multi-channel broadcast environment. On the other hand, in pull-based broad-cast, which is commonly known as on-demand broadcast, the server disseminates data items only in response to explicitqueries received from the clients. There are a number of classical on-demand scheduling algorithms. FCFS (First Come FirstServed) (Wong and Ammar, 1985) broadcasts data items sequentially according to their arrival order. MRF (Most RequestedFirst) (Wong, 1988) broadcasts the data item which has the largest number of pending requests to account for the produc-tivity of broadcast. RXW (Number of pending Requests Multiply Waiting time) (Aksoy and Franklin, 1999) calculates thenumber of pending requests for a data item multiplied by the amount of time that the oldest outstanding request for thatitem has been waiting. In each broadcast tick, the request with the maximum RXW value will be chosen to serve. SIN (Slacktime Inverse Number of pending requests) (Xu et al., 2006) is proposed for real-time scheduling. It considers both the ur-gency of requests and the productivity of data broadcast in making a scheduling decision.

Although data dissemination has been extensively studied in the network community (Aksoy and Franklin, 1999; Xuet al., 2006; Ng et al., 2008; Hu and Chen, 2009), unique characteristics in the dynamic vehicular network bring us new chal-lenges. To handle real-time requirements in a RVC model, Bohm and Jonsson (2008) proposed a deterministic MAC schemeby extending current 802.11p standard with a collision-free communication phase, which is controlled by RSUs. In order tosupport emergency communication in vehicular networks, Maeshima et al. (2007) enhanced the MAC protocol based upon atwo-channel RVC system, in which a data channel is assigned to provide general information and a control channel aims atcontrolling the RVC system and implementing emergency communication. Once an emergency notification occurred on thecontrol channel, the transmission of general information on the data channel would be suspended to ensure short transmis-sion delay of emergency messages. From the perspective of commercial profits, Mak et al. (2005) proposed a MAC protocol tosupport value-added services in ITS without compromising safety–critical applications by making the best utilization of thehigh-bandwidth in cutting-edge RVC systems. The total bandwidth is divided into seven channels: one control channel and

216 K. Liu, V.C.S. Lee / Transportation Research Part C 21 (2012) 214–229

six service channels. The RSU is in charge of synchronizing and coordinating these channels to disseminate both safety–crit-ical and value-added information effectively. To improve the communication efficiency between passing vehicles and theRSU, Jhang and Liao (2008) proposed a new channel access mechanism called PVR (Proxy-based Vehicle to Roadside) forRVC systems. The protocol assigns particular vehicles as proxies, which are responsible for transmitting data items to theRSU. Other vehicles which attempt to communicate with the RSU must forward their data items to a proxy. In such a manner,the query submitted by a vehicle may reach the RSU before the vehicle drives into the communication range (as long as itsproxy vehicle is in the coverage). Moreover, it relieves the contention for the uplink channel and improves the throughput ofthe system. Note that all these studies focused on the problems of communication requirements in vehicular networks,which are typically to be solved on the MAC layer.

Only a few studies considered the problems of information access in vehicular networks from the view point of data traf-fic characteristics, which are the issues resided on the application layer. Chang et al. (2007) proposed a scheduling algorithmcalled MFL (Maximum Freedom Last). The work investigated in a vehicular network system, where RSUs are installed alongthe road to form seamless service coverage. The handoff is occurred if a vehicle could not complete its data transmissionwithin the coverage of one RSU. To reduce the overhead caused by handoff operations, MFL is committed to minimizingthe handoff rate by incorporating several data access factors in scheduling, including remaining service dwell time, remain-ing data transmission time, queuing delay and maximum tolerable delay. Zhao et al. (2007) proposed a data pouring andbuffering paradigm, where data poured from data centers are buffered and rebroadcast at road intersections. The proposedscheme can significantly improve data delivery ratio by making use of relay and broadcast stations to offload data dissem-ination at intersections from data centers. Zhang et al. (2007) considered a RVC environment, in which the download of dataitems and the upload of updates compete for the same range of bandwidth spectrum. To maximize the overall system per-formance, a two-step scheduling scheme is proposed to strike a balance between serving updates and downloading requests.These studies considered the data services at the application level, however, none of them addressed the adaptive data dis-semination problem by considering the dynamic features in vehicular networks.

3. Preliminaries

3.1. System description

DSRC (Dedicated Short Range Communication) is a key wireless communication standard in vehicular networks. At pres-ent, there are two prominent DSRC versions worldwide. One is the Euro DSRC standard, which is developed from traditionalRFID (Radio Frequency Identification) techniques. The other is the American standard, which is compatible with IEEE 802.11p.In this work, we consider a RVC model which follows the American DSRC Standard. The spectrum ranges between 5.850 and5.925 GHz, called ITS-RS (Intelligent Transportation Systems Radio Service), is allocated for DSRC applications by US FCC (Fed-eral Communications Commission) (FCC-03-324, 2003). According to the band plan, the 75 MHz spectrum is divided into se-ven channels, which are classified as one CCH (Control Channel) and six SCHs (Service Channels) (FCC-03-024, 2004).

Based on the DSRC, we hereby present a RSU-based data dissemination system as shown in Fig. 1. This is a RVC modelwhere the RSU is installed at the road intersection and passing vehicles access information from the RSU. The radio coverageof the RSU is regarded as the service region. Only vehicles within the service region can retrieve the data items stored at theRSU. In addition, the RSUs are connected with each other by wired links to form a backbone network. The data items storedin the local database of a RSU are kept up-to-date by the information providers via the backbone network.

Generally, the service can be classified into two categories: safety–critical service (e.g. frontal collision warning, hazardwarning, intersection safety coordination, etc.) and non-safety–critical service (e.g. mobile infotainment, advertisements, con-gestion advisories, etc.). Correspondingly, data items in the database are categorized into two sets: safety–critical and non-safety–critical data items (Maeshima et al., 2007; Mak et al., 2005). The control channel, CCH, is committed to delivering allsafety–critical data items (FCC-03-024, 2004). This is viable because compared with other information, safety–critical dataitems are generally much smaller in size and much less in amount (Morsi Mahmod et al., 2008; Mak et al., 2005). In practice,providing such a service only takes a short period of time and consumes a small fraction of bandwidth. Passing vehicles areprescribed to monitor the CCH upon entering the service region to retrieve safety–critical data items (Xu et al., 2004). Mean-while, the availability of non-safety–critical services will be announced together to ensure that every passing vehicle wouldbe aware of available services. Finally, the six SCHs are responsible for the delivery of non-safety–critical data items. Thebroadcast time unit is referred to as a broadcast tick.

To better explore the potential of the service bandwidth, two types of data dissemination approaches, push-based and on-demand broadcast (Aksoy and Leung, 2004), are cooperated in supporting the non-safety–critical service. Basically, in push-based broadcast, the RSU broadcasts data items periodically, while passing vehicles retrieve data items of interest withoutsubmitting any query to the server. With respect to the resource saving, at the server side, this mechanism saves the band-width for query uploading, while for the clients, the avoiding of submitting queries can be a significant saving of their limitedpower. Besides, in terms of maximizing the business value, to periodically broadcast some informative messages mayachieve certain quality of services. On the contrary, in on-demand broadcast, the RSU broadcasts data items only in responseto explicit queries received from vehicles. It is preferable to the push-based broadcast in providing customized services. Theuploading of queries competes for the upload bandwidth allocated by the CCH. In practice, either TDM (Time Division Mul-

RSU Server

Queries

Processing Unit

Database

CCH SCH SCH SCH SCH SCH SCH

DSRC Network

Internet

Backbone Network

1 Control Channel 6 Service Channels

Fig. 1. System architecture.

K. Liu, V.C.S. Lee / Transportation Research Part C 21 (2012) 214–229 217

tiplexing) or FDM (Frequency Division Multiplexing) can be applied to the implementation of the query uploading. Givencertain upload bandwidth, the maximum number of queries which can be uploaded in a broadcast tick is considered asthe upload capacity. In a broadcast tick, if the number of queries submitted by vehicles exceeds the upload capacity, someof them have to be discarded, while the successfully uploaded queries will be added to the pending queue and wait forthe service.

The objective of the system is not only to provide safety–critical services, but also to make the best utilization of availablebandwidth in providing non-safety–critical services. As discussed, the latter mission is more challenging because, amongother reasons, the delivery of non-safety–critical data items is much more time and bandwidth consuming, and it is non-triv-ial to strike a balance between the push-based and on-demand approaches to maximize the efficiency in data dissemination.In view of this, the following of this work concentrates on the investigation and the evaluation of system performance in theprovision of non-safety–critical services. The detailed research problems are stated as follows.

3.2. Problem statement

The primary notations presented in this paper are summarized in Table 1. The database D is divided into two sets: safety–

critical data items (Ds) and non-safety–critical data items (Dn), where Ds ¼ d1s ; d

2s ; . . . ; djDs j

s

n oand Dn ¼ d1

n; d2n; . . . ; djDn j

n

n o. The

Table 1A summary of notations.

Notation Description Note

D The set of all data itemsDs The set of safety–critical data itemsDn The set of non-safety–critical data items D = Ds

SDn and Ds

TDn = ;

Dnp The set of push-based non-safety–critical data itemsDno The set of on-demand non-safety–critical data items Dnp

SDno = Dn and Dnp

TDno = ;

K The set of channels in the system jKj = 7Kc The set of control channels jKcj = 1Ks The set of service channels jKsj = 6Ksp The set of push channelsKso The set of on-demand channels Ksp

SKso = Ks and Ksp

TKso = ;

C Upload capacity Maximum number of queries can be uploaded in a time unit (C P 1)

p din

� �Access probability of the ith non-safety–critical data item di

n 2 Dn

t Dwell time of vehicles Exponentially distributed with parameter ls Inter arrival time of vehicles Exponentially distributed with parameter k

218 K. Liu, V.C.S. Lee / Transportation Research Part C 21 (2012) 214–229

channel set K is divided into one CCH, denoted by Kc = {kc}, and six SCHs, denoted by Ks ¼ k1s ; k

2s ; . . . ; kjKs j

s

n o, where jKcj = 1 and

jKsj = 6. In accordance with the two data dissemination approaches, we further classify the non-safety–critical data items in

Dn into two sets: push-based data items, Dnp Dnp ¼ d1np; d

2np; . . . ; djDnp j

np

n o� �and on-demand data items, Dno

Dno ¼ d1no; d

2no; . . . ; djDno j

no

n o� �, where 0 6 jDnpj 6 jDnj and 0 6 jDnoj 6 jDnj. Each data item di

n is either in the push-based or

the on-demand set, namely, DnpS

Dno = Dn and DnpT

Dno = ;. Correspondingly, the service channels, Ks, are divided into

two sets: push channel (Ksp) and on-demand channel (Kso), where Ksp ¼ k1sp; k

2sp; . . . ; kjKsp j

sp

n o(0 6 jKspj 6 jKsj) and

Kso ¼ k1so; k

2so; . . . ; kjKso j

so

n o(0 6 jKsoj 6 jKsj). Each service channel is either in the push or the on-demand channel set, namely,

KspS

Kso = Ks and KspT

Kso = ;.To achieve satisfactory system performance in a dynamic vehicular network, it is essential for the data dissemination to

be adaptable. For instance, in a heavy traffic scenario, the high vehicle arrival rate results in a high data access rate. Mean-while, it also implies longer dwell time of vehicles (because of the congestion), giving a looser deadline for data dissem-ination. Intuitively, in this case, the push-based service is preferred. This is because, firstly, the push-based service relievesthe burden of query uploading, which would otherwise defeat the performance of on-demand service due to the over-whelming uploading of queries. Secondly, although the push-based service is not quite responsive due to the fixed databroadcast period, the relatively looser service deadline makes this drawback not so significant. In contrast, when consid-ering light traffic environments, the data access rate is low. Meanwhile, the dwell time of vehicles will be much shorter(due to the free of congestion), which results in a tighter deadline for data dissemination. Apparently, in such a scenario,the on-demand service shall dominate because, firstly, the restricted query uploading would not be a bottleneck when thedata access rate is low. Secondly, the tight data dissemination deadline requires more timely response of the system,which is just the superiority of the on-demand service because it broadcasts data items on purpose for serving only thoseoutstanding queries.

From the above discussion, we note that the key of adaptable data dissemination is to strike a balance between the push-based and on-demand services. That is, based on current traffic conditions, to classify the total data set Dn into on-demanddata set Dno and push-based data set Dnp. Meanwhile, to allocate the service channel set Ks into push-based channel set Ksp

and on-demand channel set Kso. Therefore, the problem of this study boils down to dynamic data classification and channel

allocation. Given a data access attempt for din, no matter di

n is classified into the push-based set din 2 Dnp

� �or the on-demand

set din 2 Dno

� �, as long as it is failed to be accessed before the vehicle leaves the service region, it is an instance of missing

deadline. The total number of instances of missing deadline divided by the total number of data access attempts is definedas deadline miss ratio. To sum up, the research problem of this work is to, based upon dynamic traffic patterns, adaptivelydetermine the data item sets, Dnp and Dno, as well as the channel sets, Ksp and Kso, so that the deadline miss ratio can beminimized.

4. Analytical model

4.1. Expected deadline miss ratio

In this section, we derive an analytical model to analyze the system performance in terms of expected deadline miss ratio.Since the accessed data item di

n is either in the push-based set din 2 Dnp

� �or in the on-demand set di

n 2 Dno

� �, the expected

deadline miss ratio is analyzed in two cases.

Case 1: The data item is in the push-based set

Denote the required data item as dinp (1 6 i 6 jDnpj). di

np would be failed to be accessed by a vehicle if it was not broadcastduring the dwell time of this vehicle. Denote the broadcast period of di

np as l dinp

� �and denote the dwell time of the vehicle as

t. Obviously, if t P l dinp

� �; di

np can certainly be accessed by this vehicle. Otherwise t < l dinp

� �� �, the chance for di

np to be ac-cessed is calculated by

R t0

1l di

npð Þ dt, which equals tl di

npð Þ. So, the probability that a particular vehicle with the dwell time t fails toaccess di

np is calculated by:

PdinpðtÞ ¼

0 t P l dinp

� �1� t

l dinpð Þ t < l di

np

� �8><>: ð1Þ

For all passing vehicles which attempt to access dinp, the probability that di

np cannot be accessed is the deadline miss ratioof di

np, denoted by RdinpðtÞ. Denote the probability density function of the dwell time t as f(t), according to Eq. (1):

RdinpðtÞ ¼

Z 1

0Pdi

npðtÞ f ðtÞdt ¼

Z 1

l dinpð Þ

0 � f ðtÞdt þZ l di

npð Þ

01� t

l dinp

� �0@

1A � f ðtÞdt ¼

Z l dinpð Þ

01� t

l dinp

� �0@

1A � f ðtÞdt ð2Þ

K. Liu, V.C.S. Lee / Transportation Research Part C 21 (2012) 214–229 219

Case 2: The data item is in the on-demand set

Denote the required data item as dino (1 6 i 6 jDnoj) with the access probability of p di

no

� �. Denote the inter arrival time of

vehicles as s, then the vehicle arrival rate is 1s. Accordingly, the arrival rate of query for di

no is calculated by 1s � p di

no

� �. Given

the upload capacity C and considering that the time window for any vehicle to upload its query is 1 broadcast tick, then as

long as the query arrival rate does not exceed the upload capacity CPjDno j

i¼11s � p di

no

� �6 C

� �, all queries can be uploaded suc-

cessfully (Psuccess = 1). OtherwisePjDno j

i¼11s � p di

no

� �> C

� �, some of the queries have to be discarded and Psuccess ¼ CPjDno j

i¼11s�p di

noð Þ. To

sum up, the probability of success query uploading is calculated by:

Psuccess ¼1 s P

PjDno ji¼1

p dinoð Þ

C

s�CPjDno ji¼1

p dinoð Þ

s <PjDno j

i¼1p di

noð ÞC

8>><>>: ð3Þ

Note that a vehicle would stand a chance to access its required dino only on condition that its query for di

no is uploadedsuccessfully. With this precondition, denote Odi

noas the probability that, in a broadcast tick, di

no is not selected to broadcastin any of the on-demand channel. Suppose the selection of data items in each broadcast tick is independent, then in t broad-cast ticks, the probability that di

no is not selected to broadcast is equal to Odino

� �t. So, the probability that a particular vehicle

with the dwell time t fails to access dino is calculated by:

Pdinoðt; sÞ ¼ Odi

no

� �t� Psuccess þ 1 � ð1� PsuccessÞ ð4Þ

We have the following equation to calculate Odino

. The proof can be found in Appendix A.

Odino¼P jDno j�1

jKso j

� �s¼1

QjKso jm¼1as

m

� �P jDno j

jKso j

� �q¼1

QjKso jr¼1 bq

r

� � ðjDnoj > jKsojÞ ð5Þ

where as1; a

s2; . . . as

jKso j; 1 6 s 6jDnoj � 1jKsoj

� �� �is the sth combination of choosing jKsoj data items from the set of

p d1no

� �; p d2

no

� �; . . . ; p djDno j

no

� �n o� fp di

no

� �g

n o(1 6 i 6 jDnoj) and

QjKso jm¼1as

m is the probability of the sth combination.

bq1; b

q2; . . . bq

jKso j 1 6 q 6 jDnojjKsoj

� �� �is the qth combination of choosing jKsoj data items from the set of

p d1no

� �; p d2

no

� �; . . . ; p djDno j

no

� �n oand

QjKso jr¼1 bq

r is the probability of the qth combination.

Lastly, for all passing vehicles which attempt to access dino, the probability that di

no cannot be accessed is the deadline missratio of di

no, denoted by Rdinoðt; sÞ. Denote the probability density function of vehicle inter arrival time s as f(s), according to

Eqs. (3) and (4):

Rdinoðt; sÞ ¼

Z 1

0

Z 1

0Pdi

noðt; sÞ f ðsÞ f ðtÞdsdt

¼Z 1

0

Z 1

NOdi

no

� �tf ðsÞdsþ

Z N

0Odi

no

� �t� sNþ 1� s

N

� �f ðsÞds

� �f ðtÞdt

where

N ¼PjDno j

i¼1 p dino

� �C

ð6Þ

In summary, derived from Eqs. (2) and (6), for all data items din (1 6 i 6 jDnj), the expected deadline miss ratio is:

E½Rðt; rÞ� ¼XjDn j

i¼1

p din

� �� Rdi

nðt; sÞ ¼

XjDnp j

i¼1

p dinp

� �� Rdi

npðtÞ þ

XjDno j

i¼1

p dino

� �� Rdi

noðt; sÞ

¼XjDnp j

i¼1

p dinp

� ��Z 1

0Pdi

npðtÞf ðtÞdt þ

XjDno j

i¼1

p dino

� ��Z 1

0

Z 1

0Pdi

noðt; sÞ f ðsÞ f ðtÞdsdt ð7Þ

220 K. Liu, V.C.S. Lee / Transportation Research Part C 21 (2012) 214–229

4.2. An example

With the derived analytical model, we show an example to have a clear exposition of the effects of data classification andchannel allocation on the system performance. The calculation results are generated by the MATLAB with specific settingsintroduced below. Firstly, we examine a typical traffic model in which the arrival of vehicles follows the Poisson process withthe parameter k. So, the inter arrival time s follows the Exponential distribution and f(s) = ke�k�s (s P 0). Secondly, supposethe dwell time t of vehicles follows the Exponential distribution with the parameter l (l > 0) where f(t) = le�lt (t P 0).Without loss of generality, the Flat broadcast policy (Saxena and Pinottti, 2005) is assumed in the push-based service where

l dinp

� �¼ jDnp jjKsp j. Lastly, assume the data access pattern follows the commonly used Zipf distribution (Zipf, 1949) with the

parameter h: p din

� �¼ ð1=iÞhPjDn j

j¼1ð1=jÞh

din 2 Dn

� �. Note that the data access pattern is getting more skewed with an increasing value

of h. In addition, for a data item in such a distribution, the smaller its ID is, the higher its access probability is. Based on Eq.(7), the expected deadline miss ratio is calculated as follows. The detailed calculation can be found in Appendix B.

E½Rðt; sÞ� ¼XjDnp j

i¼1

p dinp

� �� 1þ 1

l� jKspjjDnpj

e�ljDnp jjKsp j � 1

� �� �þXjDno j

i¼1

p dino

� �� 1þ 1

N � k � ð1� e�k�NÞ ll� ln Odi

no

� 1

! !

where

N ¼PjDno j

i¼1 p dino

� �C

; p dinp

� �¼ p di

n

� �; p dj

no

� �¼ p dnpþj

n

� �and 1 6 i 6 jDnpj; 1 6 j 6 jDnoj

ð8Þ

Fig. 2 shows the different expected deadline miss ratio under different proportions of the on-demand service to the push-based service. The results are calculated by Eq. (8) with parameters jDnj = 80, h = 0.8, t = 8, k = 6 and C = 10. Specifically, the 6service channels and 80 data items are classified into the push-based and on-demand services: Ksp + Kso = 6 and Dnp + Dno = 80.We examine the system performance with different weight between the push-based and on-demand services by changing theproportion of the number of push channels to the number of on-demand channels, as well as the proportion of the number ofpush data items to the number of on-demand data items. For instance, when the number of push channels increases from 0 to6, to maintain a total of 6 service channels, the number of on-demand channel decreases from 6 to 0 correspondingly.

In Fig. 2, the x axis represents the number of data items allocated into the push-based set. The more data items are clas-sified into the push-based set, the fewer data items remain in the on-demand set, and vice versa. The y axis represents thenumber of push channels. Likewise, the more channels are allocated into the push set, the fewer channels remain in the on-demand set, and vice versa. According to the results, there are two extreme cases where the expected deadline miss ratioequals 1. One is that all the data items are classified into the push set, whilst none of the channels are allocated as a pushchannel (x = 80, y = 0). In contrast, the other extreme case is that all the data items are classified into the on-demand set,whilst none of the channels are allocated as an on-demand channel (x = 0, y = 6). Apparently, these are the two worst situ-ations for data and channel allocation, which result in a 100% deadline miss ratio. On the other hand, the results also reflectthat neither a pure push-based service (x = 80, y = 6) nor a pure on-demand service (x = 0, y = 0) can give the minimumexpected deadline miss ratio. According to the statistics collected from this example, the minimum expected deadline miss

010

2030

4050

6070

80

01

23

45

60

0.2

0.4

0.6

0.8

1

Number of push data itemsNumber of push channels

Expe

cted

dea

dlin

e m

iss

ratio

Fig. 2. Expected deadline miss ratio under different proportions of the on-demand service to the push-based service.

K. Liu, V.C.S. Lee / Transportation Research Part C 21 (2012) 214–229 221

ratio is achieved at the point (x = 30, y = 5), where 30 data items Dnp ¼ d1n; d

2n; . . . ; d30

n

n o� �and 5 channels (jKspj = 5) are allo-

cated into the push-based service. Correspondingly, the remaining 50 data items Dno ¼ d31n ; d

32n ; . . . ; d80

n

n o� �and 1 channel

(jKsoj = 1) are allocated into the on-demand service. Therefore, we have observed that only an appropriate classification ofdata items and channels can achieve the best performance.

The above example illustrates that given a certain traffic setting, an appropriate data and channel allocation will result insatisfactory system performance. Nevertheless, note that the given example is not a realistic solution to derive the data andchannel allocation, but rather a theoretical analysis to demonstrate that there is a need to strike a balance between push-based and on-demand services. This is because the calculation is based on the theoretical model, which assumes certain dis-tributions of traffic patterns such as Poisson arrivals of vehicles and exponentially distributed dwell time. Nevertheless, in adynamic changing traffic environment, a practical solution is supposed determine the data and channel allocation by makinguse of the parameter values captured from the real environment without any specific assumption of distributions. Motivatedby the above analysis, it is imperative to develop an adaptive data and channel allocation mechanism in supporting the hy-brid of push-based and on-demand data broadcast services.

5. A new algorithm

5.1. Design rationale

The goal of the proposed algorithm is to dynamically divide the database and the channels into on-demand and push-based services according to particular traffic conditions. The investigation in Liu and Lee (2010) has revealed three represen-tative traffic factors which have profound influences on system performance, including vehicle arrival rates, vehicle dwelltime and data access patterns. Illuminated by these findings, we propose a new algorithm called ACDA (Adaptive Channeland Data Allocation). It aims to make the data dissemination to be adaptable to the dynamic traffic factors. The design ratio-nale is discussed as follows:

� Adaptable to vehicle arrival rate: The vehicle arrival rate determines the workload of data access. In the on-demand ser-vice, as illustrated in the analytical model, given the vehicle arrival rate k, the on-demand query arrival rate is calculatedby k �

Pdi

n2Dnop di

n

� �. Apparently, the more data items are classified into the on-demand data set (Dno), the higher the on-

demand query arrival rate is. However, since the total query upload capacity is limited, excessive allocation of on-demanddata items will result in significant performance deterioration due to the overwhelming uploading of queries. Therefore,the classification of on-demand data items should be adaptable to the vehicle arrival rate so that the restricted uploadcapacity will not be a bottleneck of system performance. In the push-based service, intuitively, its performance is inde-pendent with the vehicle arrival rate. This is because given a fixed data broadcast period and the vehicle dwell time, boththe number of successful data access and the number of failed data access shall change proportionally with the total num-ber of access attempts for push data items. To sum up, the factor of vehicle arrival rates has more influence on the deter-mination of on-demand services.� Adaptable to vehicle dwell time: The vehicle dwell time determines the time-constraint of data broadcast. In the on-

demand service, the longer the vehicle dwell time is, the looser the data broadcast deadline is. Ideally, as long as theupload capacity is sufficient, more data items and channels should be allocated into the on-demand service when thevehicle dwell time is getting longer. However, as aforementioned, the data allocation for the on-demand service willbe typically bounded by the vehicle arrival rate. In the push-based service, its performance is determined by the relation-ship between the broadcast period of a data item and the vehicle dwell time. Specifically, given a vehicle with a certaindwell time, the longer the broadcast period of its requested data item is, the less chance the vehicle could be served. Onthe other hand, the broadcast period is determined by the number of push data items as well as the number of push chan-nels. Intuitively, when there are more data items and fewer channels allocated into the push-based service, the broadcastperiod of data items will be getting longer. Therefore, the classification of push-based data items and push channelsshould be adaptable to the vehicle dwell time so that the broadcast period will not be too long to hinder the overall sys-tem performance. To sum up, the allocation for the push-based service is more sensitive to the factor of vehicle dwelltime.� Adaptable to data access pattern: The data access pattern determines the popularity of information. Apparently, the

push-based service is suitable for the delivery of popular information, because it can significantly reduce the numberof query uploading and thus, avoid the overload of uplink bandwidth. On the other hand, for the data items with loweraccess probability, they are preferred to be served by on-demand broadcast as long as the total query arrival rate does notexceed the upload capacity. To sum up, the allocation of both on-demand and push-based services is significantly reliedon the dynamic data access patterns.

5.2. Definitions

Before going into the detailed procedures of ACDA, several preliminary definitions and policies are introduced as follows.First, we divide the database Dn into hot and cold data items according to the data access probability.

222 K. Liu, V.C.S. Lee / Transportation Research Part C 21 (2012) 214–229

Definition 5.1 (The set of hot and cold data items). Denote the access probability of data item din as p di

n

� �. The set of hot data

items is defined as Dhotn ¼ di

njp din

� �> 1jDn j

n o, while the set of cold data items is defined as Dcold

n ¼ dinjp di

n

� �6

1jDn j

n o, where jDnj

is total number of data items in the service set and jDnj ¼ Dhotn

��� ���þ Dcoldn

��� ���.Since the factor of data broadcast period has significant impact on the performance of push-based service, we define an

expected number of push channels which is supposed to ensure that the broadcast period of every push data item is no longerthan the dwell time t.

Definition 5.2 (Expected number of push channels). Given the push-based data set Dnp and the mean dwell time t of vehicles,

the expected number of push channels is defined as Kexpsp

��� ��� ¼ jDnpjt

l m.

Note that the value of jKexpsp j may be greater than the total number of service channels jKsj. Similarly, in the on-demand

service, it is expected that there is sufficient bandwidth to serve all the uploaded queries before their deadlines. We definean expected number of on-demand channels as follows:

Definition 5.3 (Expected number of on-demand channels). Given the on-demand data set Dno, the upload capacity C and the

vehicle arrival rate k, the expected number of on-demand channels is defined as Kexpso

�� �� ¼min C; k �P

din2Dno

p din

� �l m� �, where

k �P

din2Dno

p din

� �represents the on-demand query arrival rate.

To enable the algorithm to find an appropriate allocation point under different traffic environments, two rules with re-spect to the data movement between on-demand and push-based services are defined below. First, to avoid the limited up-link bandwidth become the bottleneck of the on-demand service, given an on-demand data set Dno, it is necessary to check

the value of query arrival rate k �P

din2Dno

p din

� �� �. In this regard, we define the following data movement rule to confine the

query arrival rate by moving data items from the on-demand data set Dno to the push-based data set Dnp, so that the queryuploading rate will not be too high to the upload capacity (C).

Rule 5.1. [Data Movement Rule 1 (from Dno to Dnp)] Given current on-demand data set Dno, if k �P

din2Dno

p din

� �> C, then find

the data item din from Dno which has the highest access probability p di

n

� �¼max p dj

n

� �jdj

n 2 Dno

n o� �, and move di

n from Dno

to Dnp (Dno ¼ Dno � din

n oand Dnp ¼ Dnp þ di

n

n o).

With the current data set Dnp and Dno, we can calculate the expected number of push and on-demand channels, Kexpsp

��� ��� and

Kexpso

�� ��. Then a tentative channel allocation can be obtained by jKspj ¼ jKsj �Kexp

spj jKexp

spj jþ Kexpsoj j (round to the nearest integer) and

jKsoj = jKsj � jKspj. Next, we should further examine the workload of the push-based service to avoid too many data itemsare allocated into the push-based data set Dnp. Accordingly, the following data movement rule is defined to confine the work-load of the push-based service by moving data items from Dnp to Dno.

Rule 5.2. [Data Movement Rule 2 (from Dnp to Dno)] Given current push-based data set Dnp, if the total data access probability

of push data items exceeds a certain threshold r (0 6 r 6 1), namely,P

din2Dnp

p din

� �> r, then find the data item di

n from Dnp

which has the lowest access probability p din

� �¼min p dj

n

� �jdj

n 2 Dnp

n o� �, and move di

n from Dnp to Dno

Dno ¼ Dno þ din

n oand Dnp ¼ Dnp � di

n

n o� �.

5.3. ACDA algorithm

With the above definitions and rules, the detailed procedure of ACDA is described as follows:

Step 1: InitializationInitialize the on-demand data set and the push-based data set with the cold data items and the hot data items respec-tively: Dno ¼ Dcold

n and Dnp ¼ Dhotn .

Step 2: Examine the overhead of query uploadingBased upon the current Dno, judge whether k �

Pdi

n2Dnop di

n

� �> C. If it is true, continue to execute Step 3. Otherwise, jump

to Step 4.Step 3: Move data items from Dno to Dnp

Execute the data movement rule 1 and update Dno repeatedly until k �P

din2Dno

p din

� �6 C.

Step 4: Tentative channel allocationCalculate jKexp

sp j and jKexpso j based upon the current data set Dnp and Dno respectively. Then, calculate the number of push

channels based upon the ratio of Kexpsp

��� ��� and Kexpso

�� ��: jKspj ¼ jKsj �Kexp

spj jKexp

spj jþ Kexpsoj j (round to the nearest integer).

K. Liu, V.C.S. Lee / Transportation Research Part C 21 (2012) 214–229 223

Step 5: Examine the workload of push-based service

Judge whetherP

din2Dnp

p din

� �> r. If it is true, go to Step 6. Otherwise, jump to Step 7.

Step 6: Move data items from Dnp to Dno

Execute the data movement rule 2 repeatedly untilP

din2Dnp

p din

� �6 r and get the updated Dnp and jKspj.

Step 7: Final data and channel allocationCalculate the number of on-demand channels (jKsoj = jKsj � jKspj) and return the final data set Dnp and Dno, as well as thechannel set Ksp and Kso.

The pseudo code of ACDA is shown as follows:ACDA Algorithm:

Step 1

1 Dhot

n ¼ ;;

2 Dcold

n ¼ ;;

3 for each di

n 2 Dn do� �

4 if p di

n 61jDn j thenn o

5

Dcoldn ¼ Dcold

n þ din ;

6

else n o 7 Dhot

n ¼ Dhotn þ di

n ;

8

end if 9 end for

10

Dno ¼ Dcoldn ;

11

Dnp ¼ Dhotn ;

Step 2 � �

12 while k �

Pdi

n2Dnop di

n > C do

Step 3 � � � �� �

13 find di

n which satisfies p din ¼max p dj

n jdjn 2 Dno ;

14

// update Dno and Dnpn o 15 Dno ¼ Dno � di

n ;n o

16 Dnp ¼ Dnp þ di

n ;

17

end while

Step 4 � � l m

18 Kexp

sp�� �� ¼ jDnp j

t ; � �l m� �

19 Kexp

so

�� �� ¼min C; k �P

din2Dno

p din ;

20

jKspj ¼ jKsj �Kexp

spj jKexp

spj jþ Kexpsoj j (round to the nearest integer);

Step 5 � �

21 while

Pdi

n2Dnpp di

n > r do

Step 6 � � � �� �

22 find di

n which satisfies p din ¼min p dj

n jdjn 2 Dnp ;

23

// update Dno and Dnpn o 24 Dno ¼ Dno þ di

n ;n o

25 Dnp ¼ Dnp � di

n ;

26

//update Ksp and Kexpsp

224 K. Liu, V.C.S. Lee / Transportation Research Part C 21 (2012) 214–229

27

Kexpsp

��� ��� ¼ jDnp jt

l m; � �l m� �

28

Kexpso

�� �� ¼min C; k �P

din2Dno

p din ;

29

jKspj ¼ jKsj �Kexp

spj jKexp

spj jþ Kexpsoj j (round to the nearest integer);

30

end while

Step 7

31 jKsoj = jKsj � jKspj; 32 return jKspj,jKsoj,Dnp and Dno;

As shown by the pseudo code, in Step 1, the algorithm traverses jDnj data items to classify the hot and cold data itemswith the complexity of O(jDnj). In Steps 2 and 3, the worst case is to move jDnj data items from Dno to Dnp and the complexityis O(jDnj). Step 4 requires a constant effort with the complexity of O(1). In Steps 5 and 6, the worst case is to move Dn dataitems from Dnp to Dno and the complexity is O(jDnj). Finally, Step 7 takes a constant effort with the complexity of O(1). There-fore, the computation complexity of ACDA is O(jDnj). Note that typical on-line scheduling algorithms have the same compu-tation complexity of O(jDnj) where jDnj is the number of data items in the database (Ng et al., 2008). In addition, the overheadof ACDA can be further reduced by implementing the algorithm in incremental fashion. For instance, when the data accesspattern changes, instead of checking the whole database again in Step 1, it is possible to move the affected data items be-tween the hot and cold data item sets. Similarly, in Steps 2, 3 and 5, 6, ACDA only needs to move the data items betweendifferent sets until the required conditions become true. So, the new allocation in fact can be incrementally adjusted fromthe old allocation. All in all, the proposed solution is practical in real-world systems and its scheduling overhead will notbe a hurdle of the system scalability.

6. Performance evaluation

6.1. Environments

The simulation environment is constructed based upon the system framework illustrated in Section 3.1 and it is imple-mented by CSIM19 (Schwetman, 2001). The basic flowchart of the system operation is shown in Fig. 3. When the simulationstarts, the system first collects the current traffic parameters including the mean vehicle arrival rate, the mean dwell timeand the data access pattern. These parameters can be estimated in real-time (Hu and Chen, 2002, 2005; Lin et al., 2004; Hu

a data access attemptgenerated by a vehicle

submit on-demandquery

in push-baseddata set

data broadcast in pushchannel within dwell time

Y

access succeeded

uploadsucceeded

Y

Y

access failed

N

N

N

data broadcast in on-demand channel within

dwell time

Y

N

startcollect parametersexecute the proposed algorithm

Fig. 3. Flowchart of system operation.

K. Liu, V.C.S. Lee / Transportation Research Part C 21 (2012) 214–229 225

et al., 1998). With the collected information, the proposed algorithm is executed to determine the data and channel alloca-tion. Each arriving vehicle will generate a data access attempt. According to the current data allocation, the requested dataitem is either in the push-based data set or in the on-demand data set. In the former case (push data item is requested), thevehicle only passively waits for the data on push channels. If the requested data item is broadcast during the dwell time ofthis vehicle, the data access is succeeded. Otherwise, the data access is failed. In the latter case (on-demand data item is re-quested), the vehicle needs to submit an explicit query from the uplink channel to access the on-demand data item. If theexplicit query is discarded when competing for the uplink bandwidth, the data access is failed. Only the successfully up-loaded queries are pended in the service queue. Then, the RSU broadcasts corresponding data items to serve the outstandingqueries based on a certain scheduling mechanism, such as EDF (Earliest Deadline First) (Xuan et al., 1997). The data access issucceeded only when the requested data item is scheduled to broadcast within the dwell time of the vehicle. As defined inSection 3.2, we use the metric of deadline miss ratio to quantitatively evaluate system performance in the following simula-tion study.

6.2. Simulation results

In this section, we evaluate the performance of ACDA in dynamic traffic environments. The simulation results were ob-tained when the system was in a steady state and the simulations continued until a confidence interval of 0.95 with half-widths of less than 5% about the mean was achieved.

For performance comparison, we include the results obtained in optimal allocation points (OPT). The idea of obtaining anoptimal point for a certain input setting is to enumerate all the possible combinations of data and channel allocation (thereare jDnj � jKsj combinations) by repeating the simulation jDnj � jKsj times. Each time the simulation tries a different combi-nation and computes a deadline miss ratio, and finally the best allocation point is found. Note that OPT is not applicable inon-line applications because it requires future knowledge of the coming traffic to repeat the simulation. Accordingly, it canbe only served as a benchmark for performance evaluation. To justify the superiority of ACDA, the pure on-demand (PULL)and the pure push-based (PUSH) broadcast schemes are also included in our simulation. During the data dissemination, theFLAT (Saxena and Pinottti, 2005) is adopted in the push-based broadcast, while EDF (Earliest Deadline First) (Xuan et al.,1997) is adopted in the on-demand broadcast.

To emphasize the general applicability of our analysis, we do not specify the absolute values of the data size and the chan-nel bandwidth, but rather, use broadcast ticks as the unit for performance evaluation. Similarly, we also use broadcast ticksto measure the dwell time of passing vehicles. Commonly used simulation setting in data dissemination systems (Kang et al.,2007; Zhang et al., 2007; Xu et al., 2006; Hu and Chen, 2005) are adopted to capture the key performance characteristics inroadside-to-vehicle communication. To produce a stressful setting for performance evaluation, the default parameters areset as follows: Dn ¼ 80; h ¼ 0:8; l ¼ 1

8 ; k ¼ 18 and C = 10. Except for explicit statements, simulations are conducted underthis default setting.

� Effect of vehicle arrival rate

Fig. 4 examines the performance of ACDA under different vehicle arrival rates. Since a higher vehicle arrival rate implies aheavier workload in data access, the deadline miss ratio of all the algorithms is getting higher, excepting for the pure push-based broadcast. This is because, as analyzed in Section 5.1, with an increasing of the total number of data access attempts,the number of both successful and failed data access increases proportionally in push-based broadcast, given a constantdeadline miss ratio. As shown in Fig. 4, ACDA outperforms both PULL and PUSH remarkably and achieves between 90.74%and 100% of the optimal results.

Fig. 4. Deadline miss ratio under different vehicle arrival rates.

Fig. 5. Deadline miss ratio under different dwell time.

Fig. 6. Deadline miss ratio under different data access patterns.

226 K. Liu, V.C.S. Lee / Transportation Research Part C 21 (2012) 214–229

� Effect of vehicle dwell time

Fig. 5 examines the performance of ACDA under different vehicle dwell time. Since longer dwell time gives a looser dead-line for data dissemination, the deadline miss ratio of all the algorithms is getting lower with increasing of the dwell time. Asshown in Fig. 5, ACDA consistently outperforms both PULL and PUSH and achieves between 95.95% and 100% of the optimalresults.

� Effect of data access pattern

Fig. 6 examines the performance of ACDA under different data access patterns. As demonstrated in Lee et al. (2006), agood scheduling is supposed to take advantage of skewed data access pattern. This is because when the data access is gettingmore skewed, there is higher potential to satisfy more requests in each broadcast. However, due to inappropriate data andchannel allocation, neither PULL nor PUSH can get benefit from the skewed data access pattern. As shown in Fig. 6, the supe-riority of ACDA is getting notable with an increasing value of h and it achieves between 96.53% and 100% of the optimalresults.

7. Conclusion

With efforts from different parties including automobile manufacturers, governments, and academia in doing researchesand developing infrastructures in vehicular networks, numerous potential applications like road safety and value-added ser-vices can be envisioned in the near future. In this work, we presented a RSU-based data dissemination framework and dem-onstrated that unique characteristics in vehicular networks brought new challenges in data dissemination. Then, ananalytical model was derived to reveal the importance of striking a balance between push-based and on-demand services

K. Liu, V.C.S. Lee / Transportation Research Part C 21 (2012) 214–229 227

in supporting data dissemination in dynamic vehicular networks. Motivated by the analytical results, we proposed an on-line algorithm to implement dynamic channel and data allocation so that the data dissemination can be adaptable to theever changing traffic environments. Finally, a series of simulation results demonstrated satisfactory performance of the pro-posed algorithm.

Appendix A. Proof of Eq. (5)

First to calculate the probability that the scheduler selects jKsoj data items in a broadcast tick, whilst none of the selected

data items is dino. Denote this probability as O1. There are jDnoj � 1

jKsoj

� �combinations for choosing jKsoj data items from the set

Dno � dino

n o, and O1 is the summation of the probability of each combination:

O1 ¼XjDno j�1jKso j

� �

s¼1

YjKso j

m¼1

asm

!

where as1; a

s2; . . . as

jKso j

n ois the sth 1 6 s 6

jDnoj � 1jKsoj

� �� �combination of choosing jKsoj data items from the set of

p d1no

� �; p d2

no

� �; . . . p djDno j

no

� �n o� p di

no

� �n on o(1 6 i 6—Dno—) and

QjKso jm¼1as

m is the probability of the sth combination.

Next, considering the restriction of on-demand broadcast, the selected jKsoj data items must be different in a broadcast

tick. Denote the probability of satisfying such a selection as O2. There are jDnojjKsoj

� �combinations for choosing jKsoj data items

from the set Dno and O2 is the summation of the probability of each combination:

O2 ¼XjDno jjKso j

� �

q¼1

YjKso j

r¼1

bqr

!

where bq1; b

q2; . . . bq

jKso j

n ois the qth 1 6 q 6 jDnoj

jKsoj

� �� �combination of choosing jKsoj data items from the set of

p d1no

� �; p d2

no

� �; . . . p djDno j

no

� �n oand

QjKso jr¼1 bq

r is the probability of the qth combination.

Based on the above discussion, the probability that dino is not selected in a broadcast tick is given by:

Odino¼ O1

O2¼P jDno j�1

jKso j

� �s¼1

QjKso jm¼1as

m

� �P jDno j

jKso j

� �q¼1

QjKso jr¼1 bq

r

� � ðjDnoj > jKsojÞ

Appendix B. Calculation of Eq. (8)

Based on Eq. (7),

E½Rðt; rÞ� ¼XjDnp j

i¼1

p dinp

� �� Rdi

npðtÞ þ

XjDno j

i¼1

p dino

� �� Rdi

noðt; rÞ

As l dinp

� �¼ jDnp jjKsp j and f(t) = le�lt, based on Eq. (2),

RdinpðtÞ ¼

Z jDnp jjKsp j

01� t

jDnp jjKsp j

0@

1A � le�lt dt ¼

Z jDnp jjKsp j

0le�lt dt �

Z jDnp jjKsp j

0

t � jKspjjDnpj

� le�lt dt ¼ 1� e�ljDnp jjKsp j þ jKspj

jDnpj�Z jDnp j

jKsp j

0tdðe�ltÞ

¼ 1� e�ljDnp jjKsp j þ jKspj

jDnpjjDnpjjKspj

� e�ljDnp jjKsp j þ 1

l� e�ljDnp j

jKsp j � 1l

� �¼ 1þ 1

l� jKspjjDnpj

e�ljDnp jjKsp j � 1

� �ðaÞ

As f(s) = ke�k�s, based on Eq. (6),

228 K. Liu, V.C.S. Lee / Transportation Research Part C 21 (2012) 214–229

Rdinoðt; sÞ ¼

Z 1

0

Z 1

NOdi

no

� �tke�k�s dsþ

Z N

0Odi

no

� �t� sNþ 1� s

N

� �ke�k�sds

� �le�lt dt

¼Z 1

0Odi

no

� �t� e�k�N þ 1� e�k�N �

Odino

� �t� 1

N� N þ 1

k

� �e�k�N � 1

k

� �0B@

1CAle�lt dt

¼ 1� e�k�N þN þ 1

k

� �N

� e�k�N � 1N � k

� �Z 1

0le�lt dt þ e�k�N � 1�

N þ 1k

� �N

� �þ 1

N � k

� �Z 1

0Odi

no

� �tle�lt dt

¼ 1� 1N � kþ

1N � k � e

�k�N þ 1N � k � ð1� e�k�NÞ

Z 1

0Odi

no

� �tle�lt dt

¼ 1þ 1N � k � ð1� e�k�NÞ

Z 1

0Odi

no

� �tle�lt dt � 1

� �

where

N ¼PjDno j

i¼1 p dino

� �C

and

Z 1

0Odi

no

� �tle�lt dt ¼ �

Z 1

0Odi

no

� �tdðe�ltÞ ¼ � Odi

no

� �t� e�lt

����1

0þZ 1

0e�lt d Odi

no

� �t¼ 1þ

Z 1

0e�lt d Odi

no

� �t

¼ 1þ ln Odino

Z 1

0Odi

no

� �te�lt dt ¼ 1þ 1

lln Odi

no�Z 1

0Odi

no

� �tle�lt dt )

Z 1

0Odi

no

� �tle�lt dt

¼ ll� ln Odi

no

So,

Rdinoðt; sÞ ¼ 1þ 1

N � k � ð1� e�k�NÞ ll� ln Odi

no

� 1

!¼ 1þ CPjDno j

i¼1 p dino

� �� k� 1� e�k�

PjDno ji¼1

p dinoð Þ

C

!l

l� ln Odino

� 1

!ðbÞ

According to (a) and (b):

E½Rðt; sÞ� ¼XjDnp j

i¼1

p dinp

� �� Rdi

npðtÞ þ

XjDno j

i¼1

p dino

� �� Rdi

noðt; sÞ

¼XjDnp j

i¼1

p dinp

� �� 1þ 1

l� jKspjjDnpj

e�ljDnp jjKsp j � 1

� �� �þXjDno j

i¼1

p dino

� �� 1þ 1

N � k � ð1� e�k�NÞ ll� ln Odi

no

� 1

! !

where

N ¼PjDno j

i¼1 p dino

� �C

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