Computer and Communication Networks by By Nader F. Mir

Author:By Nader F. Mir
Language: eng
Format: mobi
ISBN: 0131747991
Publisher: Prentice Hall
Published: 2018-05-02T15:42:34.458833+00:00

Equation 11.51

With the independence induction of the random variables Kqi and Tqj, we have

Equation 11.52

It is clear that we can apply the average service time as E[Tsi] = 1/μ in Equation (11.52). Also, by forcing Little's formula, where E[Kqi] = λE[Tqi], Equation (11.52) becomes

Equation 11.53

where ρ = λ/µ is the utilization. Thus,

Equation 11.54

Figure 11.17 shows an example of mean πi representing the remaining time for the completion of an in-service packet as a function of time. If a new service of Tsi seconds begins, πi starts at value Tsi and decays linearly at 45 degrees for Tsi seconds. Thus, the mean πi in the interval [0, t] with n triangles is equal to the area of all triangles () divided by total time (t):

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