Stimulating Multi-Service Forwarding under Node-Selfishness ...

IEICE TRANS. COMMUN., VOL.E99–B, NO.7 JULY 2016

1426

PAPER

Stimulating Multi-Service Forwarding under Node-Selfishness Information in Selfish Wireless Networks∗ Jinglei LI† , Nonmember, Qinghai YANG†a) , and Kyung Sup KWAK††b) , Members

SUMMARY In this paper, we investigate multi-service forwarding in selfish wireless networks (SeWN) with selfish relay nodes (RN). The RN’s node-selfishness is characterized from the perspectives of its residual energy and the incentive paid by the source, by which the degree of intrinsic selfishness (DeIS) and the degree of extrinsic selfishness (DeES) are defined. Meanwhile, a framework of the node-selfishness management is conceived to extract the RNs’ node-selfishness information (NSI). Based on the RN’s NSI, the expected energy cost and expected service profit are determined for analyzing the effect of the RN’s node-selfishness on the multiservice forwarding. Moreover, the optimal incentive paid by the source is obtained for minimizing its cost and, at the same time, effectively stimulating the multi-service delivery. Simulation validate our analysis. key words: selfish wireless networks, node-selfishness information, nodeselfishness management, forwarding multi-service

1.

Introduction

In recent years, multi-service forwarding has received much attention due to the drastic growth in demand for multiservices, e.g., multimedia streams [1] or prioritized contents [2]. With network nodes being endowed with smart autonomic functions, these individuals would prefer to act selfishly rather than altruistically by instinct for satisfying some of their own benefits, and such wireless networks consisting of selfish relay nodes (RN) are called as selfish wireless networks (SeWN). Since the RN’s selfish behavior may degrade the link performance of forwarding multi-service, we should analyze the RN’s node-selfishness. The RNs typically have different levels of available resources, referred to as their intrinsic factors, and hence may expose different degrees of selfishness while forwarding multi-services. In addition, some incentive mechanisms may be employed to suppress the RN’s node-selfishness for forwarding multiservice, and the incentive factors in such mechanisms are referred to as the RNs’ extrinsic factors. Accordingly, we should characterize the node-selfishness of selfish RNs from Manuscript received August 18, 2015. Manuscript revised December 18, 2015. † The authors are with State Key Lab. of ISN, School of Telecom. Engineering, and also with Collaborative Innovation Center of Information Sensing and Understanding, Xidian University, No.2 Taibainan-lu, Xi’an, 710071, Shaanxi, China. †† The author is with Department of Information and Communication Engineering, Inha University, #100 Inha-Ro, Nam-gu, Incheon, 22212, Korea. ∗ This research was supported in part by NSF China (61471287), 111 Project (B08038) and NRF of Korea (MSIP) (NRF-2014K1A3A1A20034987). a) E-mail: [email protected] b) E-mail: [email protected] DOI: 10.1587/transcom.2015EBP3351

the intrinsic and extrinsic points of view, and well manage the RNs’ node-selfishness for the multi-service forwarding. The multi-service forwarding in wireless networks have been investigated in many works [3]–[5]. A cross-layer resource allocation and packet scheduling scheme was investigated in [3] for minimizing the expected distortion of the received video sequence. A joint routing and rate allocation algorithm was proposed in [4] for distributing the multi-source video on-demand stream over wireless mesh networks. The scheme of maximizing the decoded video quality of multiple users was conceived in [5] for multi-hop wireless networks. The feasibility of the aforementioned schemes disregard the effect of the RN’s node-selfishness, while forwarding the multi-services. The research of the node-selfishness has been investigated in many works. The incentive mechanism based on virtual currency was studied in [6] for stimulating some selfish nodes to forward data streams. The price-based collusion-resistant scheme was conceived in [7] for combating the selfish-user collusion. A pricing framework with credit-exchange was proposed in [8] to obtain the optimal bandwidth allocation in public area WLANs, while a pricing-based incentive mechanism was employed in [9] for stimulating participation and collaboration in public wireless mesh networks. In [10], simultaneous-play and leaderfollower price competitions were proposed for a WiMAX and WiFi-based heterogeneous wireless network. In addition to some price mechanisms, the reputation-based mechanism was addressed in [11] for determining the trust nodes in ad-hoc networks, and a truth-telling mechanism was employed in [12] for improving the entire network utility. Nevertheless, the aforementioned papers only focus on how to design some mechanisms for improving the network performance, but neglect the influences of the node’s intrinsic and extrinsic factors on its selfish behavior, e.g., the effect of its residual energy. In this paper, we address the node-selfishness of RNs for the multi-service forwarding in the SeWN. The nodeselfishness information (NSI) of selfish RNs includes the degree of node-selfishness (DeNS) together with the degree of intrinsic selfishness (DeIS) and the degree of extrinsic selfishness (DeES). The RN’s DeIS and its DeES are defined as the effect of its intrinsic factor and its extrinsic factor on its multi-service forwarding, respectively, while its DeNS indicates the selfish behavior of RN’s forwarding multi-service. Based on the RNs’ NSI, the source delivers the multi-service to the destination with the aid of the RNs in a selected path

c 2016 The Institute of Electronics, Information and Communication Engineers Copyright ⃝

LI et al.: STIMULATING MULTI-SERVICE FORWARDING UNDER NODE-SELFISHNESS INFORMATION

1427 Table 1 ρi,h λh S i , S iI , S iE S˜ i , S˜ iI , S˜ iE Γi,h , Ci,h Pi,h , Ξi,h

List of important notations.

The incentive provided by the source for stimulating the i-th RN to forward service h The impact factor of service h The DeNS, DeIS and DeES of the i-th RN The extracted DeNS, DeIS and DeES of the i-th RN The service profit and the energy-consumption cost of the i-th RN for forwarding service h The expected values of the service profit and energyconsumption cost of the i-th RN for service h

and pays some incentives to stimulate these RNs for forwarding multi-service. The main contributions of this paper are outlined as follows: • A node-selfishness management framework is conceived to directly extracts the RNs’ DeNSs and DeESs in terms of their historical actions of forwarding multiservice and the incentives paid by the source, respectively and to infer the RNs’ DeISs in terms of their extracted DeNSs and DeESs. • The expected energy cost and the expected service profit are developed for analyzing the effect of the RN’s intrinsic and extrinsic factors on its multi-service forwarding; and the optimal incentives are determined for the effective multi-service delivery of the source. For the sake of reading, a list of important notations used in this paper is shown Table 1. 2. 2.1

System Model Network Model

A media stream is a continuous flow generated at a source and continues a finite period of time. Meanwhile, the media stream is split into a series of packets when this media stream is injected by a source, but these packets have different priorities for the overall received quality in [2]. These packets, referred to as the multi-services, are categorized into H prioritized classes, and each service has a impact factor, denoted as λh (∀h ∈ {1, · · · , H}), where λ1 ≥ · · · ≥ λH . In the SeWNs consisting of selfish RNs, the sources deliver the multi-services to their corresponding destinations. Due to the effect of the RN’s residual energy, the RN with limited residual energy may depress the action of forwarding multi-service, while the incentive mechanism is employed for stimulating the multi-service forwarding. Hence, the RN’s selfish behavior, namely the node-selfishness, affects the multi-service delivery between the source-destination pairs. Accordingly, a central entity is constructed for an incentive management and a node-selfishness management in such SeWNs, as shown in Fig. 1. Under the incentive management, e.g., in [13], the sources provide some receipts to the central entity for delivering their multi-services, while selfish RNs determine their actions in terms of the corresponding incentives from the central entity. Under the nodeselfishness management, the central entity obtains the RNs’ actions after the sources deliver their multi-services, and

Fig. 1 A framework of the SeWN, which includes a central entity consisting of an incentive management and a node-selfishness management.

then extracts their NSI in terms of their selfish actions observed and the incentives paid. For effectively delivering the multi-services, every source selects a reliable path by using the routing protocol [14] together with the RNs’ NSI of the central entity, which will be elaborated in our future works. When a certain RN within one path selected by a specific source is simultaneously shared by other paths selected by other sources, its available energy is simultaneously shared by these paths. Accordingly, the other paths decrease the available energy of this RN for forwarding the multi-services of their corresponding sources, thus the RN’s node-selfishness increases owing to the depletion of its available energy. In this paper, we focus on the multi-service delivery through the selected path between one source-destination pair, denoted by R = {1, · · · , N} with N being the number of all RNs. Additionally, the related information of the RNs within path R, e.g., their channel gains, is accurately obtained by the source via feedback and a truth-telling mechanism [12]. When forwarding the multi-service, the RN obtains some service profits from the source and simultaneously generates some energy-consumption costs. When the multiservices are successfully delivered to the destination, the i-th RN (∀i ∈ R) obtains the revenue of forwarding multi-service Ui . Since these services have different impact factors, the profit of the i-th RN for forwarding service h is the ratio of its revenue Ui to its impact factor λh , expressed as Γi,h = Ui /λh .

(1)

Meanwhile, for satisfying the bit-error-rate (BER) requirements of service h, the transmission rate of the i-th RN to the j-th RN via the( adaptive modulation of [15] is ex) P |g |2

i,h i, j 1.5 pressed as Ri,h = log2 1 − ln(5η , where Pi,h is the N0 h) transmit power of the i-th RN for service h, N0 is the thermal noise power, gi, j is the channel gain from the i-th RN to the j-th RN, ηh is the target BER of forwarding service h. Meanwhile, the transmission time of the i-th RN for service h is expressed as Lh /Ri,h with Lh being the length of service h, and the corresponding energy consumption is Φi,h = Pi,h Lh /Ri,h . Given the transmission rate Ri,h , the target BER ηh and the energy price π, the energy-consumption cost of the i-th RN for service h is expressed as

Ci,h = πΦi,h =

π(1 − 2Ri,h ) ln(5ηh )Lh N0 . 1.5|gi, j |2 Ri,h

(2)

Due to the RN’s selfish characteristics, its service profit

IEICE TRANS. COMMUN., VOL.E99–B, NO.7 JULY 2016

1428

and energy-consumption cost are evaluated by itself, and they have different expected values. The altruistic RN does not care the energy consumption of forwarding multiservice, but the selfish RN gradually cherishes its energy resources as its selfishness increases owing to the depletion of its residual energy. When the RN is highly selfish, the value of the energy-consumption cost is expressed as Eq. (2). When the expected value of the RN’s energyconsumption cost is larger than its service profit obtained from the source, the incentive mechanism is employed by the source for stimulating the selfish RN to highly evaluate the value of the service profit. Accordingly, the incentive mechanism is significant for guaranteeing the RN’s successful forwarding, i.e., the condition that the expected value of its received service profit is larger than that of its energyconsumption cost. 2.2

Relay’s NSI

In our SeWNs, the RN’s intrinsic and extrinsic factors, i.e., its residual energy and the incentive received, affect its action of forwarding multi-service. Owing to that the residual energy is the private information of the RN and the incentive is determined by the source, we may assume that the residual energy and the incentive are independent of each other, thus we may analyze its node-selfishness from the intrinsicfactor and extrinsic-factor points of view. Accordingly, we define the RN’s DeIS, DeES and DeNS in the following. Definition 1 (DeNS, DeIS and DeES): The RN’s DeIS S I is defined as the degree reflecting the effect of its residual energy on its action of forwarding multi-service, while the RN’s DeES S E is defined as the degree reflecting the effect of the incentive received from the source on its forwarding action. The RN’s DeNS is defined as the degree reflecting the effects of both its residual energy and the received incentive on its action, denoted by S . The DeIS, DeES and DeNS all vary from 0 (altruistic) to 1 (completely selfish). From Definition 1, the RN’s DeNS is a comprehensive formulation of the node-selfishness, which is illustrated via an increasing function of both DeIS and DeES in this paper. Furthermore, the contributions of DeIS and DeES to DeNS are decoupled, since DeIS and DeES are uncorrelated owing to the assumption that the intrinsic factor and the extrinsic factor are independent of each other. Hence, besides the impact of the intrinsic-factor associated DeIS, adjusting the DeES will help tune the DeNS. Let us consider an example that there exists a DeNS threshold, below which the RN becomes cooperative for forwarding multi-services. In other words, we have to find ways to depress the RN’s DeNS below the threshold for stimulating the RN’s cooperation, which requires to leverage either DeIS or DeES, or both. Generally, for a RN with a certain DeIS, its DeES and its DeNS will decrease as it gains the incentives from the source. Specifically, if the RN has little residual energy and thus has a high DeIS, it requires high incentives to reduces its DeES/DeNS for increasing its probability of forwarding multi-service. In this contribution, the RN’s DeNS, DeIS

and DeES are all referred to as its NSI. 3. Problem Formulation Owing to the quality and timeliness constraints of the media streams [16] and the effect of the RNs’ node-selfishness, the source should maintain the reliability of the selected path R and increase the lifetime of this path for reducing the time overhead of finding a new path. Before delivering multi-service with the aid of the selfish RNs cascaded in a selected path, the source obtains the RNs’ NSI owing to the effect of their intrinsic and extrinsic factors on their forwarding behaviors, and adjusts the incentives to stimulate their forwarding actions for the lifetime and reliability of this selected path. Although the expected value of the RN’s energy-consumption cost is raised owing to its limited residual energy, the incentives paid by the source enforce it raising the expected value of the service profit. For the i-th RN’s behavior of forwarding each service h (∀i ∈ R, ∀h ∈ {1, · · · , H}), the source pays some incentives ρi,h for guaranteeing that the expected value of the i-th RN’s service profit Pi,h is not less than the expected value of its energyconsumption cost Ξi,h , i.e., Pi,h ≥ Ξi,h . Nevertheless, owing to the limited incentive resources, the source prefers to minimize its incentive cost for effectively delivering the multiservices through the selected path. Therefore, the problem of the multi-service delivery of the source is to minimize the incentives paid by the source for guaranteeing the successful multi-service forwarding of the RN in the selected path R, formulated as ∑ min ρi,h ρi,h ,∀i∈R

i∈R

s.t. Pi,h ≥ Ξi,h , ∀i ∈ R.

(3)

For guaranteeing the constraints of this problem, the source needs to obtain the NSI of the RNs from the nodeselfishness management in the central entity. Hence, we will analyze the effects of the RNs’ intrinsic and extrinsic factors on its node-selfishness and the extraction of the RNs’ NSI in the node-selfishness management in Sect. 4. Meanwhile, we also will deeply study the effects of the RN’s node-selfishness on both its profit and cost for effectively forwarding multi-service in Sect. 5. 4. Managing NSI of Selfish RNs In our SeWNs, the selfish RNs determine their actions in terms of their intrinsic and extrinsic factors, i.e., their own residual-energy amounts and the incentives paid by the source, while forwarding multi-service. Meanwhile, the node-selfishness management in the central entity extracts the NSI of all RNs, namely their DeISs, DeESs and DeNSs, in terms of their historical actions and the corresponding incentives of forwarding multi-service. The corresponding NSM framework is illustrated in Fig. 2.

LI et al.: STIMULATING MULTI-SERVICE FORWARDING UNDER NODE-SELFISHNESS INFORMATION

1429

Accordingly, we plausibly model that the RN’s DeES exponentially decreases as the incentive increases. Mapping the incentive ρh on the RN’s DeES is plausibly formulated as (cf. the pricing function in [18]) S hE = e−ϖρh , Fig. 2 The diagram of obtaining the RNs’ NSI between the nodeselfishness management in the central entity and the selfish RNs.

4.1

Effects of Intrinsic and Extrinsic Factors at RN

Since the RN’s intrinsic and extrinsic factors affect its nodeselfishness of forwarding multi-service, we should determine the relationships between the RN’s selfishness and its intrinsic factor as well as its extrinsic factor, respectively. According to the sensitivity of the RN to its energy consumption, it is reasonable and logical to suppose its DeIS as a function of the level of its residual-energy. Here, we develop a model of intrinsic selfishness to formulate the relationship between the residual energy and the DeIS. The RN’s DeIS increases as its residual energy decreases. Typically, on the regime of the high residual-energy level, the RN has sufficiently high energy and is willing to forwarding multi-service. On the regime of the middle residual-energy level, the RN may prefer to decrease the energy depletion, thus reducing the probability of forwarding multi-service. Extremely, on the regime of the low residual-energy level, the RN may ultimately refuse to forward these services. Meanwhile, the increasing rates of the DeIS on the regimes of the high and low residual-energy levels are larger than that on the regime of the middle residual-energy level. By mapping the residual energy to the DeIS (cf. the hyperbolic selfishness behavior in [17]), we obtain ( )κ 1 − e−ψE I S =1− , (4) 1 − e−ψE¯ where E is the residual energy, E¯ is the total energy initially possessed by the RN, κ and ψ are the parameters specifying the extent of the impact of the residual energy on the DeIS. The parameter κ > 0 represents the private characteristics of the RN. The extent to the selfish prejudice against the energy consumption increases as the value of κ increases. The parameter ψ > 0 represents the useful value of the energy resource. The small value of parameter ψ causes that the RN becomes reluctant to help forward multi-service. Under the incentive mechanism, the incentive is paid by the source to the RN for stimulating its multi-service forwarding. The node-selfishness of forwarding service h decreases as the incentive ρh paid by the source increases. In the presence of the large incentive, the RN has the high willingness of forwarding multi-services. On the contrary, in the presence of the small incentive, the RN has the low willingness of forwarding multi-services. Meanwhile, the decreasing rate of the DeES in present of the large incentive is smaller than that in present of the small incentive.

(5)

where ϖ (ϖ ≥ 0) is the impact coefficient of the multiservices. When ϖ = 0, S hE = 1, meaning that the RN which is unable to be stimulated by the incentive is completely selfish. When ϖ = +∞, S hE = 0, meaning that the RN having the infinity impact of the incentive exposes an altruistic action. From Eq. (5), the RN’s DeES decreases as the paid incentive increases for forwarding service h. 4.2 Node-Selfishness Management in Central Entity In the node-selfishness management, the RN’s DeNS is directly extracted in terms of its historical actions of forwarding multi-services, whilst the RN’s DeES is also directly extracted in terms of the incentives paid by the source. However, since the RN’s DeIS is merely associated with the intrinsic factors, the DeIS is hence private to this RN, which is unable to be directly collected. The node-selfishness management may compute the RN’s DeIS based on the extracted NSI of both DeNS and DeES. 4.2.1 DeNS Extraction From Definition 1, the RN’s DeNS is related to its behavior, i.e., refusing or forwarding the multi-services, which is a binary event. For extracting the RN’s DeNS, the central entity observes its historical actions and then computes the probability distribution of the binary event based on the beta probability density function [19]. Meanwhile, the RN’s historical actions are related to both its residual energy and the received incentives. The RN’s residual energy gradually decreases over time for forwarding multi-service. The energy-consumption amount of forwarding multi-service at a time is much less than the amount of the energy resource initially possessed by the RN, thus the change rate of its residual energy is slow and the RN’s residual energy is timecorrelated during a certain time period, referred to as a time window. However, the incentives received from the source causes the fluctuation of the time-correlation of the RN’s actions, which is only affected by its residual energy. The incentive degrades the time-correlation of the RN’s actions. Within a time window, the earlier actions are less relevant with the current actions, thus the weights on the earlier actions are smaller than that on the current actions for extracting the RN’s DeNS. Here, a time window and a forgetting factor are introduced to deal with the time-correlation and the fluctuation of the RN’s historical actions. Within the time window of length T , the nodeselfishness management directly observes the i-th RN’s actions of forwarding service h, denoted by Bi,h = {Bti,h |0 ≤ t ≤ T − 1}, where Bti,h = 1 meaning that the i-th RN forwards service h at time t, and Bti,h = 0 meaning that the i-th RN

IEICE TRANS. COMMUN., VOL.E99–B, NO.7 JULY 2016

1430

refuses service h. The action B0i,h represents the latest behavior of the i-th RN for service h, while the action BTi,h−1 is its earliest action in a time window. Additionally, we use the variance of the observed actions of the i-th RN’s forwarding service h to describe this forgetting factor, expressed as τi,h = 1 −

T −1 )2 1 ∑( t Bi,h − E(Bi,h ) , T t=0

(6)

where E(Bi,h ) is the expectation of the observed actions of the i-th RN’s forwarding service h. Accordingly, the RN’s DeNS extracted by the central entity is provided by the following theorem. Theorem 1: Within the time window of length T , the extracted DeNS of the i-th RN (∀i ∈ R) for service h (∀h ∈ {1, · · · , H}) in terms of its historical actions Bi,h is expressed as ∑T −1 t t t=0 (1 − Bi,h )(τi,h ) + 1 S˜ i,h = , (7) ∑T −1 t t=0 (τi,h ) + 2 where τi,h is obtained from Eq. (6). proof: The posteriori probability density function of binary events with their numbers α > 0 and β > 0 in [19] is Γ(α+β) α−1 p (1− p)β−1 , with 0 ≤ p ≤ expressed as f (p|α, β) = Γ(α)Γ(β) ∫ +∞ 1 and Γ(z) = 0 e−t tz−1 dt, and the expectation of the beta ∫1 α distribution is given by E(p|α, β) = 0 p f ( p| α, β)dp = α+β . By using the beta distribution of the historical actions Bi,h , the central entity extracts the RN’s DeNS. Within this time window of length T , the weighted numbers of forwarding and refusing service h as ui,h =

T −1 ∑

Bti,h (τi,h )t

and

vi,h =

t=0

T −1 ∑ (1 − Bti,h )(τi,h )t , (8) t=0

Bti,h

where is the action of forwarding service h of the i-th RN at time t, τi,h is the forgetting factor to weight the actions of forwarding service h of the i-th RN, obtained from Eq. (6). By setting α = ui,h + 1 and β = vi,h + 1, the posteriori probability density function of the i-th RN’s forwarding service h is expressed as Γ(ui,h + vi,h + 2) (pi,h)ui,h (1− pi,h)ui,h , f (pi,h ui,h , vi,h ) = Γ(ui,h +1)Γ(vi,h +1)

(9)

where 0 ≤ pi,h ≤ 1 is the probability of the i-th RN’s forwarding service h. Meanwhile, the extracted DeNS of the i-th RN for service h is expressed as ) ( S˜ i,h = 1 − E pi,h ui,h , vi,h = 1 −

ui,h + 1 . ui,h + vi,h + 2

(10)

By substituting Eqs. (8) into Eq. (10), the extracted DeNS of the i-th RN for service h is obtained. ■ Remark 1: When the RN’s actions of forwarding service h is Bi,h = {1, 0, 1, 0, · · · , 1, 0}, the results τi,h = 34 , ∑ −1 t ∑ −1 ui,h = T1 Tt=0 Bi,h (τi,h )t and vi,h = T1 Tt=0 (1 − Bti,h )(τi,h )t are

19−12( 3 )T

obtained from Eqs. (6) and (8), thus S˜ i,h = 42−28( 43 )T , mean4 ing that only the latest action is used to extract the RN’s DeNS. When the RN’s actions are all forwarding or refusing ∑ −1 t T +1− Tt=0 Bi,h ˜ multi-service, S i,h = meaning that all historical T +2 actions are equally weighted by this central entity. In the case that 0 ≤ τi,h ≤ 1, the weight of the latest action is larger than that of the earliest action. Meanwhile, the accuracy of extracting the RN’s DeNS increases as the length of the time window increases. 4.2.2 DeES Extraction and DeIS Extraction In this SeWN, the DeNS-NSI collected above only explicitly represents the RN’s willingness of multi-service forwarding and is unable to be directly employed by the source for adjusting the payment of its incentive. For instance, if the RN has high DeNS, the source is unable to distinguish wether the RN’s little residual energy or the low incentive leads to the RN’s high DeNS, and thus the source is unable to determine how to adjust its incentive for stimulating the RN’s multi-service forwarding. Actually, the NSI of the RNs in the selected path is required at the source for determining the payment of the incentives and thus in essence for effectively delivering the source’s multi-service (c.f Eq. (7)). Since the RN’s DeES and DeIS are affected by the incentive paid by the source and its residual energy, the node-selfishness management has to obtain the RN’s residual-energy information and the incentive-factor information to extract the corresponding DeES and DeIS. For the DeES extraction, the node-selfishness management directly obtains the incentive-factor information from the incentive management of the central entity, and then extracts the i-th RN’s DeES for service h with Eq. (5), expressed as E E S˜ i,h = S i,h . (11) Additionally, since the incentive-factor information is directly obtained from the incentive management, the corresponding RN’s DeES extracted by the node-selfishness management is credible. Nevertheless, since the RN’s residual-energy information is private to the RN and is unable to be directly obtained by the node-selfishness management, its DeIS is also private, so that the node-selfishness management is unable to directly extract the RN’s DeIS. However, owing to that the RN’s DeIS is related with both its DeNS and DeES, the node-selfishness management computes the RN’s DeIS by Eq. (17) as E S˜ iI = S˜ i,h /S˜ i,h , ∀h ∈ {1, · · · , H}. (12) Since the extracted DeES is the RN’s credible information, the accuracy of its extracted DeIS is only related with that of its extracted DeNS. 5. Multi-Service Forwarding under RN’s NSI In this section, the effects of the RN’s DeIS and DeES on

LI et al.: STIMULATING MULTI-SERVICE FORWARDING UNDER NODE-SELFISHNESS INFORMATION

1431

the multi-service forwarding are characterized, and as well the optimal incentives paid by the source are determined. 5.1

Effects of both DeIS and DeES

The RN of high DeIS cherishes its deficient energy resource and prefers to conserve its residual energy, thus the energyconsumption cost of forwarding multi-service is regarded as a large value. On the contrary, the RN of low DeIS does not care the energy consumption of forwarding multi-service and has high willingness of forwarding multi-service, thus the energy-consumption cost is regarded as a small value. Here, we define an expected energy cost to represent the expected value of the RN’s energy-consumption cost for forwarding multi-service. Definition 2 (Expected Energy Cost): The RN’s expected energy cost is defined as the product of its DeIS and energy consumption, expressed as Ξi,h = S iI Ci,h , ∀i ∈ R, ∀h ∈ {1, · · · , H}.

(13)

In the case that the i-th RN has enough energy resource, namely S iI = 0, its expected energy cost Ξi,h = 0 meaning that this RN altruistically provides its energy resource for forwarding service h. In another case of the same energyconsumption cost, the RN of low DeIS regards this cost as smaller expected value than that of high DeIS. For instance, in the case that Ci,h = C j,h for the i-th and j-th RNs, if S iI < S Ij , then Ξi,h < Ξ j,h . Meanwhile, we study the relationship between the RN’s DeES and its service profit. If a high incentive is paid by the source, the RN has a favorable impression on the source for service h, and increases the expected value of the service profit. On the contrary, if a low incentive is paid by the source, the source may not affect the RN’s profit of forwarding multi-service. Here, we define an expected service profit of the RN in terms of its DeES. Definition 3 (Expected Service Profit): The RN’s expected service profit is defined as the ratio of its service profit to its DeES, expressed as E Pi,h = Γi,h /S i,h , ∀i ∈ R, ∀h ∈ {1, · · · , H}.

(14)

In the case that the infinite incentive is paid for the iE th RN, namely S i,h = 0, we have Pi,h = +∞, meaning that the RN cares its profit very much and altruistically forwards service h. On the contrary, if no incentive is paid for the i-th E RN, namely S i,h = 1, Pi,h = Γi,h , meaning that the expected service profit is the actual profit of forwarding service h. In another case that two RNs have the same profit of forwarding multi-service, the expected service profit of one RN receiving the more incentive is higher than that of the other RN. For instance, in the case that Γi,h = Γ j,h for the i-th and E j-th RNs, if S i,h < S Ej,h , then Pi,h > P j,h . 5.2

should obtain the NSI of all RNs in the selected path R. But the source is unable to directly obtain the RNs’ NSI from these RNs, but it obtains the NSI from the node-selfishness management. Hence, we replace the DeIS S iI and the DeES E S i,h in Eqs. (13) and (14) with the extracted DeIS S˜ iI and E the extracted DeES S˜ i,h , and then substitute the expected energy cost and the expected service profit into Eq. (3). Accordingly, the problem of forwarding multi-service under the RNs’ NSI is expressed as ∑ min ρi,h (15) ρi,h ,∀i∈R

∀i∈R

E λh ) ≥ S˜ iI πΦi,h , ∀i ∈ R. s.t. Ui /(S˜ i,h

E πΦi,h , ∀i ∈ R, where IEq. (16) is rewritten as Ui /λh ≥ S˜ iI S˜ i,h I E S˜ i S˜ i,h is related to both the intrinsic and extrinsic factors of the i-th RN. From Definition 1, the RN’s DeNS is also related to both the intrinsic and extrinsic factors, thus the RN’s DeNS S˜ i,h may be modeled as the product of its DeIS and DeES, expressed as E S˜ i,h = S˜ iI S˜ i,h .

(17)

Meanwhile, IEq. (16) becomes Ui /λh ≥ S˜ i,h πΦi,h , ∀i ∈ R,

(18)

which is common to express the multi-service forwarding using the RN’s DeNS. In order to solve the problem of the RNs’ multi-service forwarding, we find out that Eq. (15) is a linear function of the incentive for each RN in the selected path and IEq. (16) is a decreasing and convex function of the incentive. Therefore, there exist the optimal incentives for the multi-service forwarding of all RNs in the path R, expressed as ( ) ρ∗i,h = Ψ Ui /(λh πS˜ iI Φi,h ) , ∀i ∈ R, ∀h ∈ {1, · · · , H} (19) where Ψ(·) is the inverse function of Eq. (5). From Eq. (19), each optimal incentive ρ∗i,h (∀i ∈ R, ∀h ∈ {1, · · · , H}) increases, as the RN’s DeIS increases. 6. Simulation Results In this section, we simulate three priority classes of the multi-service delivered by the source with their serviceimpact factors being λ = {0.0031, 0.0064, 0.0170} and the RN’s initial energy level E¯ = 50J. Figure 3 shows the DeIS of the RN versus its residual energy in the case of its private characteristics κ = {0.1, 1, 10} and its useful value of

Solution to Problem of Multi-Service Forwarding

For the problem (3) of delivering multi-service, the source

(16)

Fig. 3

The DeIS of the RN versus its residual energy.

IEICE TRANS. COMMUN., VOL.E99–B, NO.7 JULY 2016

1432

Fig. 4

The variation of the extracted DeNS with time. Fig. 5

the energy resource ψ = {0.1, 0.4, 0.5}. If the RN has sufficient energy resource, its DeIS increases slowly as its energy resource is gradually depleted; while its residual energy decreases to a certain level, the DeIS increases sharply; but the DeIS increases slowly at the low level of the residual energy. In the case of κ = 1, the DeIS with ψ = 0.1 is larger than that with ψ = 1 at the same residual energy. In the case of ψ = 0.1, the RN with κ = 0.1 and κ = 10 respectively has different prejudice against the energy consumption. The DeIS of the RN with κ = 0.1 is smaller than that of the RN with κ = 10. Based on the time correlation and fluctuation of the RN’s actions, we develop two kinds of the RN’s serviceforwarding actions, such as Bi,h,1 = {Bti,h = 1|0 ≤ t ≤ T − 1}, and Bi,h,0 = {Bti,h = 0|0 ≤ t ≤ T − 1}. Figure 4 shows the variation of the extracted DeNS under three forgetting factors: τ in Eq. (6), τ = 1 and τ = 0.8 together with the timewindow of length T = 20. The curve of legend “Actions” illustrates the actions of refusing a certain service during the period from 1 to 100, forwarding from 101 to 200 and refusing from 201 to 300. The forgetting factor τ = 1 represents that all RN’s actions are equally weighted for extracting its DeNS, while τ = 0.8 represents that the latest action is weighted by a larger value than the previous ones. Meanwhile, τ in Eq. (6) is employed to adaptively weight the RN’s actions. When the RN’s actions are same within the time window of length T , the DeNS curves of τ in Eq. (6) and τ = 1 are overlapped, and the DeNS curve of τ in Eq. (6) is closer to the “Action” curve than that of τ = 0.8, because the extraction methods with τ in Eq. (6) and τ = 1 exploit more action information than that with τ = 0.8. However, in the case that the RN’s actions are varying in the time window during the intervals from 100 to 120 and from 200 to 220, the DeNS of τ in Eq. (6) is higher than that of τ = 1 during the interval from 100 to 120, whereas it reverses during the interval from 200 to 220, owing to the fact that the extraction method with τ in Eq. (6) has the function of maintaining the RN’s original willingness. Figure 5 depicts the DeIS of the RN versus the optimal incentive. In the above subfigure, the optimal incentive provided by the source increases as the DeIS of the RN increases for the services with λ = {0.0031, 0.0064, 0.0170}. Meanwhile, for the RN of a certain DeIS, the optimal incentive paid by the source with the larger service-impact factor is higher than that with the smaller service-impact factor. The below subfigure illustrates the difference-value of the optimal incentive paid by the source versus the ex-

Fig. 6

The optimal incentive versus the DeIS of the RN.

The DeNS and the DeES of the RN versus its residual energy.

tracted DeIS for the services with λ = 0.0064 under the true DeIS S I = {0.3, 0.5, 0.8}. The different-value ρ˜ ∗ is obtained by subtracting the value of the optimal incentive under the true DeIS from its value under the extracted DeIS. If the extracted DeIS is less than the true DeIS, the incentive paid by the source is unable to arrive at the optimal value, thus the RN may disregard the stimulation of forwarding this service. On the contrary, if the paid incentive is higher than the optimal value, it leads to the higher cost to the source. Figure 6 shows the received optimal incentive, the DeNS and the DeES of the RN versus its residual energy for forwarding three services with λ = {0.0031, 0.0064, 0.0170}. The above subfigure shows that the optimal incentive paid by the source increases as the RN’s residual energy decreases. In the middle subfigure, the RN’s DeES increases as its residual energy increases, owing to the fact that a larger incentive is paid by the source to the RN of a lower residual energy level for guaranteeing the efficient multi-service delivery. Additionally, the RN has a lower DeES when forwarding the services of higher service-impact factors. In addition, the below subfigure of Fig. 6 shows the optimal DeNS versus the residual energy. The equality of IEq. (18) holds when the minimum incentives of problem (15) are obtained, thus the optimal DeNSs of the RNs within the selected path are just related to the impact factors of their forwarded services. Accordingly, the exhibited DeNSs are unchange in the case of limited residual energy, but the RN exposes different DeNSs when it forwards different services. By contrast, when its residual energy is 45J, the exposed DeES is 1 (cf. the middle subfigure of Fig. 6). Under the consideration of the RN’s DeIS together with its DeES being 1, the optimal DeNS decreases as its residual energy increases. Figure 7 depicts the sum of the incentives paid by the

LI et al.: STIMULATING MULTI-SERVICE FORWARDING UNDER NODE-SELFISHNESS INFORMATION

1433

[4]

Fig. 7 The sum of incentives paid by the source versus the number of the RNs in the selected path.

source versus the number of the RNs in the selected path R for the service of λ = 0.0031. Meanwhile, the incentives are paid by the source to stimulate the forwarding actions of the RNs in terms of their DeISs, which are between 0.1 and 0.7 owing to the effect of their residual energy levels. Since the RN of S I = 0.7 is the bottleneck node within this path, the incentives of all RNs within the path R are paid in terms of S I = 0.7 for guaranteeing the successful forwarding of all RNs, and such method is marked by “Basedline1”. Since the RN of S I = 0.1 is the best node, the incentives of all RNs are paid in terms of S I = 0.1, by which all RNs are unable to forward the service, marked by “Basedline2”. Meanwhile, the mark “Proposed1” presents the statistical incentives paid by Eq. (19) for the RNs, whose DeISs are uniformly distributed between 0.1 and 0.7, while the mark “Proposed2” presents the incentives paid by Eq. (19) for the RNs, whose DeISs generated randomly. Additionally, the mark “Compared” presents the comparative method neglecting the effect of the RN’s residual energy in [8]. In these five methods, the incentives paid by the source increases as the number of all RNs increases. Meanwhile, the method marked by “Proposed1” is more effective than that marked by “Basedline1” and “Compared” for forwarding the multiservices, owing to the fact that the incentives obtained by method “Proposed1” are less than that obtained by the latter two methods. 7.

Conclusions

This paper developed the RN’s DeIS and DeES in terms of the RN’s residual energy and its received incentive, while the framework of the node-selfishness management was introduced to extract the RN’s NSI. Meanwhile, the RN’s expected energy cost and expected service profit have been developed for expressing the effects of its DeIS and DeES on the multi-service, and the source can determine the optimal incentives that ensure effective delivery of multi-service. References [1] Y. Xiao and H. Li, “Voice and video transmissions with global data parameter control for the IEEE 802.11e enhance distributed channel access,” IEEE Trans. Parallel Distrib. Syst., vol.15, no.11, pp.1041– 1053, Nov. 2004. [2] M. van der Schaar, Y. Andreopoulos, and Z. Hu, “Optimized scalable video streaming over IEEE 802.11 a/e HCCA wireless networks under delay constraints,” IEEE Trans. Mobile Comput., vol.5, no.6, pp.755–768, June 2006. [3] E. Maani, P.V. Pahalawatta, R. Berry, T.N. Pappas, and A.K. Katsaggelos, “Resource allocation for downlink multiuser video

[5]

[6]

[7]

[8] [9]

[10]

[11]

[12]

[13]

[14]

[15]

[16]

[17]

[18]

[19]

transmission over wireless lossy networks,” IEEE Trans. Image Process., vol.17, no.9, pp.1663–1671, Sept. 2008. Y. Ding, Y. Yang, and L. Xiao, “Multisource video on-demand streaming in wireless mesh networks,” IEEE/ACM Trans. Netw., vol.20, no.6, pp.1800–1813, Dec. 2012. H.-P. Shiang and M van der Schaar, “Multi-user video streaming over multi-hop wireless networks: A distributed, cross-layer approach based on priority queuing,” IEEE J. Sel. Areas. Commun., vol.25, no.4, pp.770–785, May 2007. Z. Li and H. Shen, “Game-theoretic analysis of cooperation incentive strategies in mobile ad hoc networks,” IEEE Trans. Mobile Comput., vol.11, no.8, pp.1287–1303, Aug. 2012. Z. Ji and K.J.R. Liu, “Multi-stage pricing game for collusionresistant dynamic spectrum allocation,” IEEE J. Sel. Areas. Commun., vol.26, no.1, pp.182–191, Jan. 2008. Y. Cui, T. Ma, and X. Cheng, “Multi-hop access pricing in public area WLANs,” Proc. IEEE INFOCOM, pp.2678–2686, 2011. R.K. Lam, D.-M. Chiu, and J.C.S. Lui, “On the access pricing and network scaling issues of wireless mesh networks,” IEEE Trans. Comput., vol.56, no.11, pp.1456–1469, Nov. 2007. D. Niyato and E. Hossain, “Competitive pricing in heterogeneous wireless access networks: Issues and approaches,” IEEE Netw., vol.22, no.6, pp.4–11, Nov. 2008. Y. Rebahi, V. Mujica, and D. Sisalem, “A reputation-based trust mechanism for ad hoc networks,” Proc. 10th IEEE Symposium on Computers and Communications (ISCC’05), pp.37–42, 2005. J. Li, Q. Yang, K.S. Kwak, and F. Fu, “Game theoretic approach for enforcing truth-telling upon relay nodes,” IEICE Trans. Commun., vol.E94-B, no.5, pp.1483–1486, May 2011. R. Kaushik and J. Singhai, “Enhanced node cooperation technique for outwitting selfish nodes in an ad hoc network,” IET Networks, vol.4, no.2, pp.148–157, March 2015. Shivashankar, G. Varaprasad, and S.H. Narayanagowda, “Implementing a new power aware routing algorithm based on existing dynamic source routing protocol for mobile ad hoc networks,” IET Networks, vol.3, no.2, pp.137–142, June 2014. X. Qiu and K. Chawla, “On the performance of adaptive modulation in cellular systems,” IEEE Trans. Commun., vol.47, no.6, pp.884– 895, JUne 1999. F. Pianese, D. Perino, J. Keller, and E.W. Biersack, “PULSE: An adaptive, incentive-based, unstructured P2P live streaming system,” IEEE Trans. Multimedia, vol.9, no.8, pp.1645–1660, Dec. 2007. E. Ataie and A. Movaghar, “Performance evaluation of mobile ad hoc networks in the presence of energy-based selfishness,” Proc. 2006 3rd International Conference on Broadband Communications, Networks and Systems, pp.1–6, 2006. J. Hou, J. Yang, and S. Papavassiliou, “Integration of pricing with call admission control to meet QoS requirements in cellular networks,” IEEE Trans. Parallel Distrib. Syst., vol.13, no.9, pp.898– 910, Sept. 2002. A. Josang, “The beta reputation system,” Proc. 15th Bled Electronic Commerce Conference e-Reality: Constructing the e-Economy, June 2002.

IEICE TRANS. COMMUN., VOL.E99–B, NO.7 JULY 2016

1434

Jinglei Li was born in 1985. He received the B.S. degree in Electronic Information Engineering in 2008 from The PLA Information Engineering University, the M.S. degree in Communication and Information Systems in 2011 from Xidian University. Now he is currently wording toward the Ph.D. degree in Communication and Information Systems at Xidian University. His research interests in wireless network connectivity and node selfishness analysis.

Qinghai Yang received his B.S. degree in Communication Engineering from Shandong University of Technology, China in 1998, M.S. degree in Information and Communication Systems from Xidian University, China in 2001, and Ph.D. in Communication Engineering from Inha University, Korea in 2007 with universitypresident award. From 2007 to 2008, he was a research fellow at UWB-ITRC, Korea. Since 2008, he is with Xidian University, China. His current research interest lies in the fields of autonomic communication, content delivery networks and LTE-A techniques.

Kyung Sup Kwak received the B.S. degree from the Inha University, Inchon, Korea in 1977, and the M.S. degree from the University of Southern California in 1981 and the Ph.D. degree from the University of California at San Diego in 1988, under the Inha University Fellowship and the Korea Electric Association Abroad Scholarship Grants, respectively. His research interests include multiple access communication systems, mobile communication systems, UWB radio systems and adhoc networks, high-performance wireless Internet. Mr. Kwak is members of IEEE, IEICE, KICS and KIEE.