A Single-Channel Queueing System with Alternating Priority

The author examines a single-channel queueing system receiving $r$ flows of the simplest kind with arbitrarily distributed servicing times. The appearance of a call in the $s$-th flow at a moment when the system is empty ensures priority for the calls of this flow for the next $s$-th cycle of operation of the system $s=\overline{1,r}$ once that cycle is completed a call from the flow with the smallest number is chosen from those existing at that moment, and so on. The case $r=2$ has been investigated in [B. Avi-Itzhak, W. L. Maxwell, and L. W. Miller, Operat. Res., 1965, vol. 13, no. 2, pp. 306–318; L. Takács, Operat. Res., 1968, vol. 16, no. 3, pp. 639–650].