Shanthikumar and Sumita proved that the stationary system queue length distribution just after a departure instant is geometric for GI/GI/1 with LCFS-P/H service discipline and with a constant acceptance probability of an arriving customer, where P denotes preemptive and H is a restarting policy which may depend on the history of preemption. They also got interesting relationships among characteristics. Those results are generalized for G/G/1 with an arbitrary restarting LCFS-P and with an arbitrary acceptance policy. Several corollaries are obtained. Fakinos’ and Yamazaki’s expressions for the system queue length distribution are extended. For a Poisson arrival case, the well-known insensitivity for LCFS-P/resume is extended, and the stationary distribution or LCFS-P/repeat is discussed.
