The Cafeteria Process—Tandem Queues with 0-1 Dependent Service Times and the Bowl Shape Phenomenon

Richard R. Weber and Gideon Weiss
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Richard R. Weber: University of Cambridge, Cambridge, England
Gideon Weiss: Georgia Institute of Technology, Atlanta, Georgia

Operations Research, 1994, vol. 42, issue 5, 895-912

Abstract: Customers move through a series of M service stations. Each customer, independent of all others, requires service from only one of the stations, for a duration of 1 time unit, this being station i with probability p i . The customer has zero service at all the other stations, but there is no overtaking between the customers, and so queueing occurs. In the case where there is unlimited waiting room between the servers, we show that the system is interchangeable—permuting the order of the stations has no effect on the distribution of the output stream. When there is no waiting room between the stations we investigate optimal loads of the servers in terms of optimal p i 's for up to 10 stations, and observe that optimal loads exhibit the bowl phenomenon . We also obtain some bounds on the throughput for equal loads as a function of M .

Keywords: production/scheduling; flexible manufacturing/line balancing: bowl shape phenomenon; queues; optimization: cafeteria process; queues; tandem: interchangeability; 0-1 dependent service times (search for similar items in EconPapers)
Date: 1994
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