Bounds for Different Arrangements of Tandem Queues with Nonoverlapping Service Times

Yat-wah Wan and Ronald W. Wolff
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Yat-wah Wan: Department of Manufacturing Engineering, City Polytechnic of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong
Ronald W. Wolff: Department of Industrial Engineering and Operations Research, University of California, Berkeley, California 94720

Management Science, 1993, vol. 39, issue 9, 1173-1178

Abstract: We bound the difference in performance measures among different orders of tandem queues when service times are nonoverlapping. Two types of nonoverlapping service times, with respect to (w.r.t.) tasks and w.r.t. customers, are defined; it is not required that service times be independent. For nonoverlapping service times w.r.t. tasks, we bound the sample-path difference in number of customers in system by one, and bound the corresponding time-average difference by the traffic intensity of the longest station. For nonoverlapping service times w.r.t. customers, we bound the difference in mean sojourn time when the service times are bounded random variables. While we are motivated by probabilistic results, our methods and results are entirely deterministic.

Keywords: deterministic bounds on finite intervals; sample-path; time-average; customer-average bounds; blocking (search for similar items in EconPapers)
Date: 1993
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