Analyzing delay in networks (queueing theory) Littles theorem Relates delay to number of users in the system Can be applied to any system Simple queueing systems single server) M/M/. M/G. M/D/1 M//m/m (T) Poisson Arrivals = P(n arrivals in interval T) n! n= arrival rate in packets /second Exponential service time = P(service time T) u= service rate in packets/secondEytan Modiano Slide 11 Analyzing delay in networks (queueing theory) • Little’s theorem – Relates delay to number of users in the system – Can be applied to any system • Simple queueing systems (single server) – M/M/1, M/G/1, M/D/1 – M/M/m/m • Poisson Arrivals => – λ = arrival rate in packets/second • Exponential service time => – µ = service rate in packets/second P e ( ( n arrivals in interval T) = T)n!n T λ − λ P(service time < T) = 1- e- Tµ