Scheduling Temporal Data for Realtime Requests inRoadsidetoVehicle Communication
Kai Liu
∗
Victor C.S. Lee
∗
Joseph K.Y. NG
†
Sang H. Son
‡
∗
Dept of Computer Science, City University of Hong Kong, Kowloon, Hong KongEmail: kevin.liu@cityu.edu.hk, csvlee@cityu.edu.hk
†
Dept of Computer Science, Hong Kong Baptist University, Kowloon, Hong KongEmail:jng@comp.hkbu.edu.hk
‡
Dept of Information and Communication Engineering, DGIST, Daegu, KoreaEmail:son@dgist.ac.kr
Abstract
—Recent advances in wireless communication technologies have spawned many new applications in vehicularnetworks. Data dissemination via roadsidetovehicle communication is a vital approach to enabling most of these applications. In this work, we investigate in the scenario wheredata items are broadcasted from the roadside unit (RSU)in response to requests submitted by passing vehicles. Dataitems are associated with temporal constraints and updatedperiodically to reﬂect dynamic states of trafﬁc information.Each request may ask for multiple temporal data items, andit is associated with a deadline, which may either be speciﬁedby the driver or imposed by the time when the vehicle drivesthrough the service region. In particular, we develop a realtime data dissemination model based on roadsidetovehiclecommunication by formulating the timeconstraint of requestsand the consistency requirement of retrieving temporal dataitems. On this basis, we propose an online scheduling algorithmto enhance the system performance in terms of maximizingrequest service and improving bandwidth utilization. Lastly, webuild a simulation model to evaluate the algorithm performancein a variety of situations. Experimental results demonstratethat the proposed algorithm outperforms existing algorithmssigniﬁcantly in both request serving and bandwidth utilization.
I. I
NTRODUCTION
Recently, there has been much progress on developingcommunication technologies in vehicular networks. In particular, the dedicated short range communication (DSRC)[1] protocol stack is being standardized by the IEEE 1609working group, which will be used exclusively for vehicularcommunications. It can be envisioned that many innovativeintelligent transportation systems (ITS), such as roadwayreservation systems [2], intelligent speed adaption systems[3] and autonomous intersection management systems [4],etc., will beneﬁt from the efﬁcient data dissemination invehicular networks. Typically, there are two communicationmodels in ITS: intervehicle and roadsidetovehicle communications [5]. In the intervehicle communication model,vehicles share information with each other via the onboardunit (OBU). One the other hand, in the roadsidetovehiclecommunication model, information is provided from theroadside unit (RSU), which is a ﬁxed infrastructure installedalong the road. In practice, the two communication modelscan cooperate with each other. For example, vehicles canretrieve data items from the RSU within its service region,while vehicles can also share information among themselvesvia vehicletovehicle communication. In this work, we focuson data dissemination in the roadsidetovehicle communication model.Although approaches for efﬁcient data dissemination havebeen extensively studied in conventional mobile computingsystems ([6], [7], [8], [9]), unique characteristics in vehicularnetworks bring us new challenges. First, due to the limitedcommunication range covered by the RSU, passing vehiclescannot retrieve data items when driving out of the serviceregion. In addition, unlike many mobile applications, wherea user may be able to stay a relatively longer time in theservice region for data access (i.e. a user carries a smartphone to retrieve data items from a WIFI access point),the high mobility of vehicles imposes tight deadlines inroadsidetovehicle data dissemination. Second, in vehicular networks, a wealth of information changes frequentlyover time, such as trafﬁc conditions, parking informationand vehicle locations, etc. Accordingly, the values of dataitems have to be updated to reﬂect the true status of theenvironment. Retrieving outdated data items cannot satisfythe request, and it is even potentially dangerous for somesafetycritical applications. Therefore, scheduling temporaldata items is another nontrivial issue in roadsidetovehiclecommunication. Lastly, it is common for a request askingfor multiple dependent data items in many ITS applications.For instance, in trafﬁc information systems, a driver mayenquire the trafﬁc condition of different roads simultaneouslyto decide which route to take. In these applications, the querycannot be fully processed until all the requested data itemsare retrieved. With the above motivations, there is a pressingneed to design an efﬁcient scheduling algorithm in roadsidetovehicle communication systems to meet the dramaticallyincreasing demand for realtime data services and enhancethe overall system performance.The main contributions of this work are outlined asfollows. First, we develop a realtime roadsidetovehicledata dissemination model by formulating the timeconstraintof requests and the consistency requirement of retrievingtemporal data items. Second, we propose an online scheduling algorithm, which aims at satisfying as many requests aspossible by exploiting the broadcast effect and utilizing the
2013 IEEE International Conference on Embedded and RealTime Computing Systems and Applications
297
9781479908509/13/$31.00 ©2013 IEEE
bandwidth efﬁciently. Third, we build a simulation modelfor performance evaluation. Two representative realtimescheduling algorithms, EDF (Earliest Deadline First) [10]and SIN (Slack time Inverse Number of pending requests)[9], are implemented for performance comparison. A comprehensive simulation study demonstrates that the proposedalgorithm can outperform existing solutions signiﬁcantly.The rest of this paper is organized as follows. Section IIreviews the related work. In Section III, we develop a realtime data dissemination model and formulate the problem.In Section IV, we propose a new scheduling algorithm.In Section V, we build the simulation model and give anextensive performance evaluation. Last, we conclude thiswork and discuss future research directions in Section VI.II. R
ELATED
W
ORK
Current research on data dissemination in vehicular networks largely focused on solving communication qualityrequirements at the MAC layer ([11], [12], [13], [14]).Fujimura and Hasegawa [11] proposed a Vehicle and Roadside Collaborative MAC protocol (VRCP) to support bothroadsidetovehicle and vehicletovehicle communications.Rather than considering data scheduling, the protocol designed two channel access modes, and investigated on modeswitching mechanisms. In particular, one is adhoc mode(ModeA) with nonpersistent CSMA scheme for decentralized vehicletovehicle communication. The other is infrastructure mode (ModeI) with TDMA scheme for centralizedroadsidetovehicle communication. Maeshima et al. [12]designed a MAC protocol for supporting emergency messagedelivery in roadsidetovehicle communication systems. Thegeneral idea is that, whenever an emergency notiﬁcationoccurred on the control channel, the transmission of generalinformation on the service channel would be suspended toensure timely delivery of emergency messages. Jhang andLiao [13] proposed a Proxybased Vehicle to RSU (PVR)communication protocol based on IEEE 802.11 DistributedCoordination Function (DCF). It is designed to mitigatequery upload contentions by electing proxy vehicles to helpthe data upload for other vehicles. Nonproxy vehicles whichattempt to communicate with the RSU must forward theirdata items to a proxy vehicle, so that it relieves the contentionfor the uplink channel and improves the throughput of thesystem. Mak et al. [14] proposed a coordinated MAC modein the presence of an RSU to compliment with ad hocapproaches when no RSU is available. It aims to improveperformance for both safety and nonsafety applications bydesigning a multichannel coordination mechanism, whichis used to minimize collisions between vehicletovehicleand roadsidetovehicle communications. The above effortsprovided solid basis with respect to improving communication qualities at the MAC layer. Nevertheless, none of themaddressed data scheduling problems from the applicationpoint of view.The data scheduling problem has been extensively examined in mobile computing environments. For nonrealtime systems, there are a number of classical schedulingalgorithms. FCFS (First Come First Served) [15] broadcastsdata items sequentially according to their arrival order. SRPT(Shortest Remaining Processing Time) [16] chooses the dataitem with the shortest service time to broadcast. Wong [17]proposed two wellknown strategies for scheduling requestsin ondemand broadcast systems: MRF (Most RequestedFirst) and LWF (Longest Wait First). MRF broadcasts thedata item which has the largest number of pending requests toaccount for the productivity of broadcast. LWF calculates thetotal time that all pending requests for a data item have beenwaiting. The data item with the longest total waiting timeis chosen for broadcast. Aksoy and Franklin [8] proposed alow overhead and scalable scheduling algorithm called RXW(Number of pending Requests Multiply Waiting time). Itcalculates the number of pending requests for a data itemmultiplied by the amount of time that the oldest outstandingrequest for that data item has been waiting. At each broadcasttick, the request with the maximum RXW value will bechosen. RXW combines the beneﬁts of MRF and FCFS toenhance scheduling performance. It has been demonstratedthat it is the most effective algorithm in minimizing theaverage response time for nonrealtime requests [18].In realtime scheduling, EDF (Earliest Deadline First)[10] is one of the foremost classical scheduling algorithms,and it has been adopted into ondemand broadcast systems.The algorithm selects and broadcasts the data item withthe shortest remaining lifetime to cater for the urgency of requests. Recently, an online scheduling algorithm for timecritical ondemand broadcast called SIN (Slack time InverseNumber of pending requests) [9] has been proposed. It ismotivated by two existing strategies: EDF, which considersthe urgency of requests, and MRF, which considers theproductivity of data broadcast. It has been demonstrated thatSIN can outperform other realtime algorithms signiﬁcantlyin ondemand broadcast environments. In this study, wewill implement these two representative realtime schedulingalgorithms for performance comparison.III. P
RELIMINARIES
A. System model
The roadsidetovehicle data dissemination model isshown in Figure 1. The system characteristics are summarized as follows.
•
Ondemand broadcast: The RSU is installed at a ﬁxedposition (i.e. at a road intersection) in providing information services to passing vehicles. The OBU ismounted on the vehicle, which enables the vehicleto submit requests and retrieve data items from theRSU. The circle represents the radio coverage of theRSU, which is called the
service region
. When thevehicle enters the service region, it can submit requeststo the RSU via the uplink channel (i.e. the controlchannel as deﬁned in IEEE 1609.4 [19]). Accordingto certain scheduling algorithms, the RSU selects anddisseminates data items from the local database to servepending requests via the downlink channel (i.e. the
298
DownlinkChannel
) ) ) ) ) ) ) ) ) ) ) ) ) ) )
) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
Wired NetworksRoadside Unit Server
Updates
Processing Unit
Database
Queries
UplinkChannel
) ) ) ) ) ) ) ) ) ) ) ) ) ) )
) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
Fig. 1. System model of roadsidetovehicle data dissemination
service channel as deﬁned in IEEE 1609.4 [19]). This isknown as the
ondemand broadcast
environment [20].
•
Temporal data item: In vehicular environments, a wealthof information changes frequently over time, such astrafﬁc conditions, available parking slots and locationbased services, etc. In order to maintain such highlydynamic information, the RSU is connected to the wirednetwork to form a
backbone network
, so that the dataitems stored in the local database can be kept uptodate by the sensors and information providers from thebackbone network. In this model, we consider that thesystem updates the values of data items periodically. Insuch a manner, a data item has multiple versions andeach version only valid for a period of time, which isknown as the
temporal data item
[21]. In other words,once an update is installed for a data item, a new versionis created and its old version becomes invalid.
•
Realtime multiitem request: In typical ITS applications, it is common for the driver to submit requestsasking for multiple dependent data items. For instance,drivers may enquire the trafﬁc condition of differentroads simultaneously to decide which route to take. Inthese applications, broadcasting part of the requesteddata items cannot satisfy the request and the query cannot be fully processed until all the requested data itemsare received. In addition, the vehicle cannot retrieve dataitems once it leaves the service region. This imposesa deadline to each request [22]. Speciﬁcally, a requestcan be satisﬁed only if all its requested data items areretrieved before its deadline expires. We call this
realtime multiitem request
.
B. Problem Formulation
The set of temporal data items in the database is denotedby
D
=
{
d
1
,
d
2
,
···
,
d

D

}
, where

D

is the total number of data items. Each temporal data item
d
i
(1
≤
i
≤ 
D

) hasmultiple versions over time due to the update, denoted by
d
i
(
j
)
(
j
=
1
,
2
,
3
···
), and each version of
d
i
(
j
)
is characterizedby a 3tuple:
<
V
,
U
,
E
>
, where
V
(
d
i
(
j
)
)
is the value of
d
i
(
j
)
;
U
(
d
i
(
j
)
)
is the update time of the current version; and
E
(
d
i
(
j
)
)
is the expiry time of the current version. At time
t
,
V
(
d
i
(
j
)
)
is valid only if
U
(
d
i
(
j
)
)
≤
t
<
E
(
d
i
(
j
)
)
. After thetime of
E
(
d
i
(
j
)
)
, a new version
d
i
(
j
+
1
)
will be created, andthe values
<
V
,
U
,
E
>
will be updated accordingly. Giventhe update interval
l
(
d
i
)
, the expiry time can be representedby
E
(
d
i
) =
U
(
d
i
)+
l
(
d
i
)
. For the sake of easier expressionand emphasizing the dynamic attribute of the values of
U
(
d
i
)
and
E
(
d
i
)
, we denote
U
(
d
i

t
)
as the update time of
d
i
in itsversion at time
t
. Similarly, we denote
E
(
d
i

t
)
as the expirytime of
d
i
in its version at time
t
. Last, the time taken tobroadcast a data item is denoted by
τ
, which is referred toas the
service time
.The request
Q
is characterized by a 3tuple:
<
RD
,
ST
,
DL
>
. For the
m
th request
Q
m
(
m
=
1
,
2
,
3
···
),
RD
(
Q
m
)
is the set of data items requested by
Q
m
(
RD
(
Q
m
)
⊆
D
), which is represented by
RD
(
Q
m
) =
{
d
1
m
,
d
2
m
,
···
d

RD
(
Q
m
)

m
}
, where

RD
(
Q
m
)

is the number of data items requested by
Q
m
(1
≤ 
RD
(
Q
m
)
 ≤ 
D

), and
d
nm
∈
D
(1
≤
n
≤ 
RD
(
Q
m
)

).
ST
(
Q
m
)
is the time when
Q
m
is submitted.
DL
(
Q
m
)
is the deadline of
Q
m
.In order to satisfy a request asking for multiple temporaldata items, the request must read the versions of the requireddata items with respect to the same time instance, which isdetermined by the time when the ﬁrst data item is broadcastfor this request. Accordingly, the three conditions to serve arequest are stated as follows:
•
The broadcast time of each data
d
nm
for
Q
m
, denotedby
BT
Q
m
(
d
nm
)
, should be later than the time when
Q
m
is submitted, because the vehicle only monitors andretrieves data items after submitting the request. Denote
FBT
Q
m
as the time to broadcast the ﬁrst data item for
Q
m
, the ﬁrst condition is represented by:
FBT
Q
m
>
ST
(
Q
m
)
(1)where
FBT
Q
m
=
min
(
BT
Q
m
(
d
nm
))
for
∀
d
nm
(1
≤
n
≤
RD
(
Q
m
)

).
•
Each requested data
d
nm
has to be retrieved before therequest deadline
DL
(
Q
m
)
. The retrieval time of
d
nm
iscalculated by
BT
Q
m
(
d
nm
)+
τ
, where
τ
is the service time.Denote
LBT
Q
m
as the time to broadcast the last data itemfor
Q
m
, the second condition is represented by:
LBT
Q
m
+
τ
≤
DL
(
Q
m
)
(2)where
LBT
Q
m
=
max
(
BT
Q
m
(
d
nm
))
for
∀
d
nm
(1
≤
n
≤
RD
(
Q
m
)

).
•
All the retrieved data items have to be valid by the timewhen the request is processed (i.e. the time when thelast data item is retrieved, which is
LBT
Q
m
+
τ
). At time
FBT
Q
m
, each requested data item
d
nm
is associated witha corresponding expiry time, denoted by
E
(
d
nm

FBT
Q
m
)
.Given the version of each data item at time
FBT
Q
m
,denote
EE
Q
m
(
FBT
Q
m
)
as the earliest expiry time of the requested data items by
Q
m
, the third condition isrepresented by:
LBT
Q
m
+
τ
≤
EE
Q
m
(
FBT
Q
m
)
(3)
299
Fig. 2. Timing example to serve a request
where
EE
Q
m
(
FBT
Q
m
) =
min
(
E
(
d
nm

FBT
Q
m
))
for
∀
d
nm
(1
≤
n
≤ 
RD
(
Q
m
)

) in their version at time
FBT
Q
m
.To have better understand, Figure 2 illustrates how arequest can be satisﬁed by showing the relationship of thetimings.Suppose
Q
m
is submitted at
t
3
, and two data items arerequested. That is,
RD
(
Q
m
) =
{
d
1
m
,
d
2
m
}
and

RD
(
Q
m
)

=
2.The deadline of
Q
m
is at
t
8
. The
j
th version of
d
1
m
isgenerated at
t
1
. Given the update interval
l
(
d
1
m
)
, the (
j
+
1)th and (
j
+
2) th versions of
d
1
m
will be generated at
t
4
and
t
7
respectively. Similarly, the
k
th version of
d
2
m
is generated at
t
2
, and given its update interval of
l
(
d
2
m
)
, the (
k
+
1) th versionof
d
2
m
will be generated at
t
9
. In order to serve
Q
m
, accordingto the ﬁrst condition, the broadcast time of
d
1
m
and
d
2
m
shouldbe later than
t
3
. In this example,
d
1
m
is the ﬁrst data itembroadcasting for
Q
m
, which gives
FBT
Q
m
=
t
5
, and it satisﬁesthat
t
5
>
t
3
. According to the second condition, both
d
1
m
and
d
2
m
have to be retrieved before the request deadline
t
8
. In thisexample,
d
2
m
is the last data item broadcasting for
Q
m
, whichgives
LBT
Q
m
=
t
6
, and it satisﬁes that
t
6
+
τ
≤
t
8
. Accordingto the third condition, at
t
5
,
d
1
m
is in its (
j
+
1) th version,and
d
2
m
is in its
k
th version. So, we have
E
(
d
1
m
(
j
+
1
)

t
5
) =
t
7
and
E
(
d
2
m
(
k
)

t
5
) =
t
9
. Accordingly, the earliest expiry time
EE
Q
m
(
FBT
Q
m
) =
min
(
t
7
,
t
9
)
, which is
t
7
. In this example,
t
6
+
τ
≤
t
7
, which satisﬁes the third condition. With thesatisfaction of the three conditions,
Q
m
can be satisﬁed bysuch a scheduling. Note that the broadcast sequence of therequested data items will not inﬂuence the service to
Q
m
(i.e.broadcasting
d
2
m
before
d
1
m
can also satisfy
Q
m
).However, note that
Q
m
cannot be satisﬁed if any of itsrequested data item is broadcast during
[
t
3
,
t
4
]
(suppose thetime duration between
t
3
and
t
4
is less than the time tobroadcast two data items, namely,
[
t
3
,
t
4
]
<
2
·
τ
). This isbecause as long as
t
3
<
FBT
Q
m
<
t
4
,
d
1
m
will be in its
j
th version, and hence
E
(
d
1
m
(
j
)

FBT
Q
m
) =
t
4
. In such a case,the earliest expiry time
EE
Q
m
(
FBT
Q
m
) =
min
(
t
4
,
t
9
)
, whichis
t
4
. However, it can never satisfy that
LBT
Q
m
+
τ
≤
t
4
because
[
t
3
,
t
4
]
<
2
·
τ
. Therefore, broadcasting either
d
1
m
or
d
2
m
during
[
t
3
,
t
4
]
will violate the third condition, causing theunsatisfactory of
Q
m
.With the above knowledge, this work is dedicated todesigning an online algorithm for scheduling realtimerequests with temporal data items in roadsidetovehicledata dissemination systems. The objective is to enhance theoverall system performance in terms of efﬁcient utilizationof the broadcast bandwidth, and satisfying as many requestsas possible. The primary notations used in this paper aresummarized in Table I.IV. PSU S
CHEDULING
A
LGORITHM
In this section, we propose an online scheduling algorithm, which considers the request characteristics of
Productivity
,
Status
and
Urgency
(PSU) in scheduling. To beelaborated below, by incorporatingthese three characteristics,PSU is able to exploit broadcast effect, improve bandwidthutilization, and enhance the service chance. Before goinginto the detailed procedures of PSU, several preliminarydeﬁnitions are stated as follows.
Deﬁnition 1:
Unserved set of a request: At time
t
, theset of unserved data items of a request
Q
m
is represented by
US
Q
m
(
t
) =
{
d
1
m
,
d
2
m
,
···
d

US
Qm
(
t
)

m
}
, where

US
Q
m
(
t
)

is thenumber of unserved data items (0
≤
US
Q
m
(
t
)
≤
RD
(
Q
m
)

),and
US
Q
m
(
t
)
⊆
RD
(
Q
m
)
.Given a pending request
Q
m
, if none of its requested dataitems have been retrieved (
US
Q
m
(
t
) =
RD
(
Q
m
)
,
Q
m
is calledas the
unserved request
. In contrast, if parts of the requesteddata items have been retrieved (
US
Q
m
(
t
)
⊂
RD
(
Q
m
)
and
US
Q
m
(
t
)
=
φ
),
Q
m
is called as the
partiallyserved request
.Recall that each multiitem request is associated with adeadline. Meanwhile, each requested data item is associatedwith an expiry time. Therefore, there is a practical timebound to serve a request when considering both the requestdeadline and the data expiry time. Moreover, for unservedrequests and partiallyserved requests, they have differentattributes in terms of the time bound. In the following, weanalyze the time bound for these two categories of requests.First, we deﬁne the
tentative time bound
for the unservedrequest. This is the time bound used to indicate that if anunserved request would start its service at time
t
, then whatis the latest time to complete the service.
Deﬁnition 2:
Tentative time bound: At time
t
, if
Q
m
is an unserved request, the tentative time bound for
Q
m
(
TTB
Q
m
(
t
)
) is either its request deadline (
DL
(
Q
m
)
), or theearliest expiry time of its requested data items at time
t
(
EE
Q
m
(
t
)
), whichever is earlier. That is,
TTB
Q
m
(
t
) =
min
(
DL
(
Q
m
)
,
EE
Q
m
(
t
))
, where
EE
Q
m
(
t
) =
min
(
E
(
d
nm

t
))
for
∀
d
nm
(1
≤
n
≤ 
RD
(
Q
m
)

) in their versions at time
t
.
TTB
Q
m
(
t
)
is not the ﬁnalized time bound of
Q
m
, and thevalue of
TTB
Q
m
(
t
)
may change with
t
. The reason is that, ithas not yet determined to serve
Q
m
at
t
. Although the requestdeadline
DL
(
Q
m
)
is a constant, the value of
EE
Q
m
(
t
)
mayvary with time. Therefore, at different scheduling points, thedynamic value of
EE
Q
m
(
t
)
may result in different
TTB
Q
m
(
t
)
.Considering the example shown in Figure 2, if
t
is in
[
t
3
,
t
4
]
, then
TTB
Q
m
(
t
) =
min
(
E
(
d
1
m
(
j
)

t
)
,
DL
(
Q
m
))
, which is
t
4
. In contrast, if
t
is in
[
t
7
,
t
8
]
, then
TTB
Q
m
(
t
)
changes tomin
(
E
(
d
2
m
(
k
)

t
)
,
DL
(
Q
m
))
, which is
t
8
.Note that the tentative time bound is only the attributeof unserved requests. As soon as the service starts for
Q
m
,the versions of its requested data items, as well as thecorresponding expiry time of these data items have beendetermined. In other words, for any requests which have been
300
TABLE IS
UMMARY OF NOTATIONS
Notations Descriptions Notes
D
set of temporal data items
D
=
{
d
1
,
d
2
,
···
,
d

D

}
d
nm
the
n
th data requested by
Q
m
d
nm
∈
DU
(
d
i

t
)
update time of
d
i
in its version at
t U
(
d
i

t
)
≤
t E
(
d
i

t
)
expiry time of
d
i
in its version at
t E
(
d
i

t
)
>
t l
(
d
i
)
update interval of
d
i
U
(
d
i

t
)+
l
(
d
i
) =
E
(
d
i

t
)
τ
service time of a data item
RD
(
Q
m
)
set of data items requested by
Q
m
RD
(
Q
m
) =
{
d
1
m
,
d
2
m
,
···
d

RD
(
Q
m
)

m
}
DL
(
Q
m
)
deadline of
Q
m
BT
Q
m
(
d
nm
)
broadcast time of
d
nm
for
Q
m
FBT
Q
m
time to broadcast the ﬁrst data for
Q
m
FBT
Q
m
=
min
(
BT
Q
m
(
d
nm
))
EE
Q
m
(
t
)
earliest expiry time of the requested data
EE
Q
m
(
t
) =
min
(
E
(
d
nm

t
))
US
Q
m
(
t
)
unserved set of
Q
m
US
Q
m
(
t
)
⊆
RD
(
Q
m
)
TTB
Q
m
(
t
)
tentative time bound for an unserved
Q
m
TTB
Q
m
(
t
) =
min
(
DL
(
Q
m
)
,
EE
Q
m
(
t
))
DTB
Q
m
determined time bound for a partiallyserved
Q
m
DTB
Q
m
=
min
(
DL
(
Q
m
)
,
EE
Q
m
(
FBT
Q
m
))
SQ
(
t
)
set of schedulable requests
EDP
d
i
(
t
)
effective data productivity of
d
i
ERP
Q
m
(
t
)
effective request productivity of
Q
m
scheduled to serve, their time bounds have been determined.In view of this, we deﬁne the
determined time bound
for thepartiallyserved request as follows.
Deﬁnition 3:
Determined time bound: If
Q
m
is apartiallyserved request, and the time to broadcast theﬁrst data item for
Q
m
is
FBT
Q
m
, then the determinedtime bound for
Q
m
(
DTB
Q
m
) is either its request deadline
DL
(
Q
m
)
, or the earliest expiry time of its requested dataitems at time
FBT
Q
m
(
EE
Q
m
(
FBT
Q
m
)
), whichever is earlier. That is,
DTB
Q
m
=
min
(
DL
(
Q
m
)
,
EE
Q
m
(
FBT
Q
m
))
, where
EE
Q
m
(
FBT
Q
m
) =
min
(
E
(
d
nm

FBT
Q
m
))
for
∀
d
nm
(1
≤
n
≤
RD
(
Q
m
)

) in their versions at time
FBT
Q
m
.Note that
DTB
Q
m
is a determined value, which will notchange with time. At each scheduling point, the system mayhave both unserved and partiallyserved pending requests.In order to check whether a request has the chance to besatisﬁed at time
t
, we deﬁne the
schedulable request
(
SQ
(
t
)
)as follows.
Deﬁnition 4:
Schedulable request: At time
t
, denote
SQ
(
t
)
as the set of requests which are schedulable. It isconstructed by the following two subsets of requests (
SQ
1
(
t
)
and
SQ
2
(
t
)
):
•
Case a):
Q
m
is an unserved request. It is schedulableif
Q
m
can retrieve all of its requested data items before the tentative time bound
TTB
Q
m
(
t
)
. The requestsubset is represented by
SQ
1
(
t
) =
{
Q
m

US
Q
m
(
t
) =
RD
(
Q
m
)
and t
+

RD
(
Q
m
)
 ·
τ
≤
TTB
Q
m
(
t
)
}
, where

RD
(
Q
m
)

is the total number of requested data items,and
τ
is the service time of a data item.
•
Case b):
Q
m
is a partiallyserved request. It is schedulable if
Q
m
can retrieve the remaining requested data itemsbefore the determined time bound
DTB
Q
m
. The requestsubset is represented by:
SQ
2
(
t
) =
{
Q
m

US
Q
m
(
t
)
⊂
RD
(
Q
m
)
and US
Q
m
(
t
)
!
=
φ
and t
+

US
Q
m
(
t
)
 ·
τ
≤
DTB
Q
m
}
, where

US
Q
m
(
t
)

is the number of unserveddata items.To sum up,
SQ
(
t
) =
SQ
1
(
t
)
∪
SQ
2
(
t
)
, and
SQ
(
t
)
⊆
Q
(
t
)
,where
Q
(
t
)
is the set of all pending requests at time
t
.In the following, we introduce how the PSU captures therequest productivity, status and urgency in scheduling to exploit the broadcast effect, improve the bandwidth utilizationand enhance the request service chance, respectively.
•
A. Exploit broadcast effect
In broadcast environments, disseminating one data itemcan to serve all the requests which are pending for it.Intuitively, scheduling the data item with more pendingrequests has the potential to achieve higher
data productivity
([8], [9]). PSU considers the data productivity in makingscheduling decisions for the sake of exploiting the beneﬁt of broadcast effect. Nevertheless, as illustrated in Def. 4, notall the pending requests are schedulable at each schedulingpoint. Therefore, different from the previous study, whichconsiders all pending requests when computing the dataproductivity, we deﬁne the
effective data productivity
asfollows.
Deﬁnition 5:
Effective data productivity: At time
t
, theeffective data productivity of
d
i
(1
≤
i
≤ 
D

), denoted by
EDP
d
i
(
t
)
, is the number of requests in
Q
d
i
(
t
)
, where the set
Q
d
i
(
t
)
is constructed by any
Q
m
which satisﬁes: a)
d
i
is in theunserved set of
Q
m
; b)
Q
m
is schedulable at time
t
. That is,
Q
m
∈
Q
d
i
(
t
)
if and only if
d
i
∈
US
Q
m
(
t
)
and
Q
m
∈
SQ
(
t
)
. Withthe constructed set of
Q
d
i
(
t
)
, we have
EDP
d
i
(
t
) =
Q
d
i
(
t
)
.Accordingly, for a multiitem request, the
effective request productivity
is deﬁned as follows.
Deﬁnition 6:
Effective request productivity: At time
301