Summary
The setting for this problem is a (single-server) service facility which is “time-shared” bym customers.A processing schedule,\(S\), is introduced to prescribe the times at which the facility is available to each customer. The processing schedule determines the random order with which customers exit from the facility.The waiting time of the j th customer \(W^1 _S \), is defined as the difference between his exit time and service time;the total waiting time,\(W_S \), is then defined by
where the |βi} are positive real numbers. The weights |βi} reflect the cost per unit time of delay and indicate an a priori customer preferrence. In this paper we shall characterize the processing schedules\(S*\) which realize
Our main result is that the schedules which minimize\(E(W_S )\) in them customer problem can be “put together” from the corresponding schedules in the 2 customer problems.
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Chazan, D., A. G.Konheim, and B.Weiss: A note on time sharing. IBM Research Paper RC 1656 (submitted to the Journal on Combinatorial Theory) July 29, 1966.
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This research was partially supported by the United States Air Force under Contract No. AF 49 (638)-1682.
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Konheim, A.G. A note on time sharing with preferred customers. Z. Wahrscheinlichkeitstheorie verw Gebiete 9, 112–130 (1968). https://doi.org/10.1007/BF01851002
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DOI: https://doi.org/10.1007/BF01851002