On the Concept of FIFOV in Queues

In several queuing situations, the order in which the units depart is not the same as the order in which they arrived at the system. We call this phenomenon, 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 we give a general discussion 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 a M/M/1 queue has been explicitly obtained. Defining X as the number of customers superseding a customer taking service from the slower channel, we obtain the distribution and the first two moments of X under a queue discipline that is a modification of the usual one. An optimality criterion has also been suggested.