Queuing Model

Queueing model
From Wikipedia, the free encyclopedia
In queueing theory, a queueing model is used to approximate a real queueing situation or system, so the queueing behaviour can be analysed mathematically. Queueing models allow a number of useful steady stateperformance measures to be determined, including:
• the average number in the queue, or the system,
• the average time spent in the queue, or the system,
• the statistical distribution of those numbers or times,
• the probability the queue is full, or empty, and
• the probability of finding the system in a particular state.
These performance measures are important as issues or problems caused by queueing situations are often related to customer dissatisfaction with service or may be the root cause of economic losses in a business. Analysis of the relevant queueing models allows the cause of queueing issues to be identified and the impact of proposed changes to be assessed.
Contents
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• 1 Notation
• 2 Models
o 2.1 Construction and analysis
o 2.2 Single-server queue
 2.2.1 Poisson arrivals and service
 2.2.2 Poisson arrivals and general service
o 2.3 Multiple-servers queue
o 2.4 Infinitely many servers
• 3 See also
• 4 External links

Notation
Main article: Kendall's notation
Queuing models can be represented using Kendall's notation:
A/B/S/K/N/D
where:
• A is the interarrival time distribution
• B is the service time distribution
• S is the number of servers
• K is the system capacity
• N is the calling population
• D is the service discipline assumed
Many times the last members are omitted, so the notation becomes A/B/S and it is assumed that K =   , N =   and D = FIFO.
Some standard notation for distributions (A or B) are:
• M for a Markovian (exponential) distribution
• Eκ for an Erlang distribution with κ phases
• D for degenerate (or deterministic) distribution (constant)
• G for general distribution (arbitrary)
• PH for a phase-type distribution
Models...