Waiting Lines
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technical note six
WA I T I N G L I N E M A N A G E M E N T
Queues defined 243
Economics of the Waiting Line Problem
Cost-effectiveness balance The practical view of waiting lines
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The Queuing System
Customer arrivals Distribution of arrivals The queuing system: factors Exit Queuing system defined Arrival rate defined Exponential distribution defined Poisson distribution defined Service rate defined
252 261 263 263
Waiting Line Models Approximating Customer Waiting Time Computer Simulation of Waiting Lines Conclusion
technical note
TECHNICAL NOTE SIX
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WAITING LINE MANAGEMENT
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WE’ VE ALL HAD TO WAIT IN LINES AND KNOW THAT WHATEVER LINE WE CHOOSE, THE OTHER ONES WILL GO FASTER . HERE PEOPLE LINE UP FOR THE ENTRANCE TO THE LOUVRE IN PARIS, FRANCE.
Understanding waiting lines or queues and learning how to manage them is one of the most important areas in operations management. It is basic to creating schedules, job design, inventory levels, and so on. In our service economy we wait in line every day, from driving to work to checking out at the supermarket. We also encounter waiting lines at factories— jobs wait in lines to be worked on at different machines, and machines themselves wait their turn to be overhauled. In short, waiting lines are pervasive. In this technical note we discuss the basic elements of waiting line problems and provide standard steady-state formulas for solving them. These formulas, arrived at through queuing theory, enable planners to analyze service requirements and establish service facilities appropriate to stated conditions. Queuing theory is broad enough to cover such dissimilar delays as those encountered by customers in a shopping mall or aircraft in a holding pattern awaiting landing slots. Recently, Internet access providers have had problems providing enough modem telephone lines for subscribers dialing into
9/3/03
2:11 PM
Page 242
technical note six
WA I T I N G L I N E M A N A G E M E N T
Queues defined 243
Economics of the Waiting Line Problem
Cost-effectiveness balance The practical view of waiting lines
245
The Queuing System
Customer arrivals Distribution of arrivals The queuing system: factors Exit Queuing system defined Arrival rate defined Exponential distribution defined Poisson distribution defined Service rate defined
252 261 263 263
Waiting Line Models Approximating Customer Waiting Time Computer Simulation of Waiting Lines Conclusion
technical note
TECHNICAL NOTE SIX
cha06369_tn06.qxd
9/3/03
2:11 PM
Page 243
WAITING LINE MANAGEMENT
technical note
243
WE’ VE ALL HAD TO WAIT IN LINES AND KNOW THAT WHATEVER LINE WE CHOOSE, THE OTHER ONES WILL GO FASTER . HERE PEOPLE LINE UP FOR THE ENTRANCE TO THE LOUVRE IN PARIS, FRANCE.
Understanding waiting lines or queues and learning how to manage them is one of the most important areas in operations management. It is basic to creating schedules, job design, inventory levels, and so on. In our service economy we wait in line every day, from driving to work to checking out at the supermarket. We also encounter waiting lines at factories— jobs wait in lines to be worked on at different machines, and machines themselves wait their turn to be overhauled. In short, waiting lines are pervasive. In this technical note we discuss the basic elements of waiting line problems and provide standard steady-state formulas for solving them. These formulas, arrived at through queuing theory, enable planners to analyze service requirements and establish service facilities appropriate to stated conditions. Queuing theory is broad enough to cover such dissimilar delays as those encountered by customers in a shopping mall or aircraft in a holding pattern awaiting landing slots. Recently, Internet access providers have had problems providing enough modem telephone lines for subscribers dialing into
Bibliography: Davis, M. M., and M. J. Maggard, “An Analysis of Customer Satisfaction with Waiting Times in a Two-Stage Service Process.” Journal of Operations Management 9, no. 3 (August 1990), pp. 324–34. Fitzsimmons, J. A., and M. J. Fitzsimmons. Service Management. New York: Irwin/McGraw-Hill, 1998, pp. 318–39. Gross, D., and C. M. Harris. Fundamentals of Queuing Theory. New York: Wiley, 1997. Hillier, F. S., et al. Queuing Tables and Graphs. New York: Elsevier– North Holland, 1981. Katz, K. L.; B. M. Larson; and R. C. Larson. “Prescription for the Waitingin-Line Blues: Entertain, Enlighten, and Engage.” Sloan Management Review 32, no. 2 (Winter 1991), pp. 44–53. Kleinrock, L., and R. Gail. Queuing Systems: Problems and Solutions. New York: Wiley, 1996. Winston, W. L., and S. C. Albright. Practical Management Science: Spreadsheet Modeling and Application. New York: Duxbury, 1997, pp. 537–79. FOOTNOTES 1 n! is defined as n(n − 1)(n − 2) · · · (2)(1). 2 We are indebted to Gilvan Souza of the Robert H. Smith School of Business, University of Maryland, for his help with this section.