Question

Assuming that a router that can be modeled as an M/M/1 queuing system with a mean arrival rate of 500 packets/second and a mean service rate of 1000 packets/second, what is the probability of packet loss if the number of packets in residence is limited to 10

Answer 1

P(10 packet) = 0.000976

Therefore, there is a 0.000976 probability of packet loss if the number of packets in residence is limited to 10.

Explanation:

We are given an M/M/1 queuing system

The mean arrival rate is

λ = 500 packets/second

The mean service rate is

μ = 1000 packets/second

The number of packets in residence is

n = 10

The probability of packet loss is given by

P(n packet) = ρⁿ

When n is the number of packets and ρ is the gateway utilization

The gateway utilization is given by

ρ = λ/μ

Where λ is the mean arrival rate and μ is the mean service rate.

ρ = 500/1000

ρ =0.50

So, the probability is

P(10 packet) = (0.50)¹⁰

P(10 packet) = 0.000976

Therefore, there is a 0.000976 probability of packet loss if the number of packets in residence is limited to 10.