Queuing Theory

Queuing Theory

Queuing theory studies waiting lines mathematically.

Components

Arrival process, service mechanism, queue discipline (FIFO, LIFO, priority), system capacity, population size.

Kendall's Notation

A/B/c/K/N/D. M=Markovian, D=deterministic, G=general.

M/M/1 Queue

Poisson arrivals, exponential service, one server. L=ρ/(1-ρ), W=1/(μ-λ).

M/M/c Queue

c servers, Erlang C formula. Pooled servers more efficient than separate queues.

Little's Law

L=λW. Holds for any steady-state system regardless of distributions.

Performance Measures

L, Lq, W, Wq, ρ, P0 guide capacity planning.

Summary

Queuing theory provides analytical tools for capacity planning and performance analysis.