© 2006 Prentice Hall, Inc.D – 1 Operations Management Module D – Waiting-Line Models © 2006 Prentice Hall, Inc. PowerPoint presentation to accompany Heizer/Render Principles of Operations Management, 6e Operations Management, 8e

© 2006 Prentice Hall, Inc.D – 2 Outline  Characteristics Of A Waiting-Line System  Arrival Characteristics  Waiting-Line Characteristics  Service Facility Characteristics  Measuring the Queue’s Performance  Queuing Costs

© 2006 Prentice Hall, Inc.D – 3 Learning Objectives When you complete this module, you should be able to: Identify or Define:  The assumptions of the four basic waiting-line models  How to apply waiting-line models  How to conduct an economic analysis of queues Describe or Explain:

© 2006 Prentice Hall, Inc.D – 4 Common Queuing Situations Situation Arrivals in Queue Service Process Supermarket Grocery shoppers Checkout clerks at cash register Highway toll booth Automobiles Collection of tolls at booth Doctor’s office Patients Treatment by doctors and nurses Computer system Programs to be run Computer processes jobs Telephone company Callers Switching equipment to forward calls BankCustomer Transactions handled by teller Machine maintenance Broken machines Repair people fix machines Harbor Ships and barges Dock workers load and unload Table D.1

© 2006 Prentice Hall, Inc.D – 5 Characteristics of Waiting- Line Systems 1.Arrivals or inputs to the system  Population size, behavior, statistical distribution 2.Queue discipline, or the waiting line itself  Limited or unlimited in length, discipline of people or items in it 3.The service facility  Design, statistical distribution of service times

© 2006 Prentice Hall, Inc.D – 6 Arrival Characteristics 1.Size of the population  Unlimited (infinite) or limited (finite) 2.Behavior of arrivals  Scheduled or random, often a Poisson distribution 3.Behavior of arrivals  Wait in the queue and do not switch lines  Balking or reneging

© 2006 Prentice Hall, Inc.D – 7 Parts of a Waiting Line Figure D.1 Dave’s Car Wash enterexit Population of dirty cars Arrivals from the general population … Queue (waiting line) Servicefacility Exit the system Arrivals to the system Exit the system In the system Arrival Characteristics  Size of the population  Behavior of arrivals  Statistical distribution of arrivals Waiting Line Characteristics  Limited vs. unlimited  Queue discipline Service Characteristics  Service design  Statistical distribution of service

© 2006 Prentice Hall, Inc.D – 8 Waiting-Line Characteristics  Limited or unlimited queue length  Queue discipline - first-in, first-out is most common  Other priority rules may be used in special circumstances

© 2006 Prentice Hall, Inc.D – 9 Service Characteristics  Queuing system designs  Single-channel system, multiple- channel system  Single-phase system, multiphase system  Service time distribution  Constant service time  Random service times, usually a negative exponential distribution

© 2006 Prentice Hall, Inc.D – 10 Queuing System Designs Figure D.3 Departures after service Single-channel, single-phase system Queue Arrivals Single-channel, multiphase system Arrivals Departures after service Phase 1 service facility Phase 2 service facility Service facility Queue Your family dentist’s office McDonald’s dual window drive-through

© 2006 Prentice Hall, Inc.D – 11 Queuing System Designs Figure D.3 Multi-channel, single-phase system Arrivals Queue Most bank and post office service windows Departures after service Service facility Channel 1 Service facility Channel 2 Service facility Channel 3

© 2006 Prentice Hall, Inc.D – 12 Queuing System Designs Figure D.3 Multi-channel, multiphase system Arrivals Queue Some college registrations Departures after service Phase 2 service facility Channel 1 Phase 2 service facility Channel 2 Phase 1 service facility Channel 1 Phase 1 service facility Channel 2

© 2006 Prentice Hall, Inc.D – 13 Measuring Queue Performance 1.Average time that each customer or object spends in the queue 2.Average queue length 3.Average time in the system 4.Average number of customers in the system 5.Probability the service facility will be idle 6.Utilization factor for the system 7.Probability of a specified number of customers in the system

© 2006 Prentice Hall, Inc.D – 14 Queuing Models Table D.2 ModelNameExample ASingle channel Information counter system at department store system at department store(M/M/1) NumberNumberArrivalService ofofRateTimePopulationQueue ChannelsPhasesPatternPatternSizeDiscipline SingleSinglePoissonExponentialUnlimitedFIFO

© 2006 Prentice Hall, Inc.D – 15 Queuing Models Table D.2 ModelNameExample BMultichannel Airline ticket (M/M/S) counter (M/M/S) counter NumberNumberArrivalService ofofRateTimePopulationQueue ChannelsPhasesPatternPatternSizeDiscipline Multi-SinglePoissonExponentialUnlimitedFIFO channel channel

© 2006 Prentice Hall, Inc.D – 16 Queuing Models Table D.2 ModelNameExample CConstant Automated car service wash service wash(M/D/1) NumberNumberArrivalService ofofRateTimePopulationQueue ChannelsPhasesPatternPatternSizeDiscipline SingleSinglePoissonConstantUnlimitedFIFO

© 2006 Prentice Hall, Inc.D – 17 Queuing Models Table D.2 ModelNameExample DLimited Shop with only a population dozen machines population dozen machines (finite) that might break NumberNumberArrivalService ofofRateTimePopulationQueue ChannelsPhasesPatternPatternSizeDiscipline SingleSinglePoissonExponentialLimitedFIFO

© 2006 Prentice Hall, Inc.D – 18 Model A - Single Channel 1.Arrivals are FIFO and every arrival waits to be served regardless of the length of the queue 2.Arrivals are independent of preceding arrivals but the average number of arrivals does not change over time 3.Arrivals are described by a Poisson probability distribution and come from an infinite population

© 2006 Prentice Hall, Inc.D – 19 Model A - Single Channel 4.Service times vary from one customer to the next and are independent of one another, but their average rate is known 5.Service times occur according to the negative exponential distribution 6.The service rate is faster than the arrival rate