Queuing theory

Queueing Theory

The mathematical study of waiting lines, or queues.

• queue lenghts and waiting times can be predicted

Why is queueing theory important ?

• Capacity problems are very common in industry and one of the main drivers of process redesign

• Queueing and waiting time analysis is particularly important in service systems

Throughput Time

The time it takes for a customer or item to pass through the entire process.

Determinants of Queues

Factors that influence how long customers or goods need to wait to be served.

Model Queuing system

Many assumptions are not always true, but queuing theory gives good results anyway

Assumptions:

• Independent arrivals

• Exponential distributions

• Customers do not leave or change queues.

• Large queues do not discourage customers.

Components of a Basic Queuing Process

Operations Research

A branch of applied mathematics that deals with the optimization of complex processes or systems.

Service Process

The sequence of activities that customers or jobs undergo to receive a service.

Queue Discipline

The rule determining the order in which customers are served from the queue.

• How are jobs / customers selected from the queue for service?
- First Come First Served (FCFS)
- Shortest Processing Time (SPT)
- Earliest Due Date (EDD)
- Priority (jobs are in different priority classes)
• FCFS default assumption for most models

FIFO (First In First Out)

A principle where the first customer to arrive is the first to be served.

LIFO (Last In First Out)

A principle where the last customer to arrive is the first to be served.

SIRO (Service In Random Order)

A principle where customers are served in a random order.

Arrival Process

The pattern in which customers or jobs arrive at the queueing system.

• Distribution of arrival times ?

• Batch arrivals ?

• Finite population ?

• Finite queue length ?

Calling Population

The population of potential customers or jobs that can join the queue.

• Size can be finite or infinite

• can be homogenous (only one type of customer/jobs)

• or heterogenous (Several ≠ kinds of customers/jobs)

Service Mechanism

The system or resources used to provide the service to customers.

Service Process

• How long does it take to service a job or costumer ?

  • Distribution of arrival times?

  • Rework or repair?

  • Service center (machine) breakdown?
    

    • Exponential service times often assume

    • Works well for maintenance or unscheduled service situations

Numbers of Servers

Multiple vs Single Customer Queue Configuration

Average Length of a Queue

The average number of customers waiting in the queue at any time.

Blocking Probability

The likelihood that a new arrival will be unable to join the queue due to it being full.

Waiting Time

The time a customer spends in the queue before receiving service.

Capacity Problems

Issues that arise when demand exceeds the service industry's ability to accommodate it.

Service Level

A measure of the quality of service provided to customers.

Customer Satisfaction

A measure of how products or services meet or exceed customer expectations.

Multiple vs Single Queue Configuration

Refers to the arrangement of queues, either having multiple lines or just one line for customers.

Processor Sharing

Customers are served equally. Network capacity is shared between customers and they all effectively experience the same delay

Single server Single stage Queue

Multiple server Single stage Queue

Single server Multiple stage Queue

Multiple server Multiple stage Queue