A buffer is filled over a single input channel and emptied by a single channel with a capacity of 64 kbps. Measurements are taken in the steady state for this system with the following results:

Average packet waiting time in the buffer = 0.05 seconds
Average number of packets in residence = 1 packet
Average packet length = 1000 bits

The distributions of the arrival and service processes are unknown and cannot be assumed to be exponential.

Required:
What are the average arrival rate λ in units of packets/second and the average number of packets w waiting to be serviced in the buffer?

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batolisis batolisis · Answer 1 · 2021-06-24T22:44:14+02:00

Answer:

a) 15.24 kbps

b) 762 bits

Explanation:

Using little law

a) Determine the average arrival rate ( λ ) in units of packets/s

λ = r / Tr --- 1

where ; r = 1000 bits , Tr = Tw + Ts = 0.05 + (( 1000 / (64 * 1000 )) = 0.0656

back to equation 1

λ = 1000 / 0.0656 = 15243.9 = 15.24 kbps

b) Determine average number of packets w to be served

w = λ * Tw = 15243.9 * 0.05 = 762.195 ≈ 762 bits

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