Queue Models

queuing model arrival rate consider as a input and service rate is consider as a output. In queuing model, two basic constituents are considered i.e. arrival rate and service rate.

Queue models:

 Most elementary queuing models assume that the inputs / arrivals and outputs / departures follow a birth and death process. Any queuing model is characterized by situations where both arrivals and departures take place simultaneously. Depending upon the nature of inputs and service faculties, there can be a number of queuing models as shown below:

a)      Probabilistic queuing model

b)      Deterministic queuing model

c)       Mixed queuing model

Probabilistic queuing model:Both arrival and service rates are some unknown random variables.

Deterministic queuing model:Both arrival and service rates are known and fixed.

Mixed queuing model:

•   Either of the arrival and service rates is unknown random variable and other known and fixed.
•   Earlier we have seen how to designate a queue. Arrival pattern / Service pattern / Number of channels / (Capacity / Order of servicing). (A /B/ S / (d / f).
•   In general M is used to denote Poisson distribution (Markovian) of arrivals and departures.
• D is used to constant or Deterministic distribution.
• Ek is used to represent Erlangian probability distribution.
•   G is used to show some general probability distribution.
•          In general queuing models are used to explain the descriptive behavior of a queuing system.

Procedure for Solution

• The various systems can be evaluated through these aspects and the system, which offers the minimum total cost is selected.
•   List the alternative queuing system
•   Evaluate the system in terms of various times, length and costs.
• Select the best queuing system.