# A note on time sharing with preferred customers

## Abstract

The setting for this problem is a (single-server) service facility which is "time-shared" by m customers. A processing schedule, {Mathematical expression}, 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 jthcustomer {Mathematical expression}, is defined as the difference between his exit time and service time;the total waiting time, {Mathematical expression}, is then defined by {Mathematical expression} 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 {Mathematical expression} which realize {Mathematical expression} Our main result is that the schedules which minimize {Mathematical expression} in the m customer problem can be "put together" from the corresponding schedules in the 2 customer problems. © 1968 Springer-Verlag.