1 Minimizing File Transfer Time in Opportunistic Spectrum Access Model

2025-04-28 0 0 3.61MB 15 页 10玖币

Minimizing File Transfer Time in Opportunistic

Spectrum Access Model

Jie Hu, Vishwaraj Doshi, and Do Young Eun

Abstract—We study the ﬁle transfer problem in opportunistic spectrum access (OSA) model, which has been widely studied in

throughput-oriented applications for max-throughput strategies and in delay-related works that commonly assume identical channel

rates and ﬁxed ﬁle sizes. Our work explicitly considers minimizing the ﬁle transfer time for a given ﬁle in a set of heterogeneous-rate

Bernoulli channels, showing that max-throughput policy doesn’t minimize ﬁle transfer time in general. We formulate a mathematical

framework for static extend to dynamic policies by mapping our ﬁle transfer problem to a stochastic shortest path problem. We analyze

the performance of our proposed static and dynamic optimal policies over the max-throughput policy. We propose a mixed-integer

programming formulation as an efﬁcient alternative way to obtain the dynamic optimal policy and show a huge reduction in computation

time. Then, we propose a heuristic policy that takes into account the performance-complexity tradeoff and consider the online

implementation with unknown channel parameters. Furthermore, we present numerical simulations to support our analytical results

and discuss the effect of switching delay on different policies. Finally, we extend the ﬁle transfer problem to Markovian channels and

demonstrate the impact of the correlation of each channel.

Index Terms—Opportunistic spectrum access, ﬁle transfer problem, minimum transfer time, shortest path problem

1 INTRODUCTION

In recent years, there has been an explosion in demand for

wireless services due to the rapid growth in the number of

wireless devices, including mobile devices and Internet of

Things (IoT) devices. This demand further exacerbates the

scarcity of allocated spectrum, which is ironically known

to be underutilized by licensed users [2]. The Opportunistic

spectrum access (OSA) model has been proposed to reuse

the licensed spectrum in an opportunistic way otherwise

wasted by licensed users [2]. Recently, the FCC has released

a new guidance in 2020, which would expand the ability of

the unlicensed devices (especially IoT devices) to operate in

the TV-broadcast bands [3]. Besides, the related IEEE 802.22

family has been developed to enable spectrum sharing [4]

to bring broadband access to rural areas.

In the OSA model, a secondary user (SU) aims to oppor-

tunistically access the spectrum when it is not used by any

other users, while also prioritizing the needs of the primary

user (PU). The SUs need to periodically sense the spectrum

to avoid interfering with PUs. We call an SU’s behavior

static if it adheres to only one channel, and dynamic if it

is free to switch channels. While the concept of this model

is simple, the design of spectrum sensing strategy faces var-

ious challenges: the interaction among multiple secondary

users [5]–[7], spectrum sensing policy in the Markovian

channels [8], [9], the trade-off between the cost of sequential

sensing (when permitted) and the expected reward [10],

•A subset of the material in this paper was presented in [1].

Jie Hu and Do Young Eun are with the Department of Electrical and

Computer Engineering, and Vishwaraj Doshi is with the Operations

Research Graduate Program, North Carolina State University, Raleigh,

NC. Email: {jhu29, vdoshi, dyeun}@ncsu.edu. This work was supported

in part by National Science Foundation under Grant CNS-1824518 and

IIS-1910749.

[11], channel selection under resource constraints [12]–[14],

to list a few.

1.1 Motivation: Throughput v.s. Latency

Nowadays, low latency has become one of the main goals

for 5G wireless networks [15] and other time-sensitive ap-

plications with guaranteed delay constraints. In many appli-

cations, data is valid only for a limited duration and should

be delivered before it expires, and vehicular communication

is one such scenario. The increased demand for intelligent

vehicular trafﬁc (e.g., autonomous car development [16])

has led to the need for vehicular communication to explore

spectrum holes for ofﬂoading vehicular users in device-to-

device mode [17]. In addition, delay-sensitive safety mes-

sages (i.e., speed and position of the vehicles) require low

latency (as low as 100 ms) [18]. Another example is medical

body sensor networks [19], where the cognitive radio is

implemented in body sensor network for life-critical moni-

toring, e.g., packets indicating a patient’s health abnormality

should be sent to a doctor as soon as possible, especially

when the patient is out of the hospital network and needs

to temporarily borrow vacant spectrum resources.

In the OSA literature, throughput is one of the most

commonly used performance metrics. Recent studies [20]–

[23], by utilizing the multi-armed-bandit (MAB) techniques,

have focused on ﬁnding max-throughput channel while the

SU needs to learn the unknown channel parameters on

the ﬂy. In order to transmit a ﬁle as quickly as possible,

common folklore might assume that the max-throughput

policy would also suggest the minimum expected ﬁle trans-

fer time. For example, Wald’s equation implies that the ﬁle

download time in an i.i.d (over time) channel is equal to the

ﬁle size divided by the average throughput of that channel,

implicitly favoring the max-throughput channel for minimal

arXiv:2210.02557v1 [math.OC] 5 Oct 2022

download time. However, as will be explained in Section 3,

we ﬁnd that this is not the case in general.

On the other hand, most delay-related works consider

average queuing delay of a large number of packets (ﬁxed

size) following Poisson arrivals [24]–[28]. However, focusing

on individual ﬁle transfers is important for small ﬁles when

the SU needs to transmit each ﬁle as soon as possible. For

instance, IEEE 802.11p protocol requires each car to generate

and send safety messages continuously at 100 ms intervals

[18], making Poisson arrivals unsuitable to model this situ-

ation. In addition, the ﬁle size can vary depending on the

application [29]. Same channel data rate across all channels

is another implicit assumption in those delay-related works

[24]–[28],1but it doesn’t reﬂect the realistic heterogeneous

channel environment assumed in the throughput-oriented

studies [20]–[23]. Clearly, allowing the SU to switch over

such channels during instances of PU’s interruption can

further reduce the ﬁle transfer time, but to the best of our

knowledge, this issue has not been fully explored.

1.2 Related Works and Their Limitations

Throughput and delay are two performance metrics com-

monly used in the OSA literature to evaluate the quality

of service (QoS) in the wireless network. For throughput-

oriented works, the PU’s behavior can be modeled as a two-

state Markov chain (thus correlated over time), for which

partially observable Markov decision processes (POMDPs)

are typically employed to formulate the spectrum sensing

strategy in order to maximize the long-term throughput

[30]. These POMDPs do not possess known structured so-

lutions in general and they are known to be Polynomial-

Space-complete (PSPACE-complete) even if all the channel

statistics are known a priori [31]. To achieve near maximum

throughput, computationally efﬁcient yet sub-optimal poli-

cies, such as myopic policy [32] and Whittle’s index policy

[8], have been proposed for the ofﬂine OSA setting (known

channel parameters). In particular, both [32] and [8] intro-

duced a concept of “belief vector” to guess the available

probability of each channel and updated the vector after

each observation of the channel state. In each time slot, the

myopic policy [32] selected the channel with the maximum

“guess” throughput, while the Whittle’s index policy [8]

selected the channel with the highest value according to the

Whittle’s index and the belief vector.

Recently, machine learning techniques have emerged

in the online setting (unknown channel parameters) that

the SU needs to learn the unknown channel environment

in order to ﬁnd the max-throughput policy. For exam-

ple, model-based MAB techniques [33]–[35] and model-free

deep neural networks [14], [36], are utilized to obtain the

max-throughput policy over Markovian channels. Explic-

itly, single-channel online policies have been developed in

[33], [34] to ﬁnd the channel with maximum long-term

throughput. [35] utilized thompson sampling to estimate

the parameters of each channel and employed the ofﬂine

policies from [8], [32]. With well-trained neural networks,

[36] showed better performance than the policies in [8], [32].

1. Channel data rate differs from the service rate in [24]–[27] because

service rate is related to the length of time the channel is available,

while data rate refers to the speed of data transfer through a channel.

[14] tackled the coordination problem among multiple SUs

with deep Q-learning. On the other hand, MAB techniques

have been extensively studied for heterogeneous channels,

each with i.i.d Bernoulli distribution, in order to ﬁnd the

channel with maximum throughput. The widely used MAB

techniques include the Bayesian approach [37], upper con-

ﬁdence bounds [23], thompson sampling [20] and its im-

provement from efﬁcient sampling [21], and coordination

approach among multiple SUs [5], [6]. In both two chan-

nel models studied in the throughput-oriented works, i.e.,

Bernoulli channels and Markovian channels, we will later

show that “the max-throughput channel does not always

minimize the ﬁle transfer time”.

For delay-sensitive applications, packet delay in cog-

nitive radio networks has been extensively studied using

queuing theory to derive delay-efﬁcient spectrum schedul-

ing strategies. In this setting, a stream of packet arrivals (of

the same size) modeled as a Poisson process with a constant

rate is a common assumption in delay related works [24]–

[28], and the goal is often to minimize the average packet

delay in the steady state. Speciﬁcally, a spectrum sensing

strategy (including queuing delay, packet priority and inter-

ruption by PU’s) was studied in the multimedia applications

[24]. A dynamic load-balancing spectrum decision scheme

was proposed in [25], where an R-learning algorithm was

introduced to deal with unknown channels and queuing

statistics. [26] controlled the transmission probability of each

SU in the random access network and proposed a random-

access strategy for two-and-three-SUs cases to minimize the

queuing delay. Later, a model-free reinforcement-learning

based strategy was studied in [27] to predict the channel

accessing schemes without information exchanges among

SUs and maximize the Quality-of-Service performance of

the target SU. [28] focused on the hybrid spectrum access

strategy with interweave and underlay spectrum access

techniques for multiple SUs in order to obtain both good

throughput and lower packet delay. However, as discussed

Section 1.1, ﬁxed packet length with Poisson arrivals and

the same channel rate assumed in [24]–[28] is not realistic in

some delay-sensitive applications. The ﬁle transfer problem

considered in this paper allows for arbitrary ﬁle sizes and

heterogeneous channel rates, and we can tackle the ﬁle

transfer problem for each single ﬁle.

1.3 Our Contributions

In this paper, we study the OSA model with the aim of

minimizing the transfer time of a single ﬁle over the het-

erogeneous Bernoulli channels with different channel rates

and channel available probabilities. We also provide prac-

tical implementations that take into account computational

costs and unknown channel environments, as well as the

extension to Markovian channels. Our main contributions

can be summarized as follows:

Theoretical Analysis of the File Transfer Problem.

•We ﬁrst analyze the expected ﬁle transfer time of a

single ﬁle for static policies.

•By using the analysis of the static policy as a stepping

stone, we interpret the ﬁle transfer problem under dy-

namic policies as a stochastic shortest path problem,

and obtain the dynamic optimal policy.

•We show that both static and dynamic optimal poli-

cies reduce the transfer time compared to the base-

line max-throughput policy, and this reduction is

even more signiﬁcant in delay-sensitive applications,

where ﬁles are relatively small.

Practical Considerations.

•By formulating a mixed-integer programming

method, we present an alternative technique to solve

the shortest path problem, which speeds up the

computation of dynamic optimal policy.

•We propose a lightweight heuristic policy to further

reduce the computational cost while maintaining

good performance compared to the max-throughput

policy.

•In the online setting, where channel parameters are

unknown to the SU, we modify an MAB algorithm

proposed in [38] and show its gap-dependent regret

bound, guaranteeing the learning of the optimal pol-

icy that minimizes the ﬁle transfer time.

Simulations.

•We empirically show that the max-throughput policy

is not the best when it comes to achieving the mini-

mum ﬁle transfer time in both known and unknown

channel environments.

•When channel switching delay is taken into account,

our lightweight heuristic policy can even outperform

the dynamic optimal policy.

Extension to Markovian Channels.

•We extend the theoretical analysis to Markovian

channels, where each channel is modeled as a two-

state Markov chain, and obtain the expected ﬁle

transfer time of a single ﬁle in each channel and show

the effect of correlation on the ﬁle transfer time.

The rest of the paper is organized as follows: In Section

2 we introduce the OSA model and characterize the ﬁle

transfer problem and its policy under the OSA framework.

In Section 3, we show the expected transfer time for static

policy and it’s performance analysis. Then, we extend from

the static policy to the dynamic policy in Section 4. The

practical concerns are discussed in Section 5. In Section 6,

we evaluate different policies in the numerical setting. We

provide additional analysis on the ﬁle transfer problem over

Markovian channels in Section 7.

2 MODEL DESCRIPTION

2.1 The OSA Model

Consider a set of Nheterogeneous channels N,

{1,2,· · · , N}available for use and each channel i∈ N

offers a stable rate of ri>0bits/s if successfully utilized

[8], [34]. In our setting, a SU wishes to transfer a ﬁle of

size Fbits using one of these Nchannels via opportunistic

spectrum access. The SU can only access one channel at any

given time, and can maintain this access for a ﬁxed duration

of ∆seconds, after which it has to sense available channels

again (even the same channel) in order to avoid the interfer-

ence to the active PU (or other SUs) in the current channel.

At this point, the SU can decide which channel to sense

and access that channel for the next ∆second interval if the

channel is available. Or the SU has to wait for ∆seconds to

sense again if that channel is unavailable, thereby unable to

transfer data for this duration. This pattern is known as the

constant access time model, and has been commonly adopted

for the SU’s behavior as a collision prevention mechanism in

the OSA literature [2], [37]. The cycle repeats itself until the

SU transmits the entire ﬁle size F, then it immediately exits

the channel in use. We omit the channel switching delay in

our OSA model and the duration ∆seconds are fully used

for ﬁle transmission, which is typically assumed in order to

simplify the mathematical model and design a throughput-

optimal policy in the OSA literature [8], [20]–[23], [39]. Note

that the duration ∆seconds is not a randomly chosen

number. For example, ∆is recommended as 100 ms because

the SU needs to vacate the current channel within 100 ms

once the PU shows up, as deﬁned in IEEE 802.22 standard

[4]. The SU can transmit up to 3.1Mb in each ∆seconds

with highest channel rate 31 Mbps in IEEE 802.22 standard

and many small ﬁles (e.g, 5KB text-only email, 800 KB GIF

image and 3MB YouTube short video) need just a few slots

to transmit.

Remark 2.1. The duration ∆does not include the sensing

time for the fair comparison between our policies in

Section 3 to 5 and the max-throughput policy in the same

OSA model [20]–[23]. In addition, as simulated in [40], if

the time duration is set to 100 ms (which is the duration

of our ∆) and the target probability of accurate sensing

is around 90%, the sensing time for a cognitive radio

network is typically chosen to be 6ms. This sensing time

is negligible compared to the whole time duration and is

omitted in our mathematical model.

We say a channel is unavailable (or busy) if it is currently

in use by the primary users (PUs) or other SUs, while it

is available (or idle) if it is not in use by any other users.

The state of a channel (idle or busy) is assumed to be

independent over all channels i∈ N , and i.i.d. over the

time instants {0,∆,2∆,· · · } following Bernoulli distribu-

tion with parameter pi∈(0,1], in line with the widely

used discrete-time channel model [2], [6], [37].2Speciﬁcally,

for each i∈ N ,{Yi(k)}k∈Nis a Bernoulli process with

pi=P[Yi(k) = 1] = 1 −P[Yi(k) = 0] for all k∈N.

Then, we can deﬁne Xi(t), the state of channel i∈ N at

any time t∈R+, as a piecewise constant random process

Xi(t),Yi(

t

∆), where b·c denotes the ﬂoor function. This

way, we write Xi(t)=1(or 0) if channel i∈ N is available

(or unavailable) for the SU with probability pi(or 1−pi).

Remark 2.2. Inaccurate sensing, including mis-detections

with probability vifor channel iin each time slot, has

been studied in the OSA literature [40], [41]. However,

this does not affect our theoretical analysis. With prob-

ability p0

i,pi(1 −vi), the SU can successfully transmit

data in the current time slot, otherwise the data trans-

mission is zero. Thus, we can take the inaccurate sensing

2. We also extend our theoretical analysis of the ﬁle transfer problem

over Markovian channels in Section 7, i.e., each channel is modeled as

a two-state Markov chain that will change its state accordingly every ∆

seconds.

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