Question

Please help with finding blocking probablity when;

-M/M/1/1 queuing model

-Generates a 1000 packet UDP stream with lambda=200 packets per second, each packet being 100 bytes.

-Mean value of the processing rate of packets (mu)=50 packets per second.

Answer 1

Hi,

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(a). It is known that the mean number of packets in this system is given by ρ/ρ-1

where, ρ=λ/μ

λ is the rate at which packets arrive at the queue (in packets/second), and μ is the rate at which packets may be served by the queue (in packets/second).

Here, λ = 200 packets/sec and μ = 50 packets/sec

ρ=λ/μ = 200/50 = 4

ρ/ρ-1 = 4/(4-1) = 1.33

Packet size = 100 bytes

M/M/1/K Queue (single server queue with K-1 waiting positions) a = b k<K otherwise (Blocking or Loss Condition) H* = 4 ksk = 0 otherwise = 0 Px= Pop = 0 for ksk For (2.23) otherwise Po = (1-2) (2.24) PO (1-pK+U)

Here K = 1

p0 = (ρ-1)/(ρK+1 - 1) = (4-1)/((4)1+1 - 1) = 3/15 = 0.2

Blocking probability pk = p0 ρk = (0.2) * (4)1 = 0.8 = 80%