A Two Server Queue with Nonwaiting Customers Receiving Specialized Service

The stationary distributions of the waiting time and number in the system are obtained for a variant of an M/M/2 queue in which non-waiting customers receive a different rate of service from those who must wait in line. Characteristics of the solution, and applications of the model are discussed. The solution has also been generalized to any finite number of servers, using the same technique. The analysis utilizes the new System Point (SP) method for analyzing queues. This method employs the relationship between virtual waiting time sample function down- and up-crossings of a level, and the probability density function of the virtual wait at that level. Brief outlines of the SP approach, and relevant theory are included.