1. Queuing Theory
By: Brian Murphy

2. Overview
Queuing Theory: the mathematical study and analysis of waiting lines (queues).
Performance Measures Involved:
Arrival Rate = λ (measured in persons per unit of time)
Service Rate = μ (measured in persons per unit of time)
Throughput = 1/ λ (rate of successful services)
Utilization = ρ = λ/ 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 = ρ/(1- ρ)
W = (1/μ) /(1- ρ)