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Random early detection protocol has used the EWMA of the delay ( q ̄ k ) as a criterion for congestion control [26].
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The new established Gronwall inequality is designed to deal with delay q-fractional difference systems.
The time delay ͌ q is interpreted as the relaxation time due to the fast-transient effects of thermal inertia, while the phase lag ͌ T represents the time required for the thermal activation in micro-scale [3].
The average queuing delay D q can be expressed as follows: {D}_{mathrm{q}}=frac{1}{mu_{mathrm{q}}hbox {lambda}_{mathrm{q}} } (6).
The average queuing delay (E[d q ]) is dependent on the number of nodes (n), the sensing range (D), the transmission range (R), and the packet generation rate.
The average queuing delay E[d q ] is a key factor that is used to express the performance of the IEEE 802.11 DCF.
The fixed interval of M=N=N opt points is from time index m to n. Fixed‐lag smoothing is commonly used for denoising if a time delay of q points is allowed [31, 32, 35, 36].
where P d denotes the propagation end-to-end delay, P q denotes a predicted value of the queuing delay, P h denotes the hop count in a path, P u denotes the link utilization value for each link delay, and P l denotes the link length between satellite and ground.
We divide the transport capacity by the average queuing delay, E[d q ] at each node, as follows: (Revised transport capacity) The revised transport capacity C T (R,Λ) is the product of the end-to-end throughput and the packet velocity: C T ( R, Λ ) = M · Λ · v ( R, Λ ) = M · Λ · R E [ d q ] = M · Λ · R log 2 ( 1 + γ i, j ( R ) ) M · T − Λ · L R (15).
Therefore, we set an initial value problem involving a nonlinear delay Caputo q-fractional difference system.
To apply the proposed results, we prove the uniqueness and obtain an estimate for the solutions of nonlinear delay Caputo q-fractional difference system.
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