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Saturday, May 9, 2020

Queuing Theory ( Introduction , Basics , Important terms )

Queuing Theory ( Introduction , Basics , Important terms ) :-



(1) QUEUE :- A line of people awaiting for their turn.

(2) Queuing Theory :- It is the mathematical study of Queue , this Technique provid basis of decision making about the resources need to provide a service.

# Reason To study the Queue :-

➤To find out the cost of offering the service.
➤To find out the cost incurred due to delay in offering service.
➤To allocate the resources.

# Components of Queuing system :- 


(1)  CALLING POPULATION / CUSTOMER :-   


(1) Size of Population :- Number of customers waiting for their turn.
        Finite :- A limit on the customers for waiting in the Queue, E.g. Doctor's Clinic.
        Infinite :- No limit for the customers, E.g. Bank , colleges.

(2) Behavior of Arrivals :-
        balking :- Customer don't join the Queue.
        Reneging :- Customer wait for some time in the queue but leave before being served.
        Jockeying :- Customer Move from one queue to another to receive service more quickly.  

(3) Pattern Of Arrivals :- 
      ➤The customer can arrive in batches or individually.
      ➤The customer may arrive in scheduled time or unscheduled time.

The arrival time is calculated using:-

(a) Poisson Distribution (入) :- Probability for the number of customers that may arrive in any specific interval of time.  

(b) Exponential Distribution (μ) :- Probability for times gap between two consecutive arrivals.


(2) QUEUING PROCESS :- 

It refers to the number of Queues and their respective lengths.

(1) Finite Source Queue :- Service are provided to limited number of customers. E.g. Cinema halls.

(2) Infinite Source Queue :- Service are provided to all customers who came. E.g. Sales Departments.


(3) QUEUING DISCIPLINE :- 

Queue discipline are ruled formed to serve the customers.

➤First come first, first out or first in , first out.
➤Last come , first out served.
➤Served in random order.
➤Emergency.


(4) SERVICE PROCESS :-

➤Service process means process of man or machine to serve the customer.


(5) CHARACTERS OF QUEUING MODEL :-

➤Finite Population
➤Infinite Population
➤Finite Queue
➤Infinite Queue
➤Single- Server
➤Multi- Server
➤Queue discipline
➤Process / Steps to serve


IMPORTANT TERMS :-


(a) Transient State :- It is a Starting / Initial State of a system, when the system is started or the service is initiated the service then that state is called Transient State.

(b) Steady- State :- After Sufficient time has passed , the system is said to be in steady state.

(c) Queue Length ( Lq ):- Length of the Queue.

(d) Length of the System ( Ls ):- Length of system. ( C + S.C ) = ( Waiting + Taking service ).

(e) Waiting time in a system ( Ws ) :- Average waiting time for an individual person to receive service.

(f) Waiting time in Queue ( Wq ) :- Waiting time of the customer in a queue to receive service .



Thank You.    

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