Queuing Theory or Waiting Line Theory

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Definition: Queuing Theory or Waiting Line Theory

Queuing Theory is a branch of operations research which is used to predict the length of queues and waiting times in order to decide the amount of resources required to provide any service.

As per Little’s Theorem the average number of customers (N) that arrive can be determined form the equation:

N = λ T , where λ is the customer arrival rate and T is the average service time for a customer.

The queuing system can be classified as per the following convention:

A/S/n – A is the arrival process, S is the service process and n is the number of servers.

Examples of Queuing Systems are:

  • M/M/1 – This is the simplest type with only 1 server and the arrival and service times are exponentially distributed (Poisson Process). Eg: Arrival of telephone calls to a telephone exchange.
  • M/D/n – Here there are n servers, the arrival process follows Poisson distribution whereas the service time is deterministic and can be assumed to be fixed for all customers. Eg: Ticket booking counters in a railway station.
  • G/G/n – This system has n servers but the arrival and service times are both arbitrary.

M = Markovian or exponentially distributed

D = Deterministic or constant

G = General or Binomial Distribution


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