Queueing theory

__toc__

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Queueing theory is the mathematical study of waiting lines (or queues). There are several related processes, arriving at the back of the queue, waiting in the queue (essentially a storage process), and being served by the server at the front of the queue. It is applicable in transport and telecommunication and is occasionally linked to ride theory.

Related Topics:
Queue - Transport - Telecommunication - Ride theory

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Agner Krarup Erlang, a Danish engineer who worked for the Copenhagen Telephone Exchange, published the first paper on queueing theory in 1909.

Related Topics:
Agner Krarup Erlang - Danish - 1909

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Kendall's notation for describing Queues and their characteristics can be found in . Kendall introduced a A/B/C queueing notation in 1953. It has since been extended to 1/2/3/(4/5/6) where the numbers are replaced with:

Related Topics:
Kendall - 1953

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

• A code describing the arrival process. The codes used are:
• * M stands for "Markovian", implying exponential distribution for service times or inter-arrival times.
• * D stands for "degenerate" distribution, or "deterministic" service times.
• * Ek stands for an Erlang distribution with k as the shape parameter.
• * G stands for a "General distribution".
• A similar code representing the service process. The same symbols are used.
• The Number of service channels.
• The Priority order that jobs in the line are served:
• * First Come First Served (FCFS),
• * Last Come First Served (LCFS),
• * Service In Random Order (SIRO) and
• * Processor Sharing.
• The maximum size of the system. The maximum number of customers allowed in the system including those in service. When the number is at this maximum, further arrivals are turned away.
• The size of calling source. The size of the population from which the customers come. This limits the arrival rate. As more jobs queue up there are fewer available to arrive into the system.

The word queue comes from the Latin cauda, meaning tail. Most researchers in the field prefer the spelling 'queueing' over 'queuing', although the latter is somewhat more common in other contexts.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Queueing theory is directly applicable to intelligent transportation systems, call centers, PABXs, networks, telecommunications, server queueing, mainframe computer queueing of telecommunications terminals, advanced telecommunications systems, and traffic flow.

Related Topics:
Intelligent transportation system - Call center - PABX - Networks - Telecommunication - Server - Mainframe - Computer

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

 
Queueing theory: Application of queueing theory to telephony ►