1 Introduction
2 Related work
2.1 Comparison and main contributions
3 Embedded game model for F-RAN control algorithms
-
\( \mathbb{N} \) is the finite set of \( {\mathbb{G}}^{super} \) game players \( \mathbb{N}=\left\{\mathrm{CS}, F-{AP}_1, F-{AP}_2\dots F-{AP}_n\right\} \) where the total n + 1 number of \( {\mathbb{G}}^{super} \) players; one CS and n F-APs.
-
The total spectrum resources of CS is ℛ CS , which would be distributed to n F-APs.
-
\( {\boldsymbol{S}}_{CS}^{\mathrm{\mathcal{R}}} \) = {δ 1, δ 2,…. δ n } is the sets of CS’s strategies for the spectrum resource allocation. δ t in \( {\boldsymbol{S}}_{CS}^{\mathrm{\mathcal{R}}} \) is the allocated spectrum amount for the F ‐ AP t,1 ≤ i ≤ n .
-
The U t, 1 ≤ i ≤ n is the payoff received by the F ‐ AP t . It is estimated as the obtained outcome minus the cost from the spectrum resource allocation.
-
The T is a time period. The \( {\mathbb{G}}^{\mathrm{super}} \) is repeated t ∈ T < ∞ time periods with imperfect information.
-
\( {\mathbb{M}}_i \) is the finite set of \( {\mathbb{G}}_i^{\mathrm{sub}} \) game players \( {\mathbb{M}}_i \) = {F ‐ AP i , \( {\mathrm{MU}}_1^i \),…, \( {\mathrm{MU}}_m^i \)} where \( {\mathrm{MU}}_{j,1\le j\le m}^i \) is the jth MU in the area covered by the F ‐ AP i .
-
The set of F ‐ AP i ’s resources is ℜ i = {δ i , \( {\mathcal{C}}_i \), σ i } where δ i , \( {\mathcal{C}}_i \), σ i are the allocated spectrum resource, the computation capacity, and the placed cache files in the F ‐ AP i , respectively.
-
\( {\boldsymbol{S}}_{F- A{P}_i}^{\delta_i} \), \( {\boldsymbol{S}}_{F- A{P}_i}^{{\mathcal{C}}_i} \) and \( {\boldsymbol{S}}_{F- A{P}_i}^{\sigma_i} \) are the sets of F ‐ AP i ’s strategies for the spectrum allocation for MUs, the computation capacity assignment for MUs, and cache placement in the F ‐ AP i , respectively.
-
The \( {\mathcal{U}}_{j,1\le j\le m}^i \) is the \( {\mathrm{MU}}_j^i \)’s payoff received by the F ‐ AP i .
-
The T is a time period. The \( {\mathbb{G}}_i^{\mathrm{sub}} \) is repeated t ∈ T < ∞ time periods with imperfect information.
Notations | Explanation |
---|---|
CS | Cloud server |
F-APs | Fog-computing-based access points |
MUs | Mobile users |
ENs | Edge nodes |
ℕ | The finite set of superordinated game players |
ℛ
CS
| The total spectrum resources of CS |
δ
i
| The allocated spectrum amount for the F ‐ AP
i
|
δ
i
(t − Δt) | The δ
i
value at the time period [t − Δt]. |
U
i
(Δt) | The payoff received by the F ‐ AP
i
during the recent Δt time period |
\( {\mathbb{M}}_{\mathrm{i}} \)
| The finite set of subordinated game players |
ℜ
i
| The set of F ‐ AP
i
‘s resources |
C
i
| The computation capacity in the F ‐ AP
i
|
σ
i
| The placed cache files in the F ‐ AP
i
|
\( {\mathrm{U}}_{\mathrm{j}}^{\mathrm{i}} \)
| The \( {\mathrm{MU}}_{\mathrm{j}}^{\mathrm{i}} \) ‘s payoff received by the F ‐ AP
i
|
β
| The parameter weighs the past experience by considering a trust decay over time |
ϕ
| The parameter specifies the impact of past experience |
T
i
(t) | At time t, the F ‐ AP
i
‘s trust assessment |
\( {\mathrm{F}}_{\mathrm{KSBS}}^{\mathrm{t}} \)
| KSBS at time t
|
d = (d
1, .. d
n) | Disagreement point when players cannot reach an agreement |
\( {\upomega}_{\mathrm{i}}^{\mathrm{t}} \)
| The player F ‐ AP
i
‘s bargaining power at time t
|
ℝn
| A jointly feasible utility solution set |
τ
| Factor to characterize the file popularity |
\( \mathbb{M}= \) {ℳ1.. ℳ
L
} | A multimedia file set consists of L popular multimedia files |
\( \mathcal{Q}=\left[{\mathrm{\mathcal{M}}}_1,\dots, {\mathrm{\mathcal{M}}}_{\mathrm{L}}\right] \)
| Vector to represent the popularity distribution among \( \mathbb{M} \)
|
\( \mathbb{I}={\left[0,1\right]}^{\mathrm{n}\times \mathrm{L}} \)
| A two-dimensional matrix to indicate the caching placement |
\( {\mathcal{Z}}_{\mathrm{i}}^{\mathrm{l}} \)
| The revenue from the lth file caching in the F ‐ AP
i
, |
\( {\mathrm{\mathfrak{C}}}_{\mathrm{i}}^{\mathrm{l}} \)
| The cost from the lth file caching in the F ‐ AP
i
, |
\( {\Theta}_{\mathrm{j}}^{\mathrm{i}} \)
| New service request of \( {\mathrm{MU}}_{\mathrm{j}}^{\mathrm{i}} \)
|
Min_S(\( {\Theta}_{\mathrm{j}}^{\mathrm{i}} \)) | The minimum spectrum requirement of \( {\Theta}_{\mathrm{j}}^{\mathrm{i}} \)
|
Min_C(\( {\Theta}_{\mathrm{j}}^{\mathrm{i}} \)) | The minimum computation requirement of \( {\Theta}_{\mathrm{j}}^{\mathrm{i}} \)
|
χ
i
| The currently using spectrum amount in the F ‐ AP
i
|
y
i
| The currently using computation amount in the F ‐ AP
i
|
\( {\mathfrak{X}}^{\mathrm{i}} \)
| The current fronthaul transmission rate |
\( {\mathfrak{M}}^{\mathrm{i}} \)
| The maximum fronthaul transmission rate |
Application type | Computation offloading | Computation requirement | Minimum spectrum requirement | Maximum spectrum requirement |
---|---|---|---|---|
I | Y | 300 MHz/s | 128 kbps | 128 kbps |
II | N | N/A | 256 kbps | 768 kbps |
III | Y | 600 MHz/s | 384 kbps | 640 kbps |
IV | N | N/A | 512 kbps | 1.28 Mbps |
Parameter | Value | Description | ||
n
| 10 | The number of F-APs | ||
ℛ
CS
| 200 Mbps | The total spectrum resources of CS | ||
\( \mathcal{C} \)
| 5 GHz | The F-AP’s computation capacity | ||
ϕ
| 0.2 | A factor to specify the impact of recent experience | ||
Δt
| 1 s | The time interval to monitor the F-RAN system | ||
\( \mathcal{Z} \)
| 5 / one bps | The revenue from the caching per one bps | ||
ℭ | 1 / one bps | The cost from the caching per one bps | ||
τ
| [0.1–0.9] | A factor to characterize the file popularity: randomly selected for F-AP | ||
L
| 10 | The popular multimedia files in the CS for caching | ||
\( \mathfrak{M} \)
| 30 Mbps | The maximum fronthaul transmission rate | ||
ϵ
| 0.95 | A control factor to consider the fronthaul congestion |
4 Performance evaluation
-
The simulated system consists of one CS, 10 F-APs and multiple MUs. The number of MUs (m) for each F-AP is generated based on the process for new service requests.
-
The process for new service requests is Poisson with rate λ (services/s), and the range of offered service load was varied from 0 to 3.
-
There are four different service applications. They are randomly generated from MUs, and some of them are computation offloading tasks.
-
The durations of service applications are exponentially distributed.
-
The total spectrum resources of CS (ℛ CS ) is 200 Mbps.
-
For each F-AP, the computation capacity (\( \mathcal{C} \)) is 5 GHz, and the fronthaul link capacity is 30 Mbps.
-
The cache size in each F-AP is the same as the file set \( \mathbb{M} \) in the CS.
-
System performance measures obtained on the basis of 100 simulation runs are plotted as functions of the service generation rate.
-
For simplicity, we assume the absence of physical obstacles in the experiments.