On the departure process of the split and match queue

In this paper we study the departure process from an exponential queuing system in which an arriving unit ‘splits’ into two subunits to be served by two independent servers. After service is completed on each of the subunits the ‘matched’ units leave the system. By exploiting the fact that the interval between any two departures of ‘matched’ units can be viewed as a random variable with phase type distribution, expressions are obtained for the distribution of the interdeparture time and the lag 1 autocorrelation. Numerical results indicate that the departure stream of units behaves very similar to a Poisson process. Results from a simulation model, used to study the higher lag autocorrelations and tandem behavior of this system, provide further confirmation of this observation.