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Table 1 Parameters used in the proposed algorithm

From: Fog radio access network system control scheme based on the embedded game model

Notations Explanation
CS Cloud server
F-APs Fog-computing-based access points
MUs Mobile users
ENs Edge nodes
The finite set of superordinated game players
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
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
n A jointly feasible utility solution set
τ Factor to characterize the file popularity
\( \mathbb{M}= \) {1.. 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