Queuing Theory

1
Queuing Theory

• By Brian Murphy

2
Overview

• Queuing Theory the mathematical study and
  analysis of waiting lines (queues).
• Performance Measures Involved
• Arrival Rate ? (measured in persons per unit of
  time)
• Service Rate µ (measured in persons per unit of
  time)
• Throughput 1/ ? (rate of successful services)
• Utilization ? ?/ µ (portion of time a server
  is servicing a customer)
• Number of people in the system L
• System Response Time W (average time customer
  spends in system)

3
Characterizing Queues

• A/B/C/N/K
• A denotes type of arrival process
• B denotes type of service process
• C denotes number of servers
• N denotes system capacity
• K denotes customer population
• Types of arrival and service processes
• M exponential distribution
• G general distribution
• D deterministic distribution
• E Erlang distribution
• H hyperexponential distribution

Generally used because of its memoryless
property
4
Common Queue M/M/1

• M/M/1 Queue exponential arrival and service
  process, one server
• Formulas Involved
• L ?/(1- ?)
• W (1/µ) /(1- ?)