# Waiting Line Theory

## Waiting Line Theory

• Submitted By: ncround
• Date Submitted: 09/14/2016 4:38 PM
• Words: 1605
• Page: 7

Today
 More on Queuing System
 Lessons from queuing theory

 Short discussion on SanteMarie Hospital case (due Thursday)
 Instructions are posted on Blackboard
 Due at noon on Thursday 9/15
 Instructions are on Blackboard
 Questions will be added on ForClass
o You’ll be notified via email
 You can do it in groups of at most 5.

Waiting Line Theory

Session 7

2

Next Class
Which one of these will have a shorter average wait time?

Single queue
system

Multiple queue
system

Objectives
 Classification of waiting line systems
 Formulae for waiting line calculation
“Some” time later…
Hello!!!……
ARE YOU THERE?

Two causes of waiting lines
 Capacity is lower than demand rate (even in the absence of
variability)
 Capacity is higher than demand rate but there is variability

In the arrival process: the time between the arrival of two flow
units is not constant
In the service process: the time to process flow units differ from
one to the other

From now on we assume that
Process capacity > Demand rate

Terminology/characteristics of queues
Arrival
Pattern

Service
Pattern

• Distribution
of Arrival
Process

• Distribution
of Service
Times

Number of
servers

Buffer Size
• Can the
queue be
arbitrarily
long?
• E.g.,
Waiting
room size

Service
Discipline
• First-in
First-out
• Priority
• Shortest
processing
time
• Other

Queue Discipline

7

Terminology and Classification of Waiting Lines
Define a queuing system by:
Arrival Pattern / Service Pattern / # of Servers / Queue Capacity / Discipline
Examples:
 M/M/2 - Exponential interarrival times, exponential service times,
2 severs, infinite capacity, first-come-first-serve
 M/G/8 – Exponential interarrival times, general service times,
8 servers, infinite capacity, first-come-first-serve

Notation:
M: Exponential
G: General...