Queuing Theory - Operation Research


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Queuing Theory - Operation Research,
Queuing Theory discussed with expected short answer question and expected long answer questions

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Queuing Theory - Operation Research

  1. 1. M.S.Ramaiah Management Institute, Bangalore | MBA PRIST(A) 2009-11
  2. 2. Presented By Danny Singh Karthikey Yamdagini Krishna Kumar Kumar Shubham Monalisa Ghosh Man Mohan Anand
  3. 3. Introduction  Developed by A.K.Erling in 1903  It analyze the shared facility needs to be accessed for service by a large number of jobs or customers  Examples: Waiting lines in cafeterias, hospitals, banks, theaters, airports etc.
  4. 4. Expected Short Answer Questions
  5. 5. Discussion Slide -1 Define Queuing Model or Queuing Theory Queuing theory is the mathematical study of waiting lines (or queues) that enables mathematical analysis of several related processes, including arriving at the (back of the) queue, waiting in the queue, and being served by the Service Channels at the front of the queue. What do you mean by Traffic Intensity? The ratio ‫/ג‬µ is called the traffic intensity or the utilization factor and it determines the degree to which the capacity of service station is utilize Mean Rate of Arrival in the Queue( )  Mean Service Rate (  )
  6. 6. Discussion Slide -2 What do you mean by Balking, Reneging, Jockeying? Balking If a customer decides not to enter the queue since it is too long is called Balking Reneging If a customer enters the queue but after sometimes loses patience and leaves it is called Reneging Jockeying When there are 2 or more parallel queues and the customers move from one queue to another is called Jockeying
  7. 7. Discussion Slide -3 What is Waiting Time Cost & Idle Time Cost?  The cost of waiting customers include either the indirect cost of lost business or direct cost of idle equipment and persons.  The cost of idle service facilities is the payment to be made to the servers for the period for which they remain idle. What is Transient & Steady State of the system?  Queuing analysis involves the system’s behavior over time. If the operating characteristics vary with time then it is said to be transient state of the system.  If the behavior becomes independent of its initial conditions (no. of customers in the system) and of the elapsed time is called Steady State condition of the system
  8. 8. Expected Long Answer Questions
  9. 9. Applications of QM Queuing Model can be applied to various situations :  Where customers are involved such as restaurants, café, super market, airports etc.  Very useful in Manufacturing units  Applicable for the problem of machine breakdown & repairs  Applicable for the scheduling of jobs in production control  Applicable for the minimization of traffic congestion at tollbooth  Provide solution of inventory control problems
  10. 10. Characteristics of Queuing The basic characteristics of queuing phenomenon are: Customer Arriving 1  Service Center  Service Channel 2 Major Constituents of a Waiting Line 3 Queuing System Service Facility Customer  Customer Leaving  Queue  Service Channel System
  11. 11. Elements of Queuing System Arrival Distribution Service Distribution Service Channel Elements of Queuing Service Discipline Models Max. No. of Customer allowed Calling Source Customer’s Behavior
  12. 12. Operating Characteristics of QM Operating Characteristics of Queuing Models Waiting Time in Total Time in Utilization Queue Length System Length the queue the system Factor
  13. 13. Assumption in Queuing Model  The customer arrive for service at a single service facility at random according to Poisson distribution with mean arrival rate ‫.ג‬  The service time has exponential distribution with mean service rate µ.  The service discipline followed is First Come First Served.  Customer Behavior is Normal  Service facility behavior is Normal  The calling source has infinite size  The mean arrival rate is less than the mean service rate  The waiting space available for customer in the queue is infinite
  14. 14. Limitations of Queuing Model  The waiting space for the customer is usually limited  The arrival rate may be state dependent  The arrival process may not be stationary  The population of customers may not be infinite and the queuing discipline may not be First Come First Serve  Services may not be rendered continuously  The Queuing system may not have reached the steady state. It may be, instead, in transient state
  15. 15. References Books – Operation Research – D.S.Hira Websites – http://en.wikipedia.org – http://www.google.co.in – http://www.answers.com
  16. 16. Thank You