1 Introduction
2 Technical concepts and main contributions
-
We design the integrative platform of TBs, UAVs and IoBT devices, and develop a new IoBT offload control scheme. To capture dynamic interactions among TBs, UAVs and IoBT devices, the proposed scheme is formulated as two cooperative game models.
-
Individual IoBT devices split their computation-intensive tasks to get the partial offload services. In a distributed manner, each task partitioning problem is modeled as a cooperative bargaining game, and it is addressed based on the idea of SRBS.
-
Multiple UAVs collect the offloading tasks from their corresponding IoBT devices, and provide them to their contacting TBs. The computation capacity of each TBC server is shared to different offloading tasks by using the concept of ASV.
-
To achieve a mutually desirable solution, the sequential interactions of different system agents are explored, and their strategies are adaptively adjusted. Therefore, our jointly designed IoBT offload control scheme can obtain the synergy effect through reciprocal negotiation process and self-adaptability.
-
Numerical simulations are conducted and the results demonstrate the effectiveness of our proposed scheme over the existing IoBT control protocols. A detailed comparative analysis shows the superiority of our cooperative game approach in terms of system throughput, device payoff and service failure probability.
3 Related work
4 Offloading control scheme in the UAV-TB-assisted IoBT system
4.1 UAV-TB-assisted IoBT infrastructure and problem formulations
-
\({\mathbb{B}}\), \({\mathbb{V}}\) and \({\mathbb{D}}\) represent the sets of TBs, UAVs, and IoBT devices, respectively. They are mutually and reciprocally interdependent in a coordinated manner, and they work together in the UAV-TB-assisted IoBT platform.
-
At the first phase, the \({\mathbb{G}}_{{\mathcal{D}}_{l}}\) is designed to split the \({\mathcal{D}}_{l}\)’s computation task \(\left({\mathcal{W}}_{{\mathcal{D}}_{l}}\right)\) for the offload service, and \({\mathfrak{M}}_{{\mathcal{D}}_{l}}\) is the \({\mathcal{D}}_{l}\)’s local computing power. In the \({\mathbb{G}}_{{\mathcal{D}}_{l}}\), the subtasks for the local processing \(\left({\mathcal{P}}_{{\mathcal{D}}_{l}}^{L}\right)\) and for the offloading service \(\left({\mathcal{P}}_{{\mathcal{D}}_{l}}^{\mathcal{B}}\right)\) are game players.
-
In the \({\mathbb{G}}_{{\mathcal{D}}_{l}}\), The \({S}_{{\mathcal{D}}_{l}}\) is the splitting ratio for the \({\mathcal{W}}_{{\mathcal{D}}_{l}}\). \({S}_{{\mathcal{D}}_{l}}\) and \({U}_{{\mathcal{D}}_{l}}^{L}\left(\cdot \right)\) are the strategy and utility function of \({\mathcal{P}}_{{\mathcal{D}}_{l}}^{L}\), and \(\left(1-{S}_{{\mathcal{D}}_{l}}\right)\) and \({U}_{{\mathcal{D}}_{l}}^{\mathcal{B}}\left(\cdot \right)\) are the strategy and utility function of \({\mathcal{P}}_{{\mathcal{D}}_{l}}^{\mathcal{B}}\), respectively.
-
Individual device \({\mathcal{D}}_{1\le l\le n}\in {\mathbb{D}}\) operates the \({\mathbb{G}}_{{\mathcal{D}}_{l}}\) game in a distributed manner.
-
The UAV \({\mathcal{V}}_{j}\in\) \({\mathbb{V}}_{{\mathcal{B}}_{i}}\) is associated with its corresponding \({\mathcal{B}}_{i}\) and IoBT devices in the \({\mathbb{D}}_{{\mathcal{V}}_{j}}^{{\mathcal{B}}_{i}}\).
-
At the second phase, the \({\mathbb{G}}_{{\mathcal{B}}_{i}}\) is designed to share the \({\mathcal{B}}_{i}\)’s computing resource \(\left({\mathfrak{M}}_{{\mathcal{B}}_{i}}\right)\) for each individual \({\mathcal{V}}_{j}\in {\mathbb{V}}_{{\mathcal{B}}_{i}}\). In the \({\mathbb{G}}_{{\mathcal{B}}_{i}}\), \({\mathcal{V}}_{j}\) is a game player, and \(v\left(\cdot \right)\) is a characteristic function for each players’ coalition. The \({\mathcal{U}}_{{\mathcal{B}}_{i}}^{{\mathcal{V}}_{j}}\left(\cdot \right)\) is the \({\mathcal{V}}_{j}\)’s utility function.
-
Like as the first phase, each individual TB \({\mathcal{B}}_{i}\in {\mathbb{B}}\) operates its \({\mathbb{G}}_{{\mathcal{B}}_{i}}\) game in a distributed parallel fashion.
-
Discrete time model \(T\in \left\{{t}_{1},\dots ,{t}_{c},{t}_{c+1},\dots \right\}\) is represented by a sequence of time steps. The length of \({t}_{c}\) matches the event time-scale of \({\mathbb{G}}_{{\mathcal{D}}_{l}}\) and \({\mathbb{G}}_{{\mathcal{B}}_{i}}\).
4.2 Sequential Raiffa bargaining solution and average-surplus value
4.2.1 The main idea of SRBS and its formulation
4.2.2 The main idea of ASV and its characteristics
-
efficiency: for all \(\left(N,v\right)\), \({\sum }_{i\in N}{ASV}_{i}\left(N,v\right)=v\left(N\right)\).
-
symmetry: for all \(\left(N,v\right)\), if \({ASV}_{i}\left(N,v\right)={ASV}_{j}\left(N,v\right)\) whenever \(i,j\in N\) are symmetric, that is, \(v\left(S\cup \left\{i\right\}\right)=v\left(S\cup \left\{j\right\}\right)\) for all \(S\subseteq N\setminus \left\{i,j\right\}\).
-
additivity: for all (\(N,v\)) and (\(N,{v}{\prime}\)), \({ASV}_{i}\left(N,v\right)+{ASV}_{i}\left(N,{v}{\prime}\right)={ASV}_{i}\left(N,v+{v}{\prime}\right)\).
-
a-null surplus player: when \({MS}^{v}\left(S\right)=\) 0 for all \(S\), a player \(i\in S\subseteq N\) is a null surplus player. For all \(\left(N,v\right)\), if the player \(i\in N\) is a null surplus player, \({ASV}_{i}\left(N,v\right)=v\left(i\right)\).
-
revised balanced contributions: for all \(\left(N,v\right)\) and each pair of players \(\left\{i,j\right\}\subseteq N\), \(\left({ASV}_{i}\left(N,v\right)-{ASV}_{i}\left({N\setminus j,v|}_{N\setminus j}\right)-\frac{1}{n}\left(v\left(N\right)-v\left(N\setminus j\right)-v\left(j\right)\right)\right)=\left({ASV}_{j}\left(N,v\right)-{ASV}_{j}\left({N\setminus i,v|}_{N\setminus i}\right)-\frac{1}{n}\left(v\left(N\right)-v\left(N\setminus i\right)-v\left(i\right)\right)\right)\).
4.3 The proposed task offloading scheme for UAV-TB-assisted IoBT platform
4.4 Main steps of the cooperative game-based partially offloading scheme
5 Simulation results and discussion
5.1 Experimental method
-
Simulated UAV-TB-assisted IoBT platform consists of five TBs, twenty UAVs and one hundred IoBT mobile devices (\(\left|{\mathbb{B}}\right|=\) 5, \(\left|{\mathbb{V}}\right|=\) 20, and \(\left|{\mathbb{D}}\right|=\) 100).
-
Each IoBT device \({\mathcal{D}}_{1\le l\le 100}\) generates different computation-intensive tasks \(\left({\mathcal{W}}_{{\mathcal{D}}_{l}}\right)\) where the arrival process of \({\mathcal{W}}_{{\mathcal{D}}_{l}}\) is the rate of Poisson process (\(\rho\)). The offered range is varied from 0 to 3.0.
-
Five TBs are deployed to cover the battlefield area, and individual IoBT devices are randomly distributed over there. Four UAVs work as flying relay nodes for one TB. Each individual UAV has its corresponding IoBT devices, and each device can contact only one UAV.
-
UAVs are evenly distributed over the TB coverage area, and we assume the absence of physical obstacles in the experiments.
-
The total computation power of each TB \(\left({\mathfrak{M}}_{\mathcal{B}}\right)\) is 50 GHz, and the local computation power of each IoBT device \(\left({\mathfrak{M}}_{\mathcal{D}}\right)\) is 1 GHz.
-
To reduce the computation complexity, the offloading service amount is specified in terms of basic unit \(\left({u}_{\mathfrak{M}}\right)\) where one \({u}_{\mathfrak{M}}\) is 2 Mbps in this study. For practical implementations, the task split is negotiated discretely by the size of one \({u}_{\mathfrak{M}}\).
-
The UAV-TB-assisted IoBT system performance measures obtained on the basis of 100 simulation runs are plotted as functions of the Poisson process (\(\rho\)).
Parameter | Value | Description |
---|---|---|
\(k\) | 5 | Total number of TBs |
\(m\) | 20 | Total number of UAVs |
\(n\) | 100 | Total number of IoBT devices |
\({\mathfrak{M}}_{\mathcal{B}}\) | 50 GHz | Total computation power of each TB |
\({\mathfrak{M}}_{\mathcal{D}}\) | 1 GHz | Total computation power of each IoBT device |
\({u}_{\mathfrak{M}}\) | 2 Mbps | The minimum amount of offloading services |
\(\eta\),\(\alpha\) | 1, 2 | Control parameters for the \({U}_{\mathcal{D}}^{L}\left(\cdot \right)\) |
\(\xi\),\(\beta\) | 0.1, 2 | Control parameters for the \({U}_{\mathcal{D}}^{L}\left(\cdot \right)\) |
\(\varepsilon\) | 1 | Control parameters for the \({U}_{\mathcal{D}}^{\mathcal{B}}\left(\cdot \right)\) |
\(\Delta\) | 2 Mbps | Pre-defined minimum bound for the negotiation |
\(\varrho\), \(\theta\) | 1, 2 | Control parameters for the \({\mathcal{U}}_{\mathcal{B}}^{\mathcal{V}}\left(\cdot \right)\) |
\(\psi\), \(\Gamma\) | -4, 1 | Control parameters for the \({\mathcal{U}}_{\mathcal{B}}^{\mathcal{V}}\left(\cdot \right)\) |
Parameter | Initial | Description | Values |
---|---|---|---|
\({S}_{\mathcal{D}}\) | 1 | The splitting ratio for \({\mathcal{W}}_{\mathcal{D}}\) | 0 \(\le {S}_{\mathcal{D}}\le\) 1 |
Collected data type | Spectrum amount for service | Connection duration average /\({\varvec{t}}\) |
---|---|---|
\({\mathcal{W}}_{\mathcal{D}}\in\) I | 4 MHz | 90 time-periods |
\({\mathcal{W}}_{\mathcal{D}}\in\) II | 8 MHz | 100 time-periods |
\({\mathcal{W}}_{\mathcal{D}}\in\) III | 10 MHz | 50 time-periods |
\({\mathcal{W}}_{\mathcal{D}}\in\) IV | 6 MHz | 80 time-periods |
\({\mathcal{W}}_{\mathcal{D}}\in\) V | 12 MHz | 60 time-periods |
\({\mathcal{W}}_{\mathcal{D}}\in\) VI | 14 MHz | 45 time-periods |