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on Selected Areas in Communications
3
on the total number T of time slots that is usually large,
and moreover, we further investigate the generalized AD task
model by developing an O(ln
2
L)-competitive algorithm in
Section VI. Section VII performs the simulations for our
online algorithms and validates their efficiency. Finally, we
conclude the paper in Section VIII.
II. RELATED WORK
Extensive research work has been done respectively in the
field of participatory sensing and rate scheduling. We only
review the most related ones due to space limit.
Participatory sensing: Recently, with its attractive appli-
cations, participatory sensing has attracted extensive research
attention, both from industry and academia. Various issues
in participatory sensing have been addressed in the literature
[1], [2], [12], [13]. For example, [14], [15], [16] use social-
media-based crowdsourcing to build knowledge base of urban
emergency events; [18], [19] consider the privacy preserving
problem in participatory sensing; [20], [21] study the incentive
mechanism design problem in incentivizing truthfulness and
users’ participation; [17] considers location-aware collabora-
tive sensing in mobile crowdsourcing. The task allocation
issues in crowdsourcing markets are investigated in [22], [23],
without concerning about data sharing, however. The data shar-
ing problem within multiple applications is initially formulated
in the field of wireless sensing systems, in which Tavakoli et
al. [3] and Fang et al. [4] consider constant-rate schedules and
develop algorithms to minimize the communication overhead.
Observing the data sharing nature, Zhao et al. [24] extend
their work to study the sensing task allocation problem in
participatory sensing system with the aim of load balancing
over multiple participants.
Energy-efficient rate-adaptive scheduling: Much research
effort has been made to design rate-adaptive transmission
algorithms (without considering data sharing). Various ob-
jectives (e.g., throughput, delay, energy consumption) are
investigated in prior works which can be referred to in a
recent survey [25]. [26], [9], [27] devise the optimal rate
schedule to minimize the energy consumption in the offline
setting, respectively with the input of common deadline tasks
and FIFO tasks. Gatzianas et al. [28] investigate the system
utility maximization problem from a stochastic aspect. [29],
[30], [31], [32] are the first works to theoretically study the
algorithms in the general online setup, without relying on
any prior information. Among them, Vaze et al. [29] develop
online algorithms to minimize the completion time; [30],
[31], [32] propose online algorithms with competitive ratios
to maximize the data throughput. In the literature, no online
rate scheduling algorithms with competitive ratios are known
for minimizing the energy consumption.
To the best of our knowledge, no prior works considered
the rate-adaptive transmission policies with data sharing in
participatory sensing systems. This paper addresses such a
problem and we notice that there is a surprising conflict
between the data traffic and energy consumption in such a
rate-adaptive scenario, which is in contrast to the constant-rate
scenario [4], [24] where data traffic minimization is consistent
TABLE I
KEY NO TATIONS
Symbol Semantics
J input task set
J
i
i
th
task
r
i
arrival time of task J
i
d
i
deadline of task J
i
w
i
amount of data requested by task J
i
L the longest length of the time duration among all tasks in J
T the latest deadline of the tasks in J
p = G(s) rate-power function, the power consumed to achieve the rate s
s(t) data rate specified in time t
W (A) data traffic caused by schedule A
E(A) energy consumption caused by schedule A
with the energy minimization, thus we attempt to balance such
a trade-off by developing online algorithms with performance
bounds in terms of bi-objectives.
III. PRELIMINARIES
In this section, we first introduce the system model, and
then present the problem formulation.
A. System model
We model a QoS-constrained request in a participatory
sensing system as a task with an arrival time and a deadline,
specifying the timeliness of the data request. The time is
partitioned into discrete time slots, 1, 2, ..., T, and we use time
interval [t
1
, t
2
] to refer to time slots t
1
, t
1
+ 1, . . . , t
2
. Thus
the length of the interval is t
2
− t
1
+ 1 time slots. A task
J
i
, i = 1, . . . , n, can be defined by (r
i
, d
i
, w
i
), where r
i
is
the arrival time, d
i
is the deadline, and w
i
is the amount of
data requested. To be specific, task J
i
can receive data from
the beginning of time slot r
i
to the end of time slot d
i
. For
simplification, we just say task J
i
arrives at r
i
and departures
at d
i
. The amount of transmitted data in interval [r
i
, d
i
] should
be at least w
i
, which is called the delay/time constraint.
All tasks form the input task set J = {J
1
, J
2
, ..., J
n
}. Let
L = max
1≤i≤n
d
i
− r
i
+ 1 be the longest length of the time
duration of the tasks.
Without loss of generality, we assume min
i
r
i
= 1 and
max
i
d
i
= T . For each task J
i
= (r
i
, d
i
, w
i
), we say that
task J
i
remains alive at t ∈ [r
i
, d
i
]. Also, r
i
(d
i
) is called an
arrival (deadline) time/point, and consequently, from time 1
to T , there are 2n such points. The time interval between two
adjacent points is called a block/epoch.
In this paper, we consider two task models, FIFO task model
and AD task model. The FIFO models the first-in-first-out
service rule where tasks have deadlines in the same order as
the arrival times, which is the most general task model studied
in the literature of rate scheduling [8], [9]. The AD task model
further generalizes FIFO to tasks with Arbitrary Deadlines to
model the most general QoS requirement.
We consider a single user point-to-point transmission chan-
nel and make the same assumption as previous works that
the transmitter can adaptively change its transmission rate s,
which is related to transmission power p through a function
p = G(s) called rate-power function. In many systems with
realistic encoding/decoding schemes, the rate-power function