On the Concept of Fifov in Queues and a Detailed Study of the Case of a Poisson Queue with Two Heterogeneous Servers

摘要

In several queuing situations the order in which the units depart is not the same as the order in which they arrive at the system. This phenomenon is called 'The Violation of the 'First-In, First-Out' Principle,' (FIFOV). A quantitative study of FIFOV is of operational importance in tandem queuing and many other situations. In this paper, a general discussion is given of the concept and study a special aspect of FIFOV in a Poisson queue (Poisson input and exponential service times) with two heterogeneous servers working in parallel. In this connection the time-dependent distribution of the output in and M/M/1 queue has been explicitly obtained. Defining X as the number of customers superseding a customer taking service from the slower channel one obtains the distribution and the first two moments of X under a queue discipline which is a modification of the classical one. An optimality criterion is suggested and a numerical illustration is given.