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Operations Research

Types Queuing Problems

Introduction:In queuing model we have some waiting line problem that is depend over the nature and probability distribution of arrivals and service program.

Queuing problem:The most important information required to solve a waiting line problem is the nature and probability distribution of arrivals and service pattern. The answer to any waiting line problem depending on finding:

a)      Queue length

b)      Waiting time

(a)   Queue length:

(b)   Waiting time:

  •        The probability distribution of queue length or the number of persons in the system at any point of time.
  •         Further we can estimate the probability that there is no queue.
  •        This is probability distribution of waiting time of customers in the queue.
  •          That is we have to find the time spent by a customer in the queue before the commencement of his service, which is called his waiting time in the queue.
  •        The total time spent in the system is the waiting time in the queue plus the service time.

The waiting time depends on various factors, such as:

(i)The number of units already waiting in the system,

(ii)The number of service stations in the system,

(iii)The schedule in which units are selected for service,

(iv)The nature and magnitude of service being given to the element being served.

(c)    Service time:

(d)   Average idle time or Busy time distribution:

  •       It is the time taken for serving a particular arrival.
  •        The average time for which the system remains idle.
  •       We can estimate the probability distribution of busy periods. If we suppose that the server is idle initially and the customer arrives, he will be provided service immediately. During his service time some more customers will arrive and will be served in their turn according to the system discipline.
  •       This process will continue in this way until no customer is left unserved and the server becomes free again after serving all the customers.
  •        At this stage we can conclude, that the busy period is over. On the other hand, during the idle periods no customer is present in the system. A busy period and the idle period following it together constitute a busy cycle. The study of busy period is of great interest in cases where technical feat.