In this paper, the authors analyze an exogenous priority queue M1,M2/M1,M2/1 in which priority calls may interrupt the processing for non-priority call under a restriction. The restriction is as follows: Suppose that a priority call, CH, of which processing time length is XH, arrives during processing time for a non-priority call, CL. Let Y denote the total sum of the processing times for priority calls arrived between the start of the processing for CL and the arrival time of CH. If Y<T, then CH interrupts the processing for CL. Furthermore, in case that Y+XH•T, the processing of CH is completed without interruption. However, in case that Y+XH>T, the processing for CH is interrupted with residual processing time of which length is Y+XH-T, and returns to the queue. On the other hand, if Y≥T, then CH cannot interrupt the processing for CL. Also, the processing for preempted priority or non-priority call is resumed from the point where it was interrupted. Clearly, if T=0 (or=•), then the discipline is the ordinary non-preemptive (or preemptive-resume) priority discipline. For the above queue, the authors derive the average waiting times of priority and non-priority calls by using Kleinrock’s conservation law. [In Japanese.]
