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Thus, for any M/D/∞ queue the probability that n customers reside in the queue, P(n), equals P n n = λ t s n n ! e - λ t s. (14).
In Fig. 8a, network-coding node N has three packets in its recQueue P 1, P 2, and P 3. Relay node R has one packet in its putout queue P 1.
There was a strong tendency for respondents to place patients of higher clinical acuity ahead of themselves in the queue (P < 0.0001).
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In order to analyze the average end-to-end delay of a packet in the corresponding queue Q p, we first define two state transition probabilities as follows: λ p n = Pr Q p t + 1 = n + 1 Q p ( t ) = n, μ p n = Pr Q p t + 1 = n − 1 Q p ( t ) = n, (40).
The probability that the system is blocked (i.e., the failed unit is not allowed to join the queue) is P SB F = ∑ n = 0 L P n, 0 = 1 + δ F 1 + δ L − F P 0, 0, (40, 6.
Thus, the average end-to-end delay of the PU's packet consists of two parts, one delay in the queue Q p and the other delay in the queue Q s p. Theorem 4. The average end-to-end delay for a packet of the PU in the proposed cooperative access scheme is T ¯ PC = 1 − λ p μ PC max − λ p + 1 − λ sp μ SP max − λ sp 1 − μ PN max μ PC max.
According to Little's theorem, the average end-to-end delay of a packet in the queue Q p can be modeled as T ¯ PN = 1 λ p lim T → ∞ ∑ t = 1 T Q p ( t ) T = E Q p λ p, (38).
To this end, the average end-to-end delay for the packet of the queue Q p in the proposed cooperative scheme is given by T ¯ PC = T ¯ P Pr A + T ¯ P + T ¯ SP Pr A ¯. (47).
Where η is the estimated acceptable maximum queue length, p is the probability calculation function.
Therefore, the stable distribution of the queue Q p can be derived by solving the balance equation [23].
For the proposed cooperative access scheme, the packet is dropped from the queue Q p as long as it is successfully received by the PR or the SU.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com